Multiresolution Source/Filter Model for Low Bitrate Coding of Spot Microphone Signals
© Athanasios Mouchtaris et al. 2008
Received: 2 October 2007
Accepted: 6 March 2008
Published: 23 March 2008
A multiresolution source/filter model for coding of audio source signals (spot recordings) is proposed. Spot recordings are a subset of the multimicrophone recordings of a music performance, before the mixing process is applied for producing the final multichannel audio mix. The technique enables low bitrate coding of spot signals with good audio quality (above 3.0 perceptual grade compared to the original). It is demonstrated that this particular model separates the various microphone recordings of a multimicrophone recording into a part that mainly characterizes a specific microphone signal and a part that is common to all signals of the same recording (and can thus be omitted during transmission). Our interest in low bitrate coding of spot recordings is related to applications such as remote mixing and real-time collaboration of musicians who are geographically distributed. Using the proposed approach, it is shown that it is possible to encode a multimicrophone audio recording using a single audio channel only, with additional information for each spot microphone signal in the order of 5 kbps, for good-quality resynthesis. This is verified by employing both objective and subjective measures of performance.
Multichannel audio offers significant advantages regarding music reproduction when compared to two-channel stereo audio. (In the following, when we are referring to stereo audio, we always mean two-channel stereo.) The use of a large number of channels around the listener results in a more realistic acoustic space, adding more sound directions, and thus immersing the listener into the acoustic scene. By using a higher number of channels than in stereo systems, multichannel audio recordings require higher datarates for transmission. Stereo and multichannel audio coding methods attempt to significantly reduce the datarates of audio recordings for networked audio applications or for relaxing their storage requirements. This paper focuses on reducing the transmission (and storage) requirements of spot microphone signals (before those are mixed into the final multichannel audio mix), by exploiting the similarities between such signals of the same multimicrophone recording.
MPEG-1 audio coding [1, 2] (including the popular Layer III also known as MP3 audio coding), MPEG-2 AAC (advanced audio coding) [3–5], and Dolby AC-3 [6, 7] are some well-known audio coding methods for stereo and multichannel audio content. These methods mainly exploit the masking property of the human auditory system for shaping the quantization noise so that it will be inaudible. In addition to reducing the intrachannel redundancies and irrelevancies, these methods also include algorithms for exploring the interchannel redundancies, irrelevancies, more specifically mid/side coding , for frequencies below 2 kHz, and intensity stereo coding  above 2 kHz. M/S codes the sum and difference signals instead of the actual channels, operating in an approximate Karhunen-Loeve (K-L transform) manner. Intensity stereo is based on coding only the sum signal of the channels, as well as the time envelopes for each channel as side information, given that these envelopes are adequate for synthesizing the spatial image at the decoder. A useful introduction to several technologies for the more general area of audio compression can be found in . More recently, exact KLT methods have been derived (e.g., ), while intensity stereo has been generalized for the entire frequency spectrum by MPEG Surround .
With the exception of MPEG Surround, the above-mentioned multichannel audio coding algorithms result in datarates which remain highly demanding for many practical applications when the available channel bandwidth is low. This is especially important given the fact that possibly future multichannel audio systems will require more than the 5.1 channels of currently popular formats  and thus even higher datarates. In MPEG Surround, the concept of spatial audio coding (SAC) has been introduced with the objective of further taking advantage of interchannel redundancies and irrelevancies in multichannel audio recordings. Under this approach, the objective is to decode an encoded downmix (monophonic) channel of audio using some additional (side) information, so as to recreate the spatial rendering of the original multichannel recording. The side information is extracted during encoding and includes the cues which are necessary for synthesizing the spatial image of the uncompressed multichannel audio recording. MPEG Surround is based on combining two theoretical approaches on SAC, namely, binaural cue coding (BCC) and parametric stereo (PS). In BCC [14, 15], the side information contains the per subband interchannel level difference, time difference, and correlation. The resulting signal contains one channel of audio (downmix) only, along with the side information with bitrate in the order of few kbps per channel. Parametric stereo (PS) , operates in very similar philosophy.
At a point where MPEG Surround achieves coding rates for 5.1 multichannel audio that are similar to MP3 coding rates for 2-channel stereo, it seems that the research in audio coding might have no future. However, this is far from the truth. Current multichannel audio formats will eventually be substituted by more advanced formats. Future audiovisual systems will not distinguish between whether the user will be watching a movie or listening to a music recording; audiovisual systems of the future are envisioned to offer a realistic experience to the user who will be immersed into the content. Thus immersive audio focuses on applications where the environment of the listener will be seamlessly transformed into the environment of his/her desire. Immersive audio, as opposed to multichannel audio, is based on providing the listener the option to interact with the sound environment. This interactivity can be accomplished when the content can be dynamically modified, which in practice is possible only when the decoder has access to the microphone signals and locally creates the final mix (remote mixing). We note that these microphone signals are the recordings captured by the various microphones that are placed in a venue for recording a music performance. The number of these microphone signals is usually higher than the available loudspeakers, thus a mixing process is needed when producing a multichannel audio recording. As mentioned, remote mixing is imperative for immersive audio applications, since it offers the amount of freedom for the creation of the content that is needed for interactivity. Consequently, in this paper, the focus is on the spot microphone signals of a multimicrophone recording, before those that are mixed into the final multichannel audio mix. In Section 2, useful information about the recording process for multichannel audio and about the particular type of those signals that are examined here (spot signals) is given.
In order to better explain the emphasis on remote mixing, we briefly mention some possible immersive audio applications, such as (network-based) telepresence of a user in a concert hall performance in real time, where interactivity would translate into him/her being able to move around in the hall and appreciate the hall acoustics. In practice, (when the user is not an experienced audio engineer) this could be accomplished by storing at the decoder a number of predefined mixing "files" that have been created by experts for each specific recording. Another application of interest is virtual music performances, where the musicians are located all around the world. Consider for simplicity a scenario where half members of an orchestra are located in one venue and half at another venue. For producing the multichannel audio mix, the spot signals must be first transmitted to a central location where the audio engineer will have access to all individual recordings. More generally, access to spot signals is important in remote collaboration of geographically distributed musicians, which is a field of significance with extensions to music education and research. Current experiments have shown that high datarates are needed so that musicians can perform and interact with minimal delay . Remote mixing is also a central component in collaborative environments for the production of music, which is of importance in the audio engineering community.
The model proposed in this paper is a source/filter representation of spot microphone signals, allowing for transmission of the multiple microphone signals of a music performance with moderate datarate requirements. This would allow for transmission through low bandwidth channels such as the current Internet infrastructure or wireless networks for broadcasting. The proposed model is tailored towards the transmission of the various microphone signals of a performance before they are mixed and thus can be applied to applications such as remote mixing and distributed performances. Our approach relaxes the current bandwidth constraints of these demanding applications, enabling their widespread usage and more clearly revealing their value. Our method operates in similar philosophy as spatial audio coding, that is, it reduces a multichannel recording into a single audio channel (which can be a sum of the multiple microphone signals) and some side information of the order of few kbps per channel. However, the focus on spot signals instead of the audio channels after the mixing process is a clear distinction between these two methods. In SAC, the side information can be used to recreate the spatial rendering of the various channels. In our method, the side information focuses on encoding the microphone signals of the multichannel recording. This is due to the fact that, for audio mixing (remote or not), not only the spatial image (as in SAC, including the "flexible rendering" approach of BCC) but the actual content of each (monophonic) microphone recording must be encoded, so that the audio engineer will have full control on the available content. Our algorithm results in bitrates of the same order with SAC, while being able to encode an approximate version of each mono spot signal. We note that, as in SAC, the single wideband audio channel, that needs to be transmitted for our algorithm, can be encoded using any existing method of monophonic audio compression (e.g., using perceptual audio coders). We also note our focus in low bitrate coding applications. Our objective is to obtain subjective results above 3.0 perceptual grade compared to the original recording, which can be considered a good performance for low bitrate coding applications.
The remainder of this paper is organized as follows. In Section 2, a brief overview is given on how recordings are made for multichannel rendering, with emphasis on concert hall performances. In Section 3, the theoretical background for the model used and the motivation behind the choice of this particular model are provided. In Section 4, it is explained how the derived model parameters can be encoded for transmission, based on previous work of  derived for coding of speech LSF parameters. In Section 5, objective and subjective results are provided for both the model and coding performance (emphasis on the modeling rather than the coding method), which show that the proposed algorithm can produce good-quality audio resynthesis with rates of only 5 kbps per microphone signal. Finally, concluding remarks are made in Section 6.
2. Recording for Multichannel Audio
Before proceeding to the description of the proposed method, a brief description is given of how the multiple microphone signals for multichannel rendering are recorded. In this paper, we mainly focus on live concert hall performances, although this does not result in a loss of generality of our methods as we show in Section 5. A number of microphones are used to capture several characteristics of the venue, resulting in an equal number of microphone signals (stem recordings). These signals are then mixed and played back through a multichannel audio system. Our objective is to design a system based on available microphone signals, that is able to recreate all of these target microphone signals from a smaller set (or even only one, which can be the sum of all microphone signals) of reference microphone signals at the receiving end. The result would be a significant reduction in transmission requirements, while enabling remote mixing at the receiving end. In our previous work , we were interested to completely synthesize the target signals using the reference signals, without any additional information. Here we propose using some additional information for each microphone for achieving good-quality resynthesis (above 3.0 perceptual grade compared to the original), with the constraint that this additional information requires minimal datarates for transmission. By examining the acoustical characteristics of the various stem recordings, the distinction of microphones is made into reverberant and spot microphones.
Spot microphones are microphones that are placed close to the sound source. Because the source of sound is not a point source but rather distributed such as in an orchestra, the recordings of these microphones depend largely on the instruments that are near the microphone and not so much on the hall acoustics. Resynthesizing the signals captured by these microphones, therefore, involves enhancing certain instruments and diminishing others, which in most cases overlap in the time and frequency domains. Reverberant microphones are the microphones placed far from the sound source, that mainly capture the reverberation information of the venue. In our earlier work , we showed that the reverberant recordings can be resynthesized from a reference recording using specially designed LTI filters. Here we focus on the spot microphone signals. Our objective is to design a system that recreates these signals from a smaller subset of the microphone recordings, with minimal error. We note that the methods proposed in this paper are based on our previous work in multichannel audio synthesis  and resynthesis .
In order to achieve audio compression, especially in low bitrate applications which is the case in this paper, it is generally accepted to introduce an amount of distortion to the coded signals. Here, the distortion corresponds to an amount of crosstalk that is introduced during encoding. We consider that in many applications, a small amount of crosstalk is more acceptable than a considerable degradation in quality. As we showed in later sections, the amount of crosstalk introduced by our methods is small, while the quality remains good for low bitrate applications. In order to better explain the nature of the introduced crosstalk, a simple example is given. If a microphone was placed, for example, near the chorus of an orchestra, then the main objective of the microphone placement is to capture a recording of the music where the chorus sounds as the most prevailing part with respect to the remaining parts of the orchestra. If this microphone signal is substituted by a different (i.e., resynthesized) one, which again contains the same performance and the chorus is the prevailing part of the new signal, this is considered as a signal that retains the "objective" of the initial microphone signal. Crosstalk refers to the case when in the resynthesized signal, apart from the chorus, other parts of the orchestra might be now more audible than in the initial signal. Subjectively, this will have the effect that the new signal sounds as if it was captured by a microphone that was placed farther from the chorus compared with the microphone placement of the original recording. However, given that the amount of crosstalk is small, the chorus will remain the most prominent part in the recording and the resynthesized signal will still sound as if it was made with a microphone placed close to the chorus. The crosstalk is introduced since in our model all spot signals are resynthesized based on a single reference recording.
3. Spot Signals Modeling
The th-dimensional vector is the low-dimensional representation of the signal spectral properties. If is an AR process, the noise is white, thus completely characterizes the signal spectral properties. In the general case, the error signal (or residual signal) will not have white noise statistics and thus cannot be ignored. In this general case, the all-pole model that results from the LP analysis gives only an approximation of the signal spectrum, and more specifically the spectral envelope. For the particular case of audio signals, the spectrum contains only the frequency components that correspond to the fundamental frequencies of the recorded instruments and all their harmonics. (For simplicity, at this point we consider only harmonic sounds. The proposed model is tested for complex music signals in Section 5.) The AR filter for an audio frame will capture its spectral envelope. The error signal is the result of the audio frame filtered with the inverse of its spectral envelope. Thus we conclude that the error signal will contain the same harmonics as the audio frame, but their amplitudes will now have significantly flatter shape in the frequency spectrum.
From the previous discussion it follows that the two residual signals and will contain the same harmonic frequency components. If the envelope modeling was perfect, then it follows that they would also be equal (differences in total gain are of no interest for this application), since they would have flat magnitude with exactly the same frequency components. In that case, it would be possible to resynthesize each of the two audio frames using only the AR filter that corresponds to that audio frame and the residual signal of the other microphone. The final signal is resynthesized from the audio frames using the overlap-add procedure. If, similarly, the source/filter model was used for all the spot microphone signals of a single performance, it would be possible to completely resynthesize these signals using their AR vector sequences (one vector for each audio frame) and the residual error of only one microphone signal. This would result in a great reduction of the datarate of the multiple microphone signals.
3.1. Multiresolution Analysis
3.2. Crosstalk Issue
In practice, the prediction error signals cannot be made exactly flat (and thus equal), thus the resynthesized signals will not sound exactly the same as the originally recorded signals. Additionally, if the reference signal is the sum of the various spot signals (which is necessary when the various microphone signals do not contain common information), frequency components will appear in the downmix that should not be included in the residual of all spot signals. These issues will result in the introduction of crosstalk in the spot recordings that was discussed in Section 2. We claim that the use of the multiband source/filter model results in audio signals of good quality which retain the "objective" of the initial recordings (i.e., the main music part of the recording remains prominent), with only a small amount of crosstalk. In other words, the "main" instrument that is captured still remains the prominent part of the microphone signal, while other parts of the orchestra might be more audible in the resynthesized signal than in the original microphone signal (crosstalk). Returning to the example of the two microphones and the two instruments, if the residual of microphone 1 is used in order to resynthesize the signal of microphone 2, then in the result the violin will most likely be more audible than in the original microphone 2 signal. This happens because some information of the first microphone signal remains in the error signal, since the spectral envelope modeling is not perfect. However, the trumpet will still be the prominent of the two instruments in the resynthesized signal for microphone 2, since we used the original spectral information of that microphone signal. It is also of interest to note the fact that the amount of crosstalk and the final audio quality of the multiband source/filter model depends on the following parameters: (1) the duration of the audio frames for each band, (2) the AR order for each band, (3) the percentage of frame overlapping, (4) the total number of bands, and (5) the filterbank used. By changing these parameters we can achieve various datarates with the corresponding varying audio quality. However, a particular choice for all these parameters can be found experimentally to achieve the best possible modeling performance (example values are given in Section 5 for the particular waveforms we used for testing the method).
3.3. Model Overview
As mentioned in Section 1, given that the remaining microphone signals require minimal rates for encoding (in the order of 5 kbps), our approach is to encode the various microphone signals before those are mixed; thus mixing can take place at the receiving end. We note that the residual of the reference signal will be used to resynthesize all the remaining microphone signals, so the reference signal must be carefully chosen. For the example of concert hall performances, empirically, it is best if this signal corresponds to a microphone location that is in some distance from the orchestra so that it contains the instruments with equal weight. At the same time, it is important that this microphone is not placed in a large distance from the orchestra, so that it does not capture a large degree of the hall reverberation. In that case, the resynthesized signals will sound more reverberant than the original recordings, since the short-time spectral whitening we perform cannot capture a long-term effect such as reverberation. The choice of the reference signal is an open question, and it is a problem that depends on the properties of the particular recording to be encoded. We remind the reader the fact that the reference signal can be a sum of all microphone signals, and the practical implications of this latter approach are examined in Section 5.
In Section 5, it is verified experimentally that our claims hold for other cases of harmonic signals, such as speech signals. It should be noted that some specific types of microphone signals, such as percussive instruments and signals from microphones far from the source, present different challenges that were considered in our previous work . The method proposed in this paper focuses on the large class of audio signals that can be modeled using a short-time analysis approach with emphasis on their spectral envelope (as opposed to the residual signal).
4. Spot Signals Coding
where is the normal multivariate distribution with mean vector and covariance matrix , is the number of clusters, and is the prior probability that the observation has been generated by cluster . The LSF vector order is denoted as (i.e., th order linear prediction). GMMs are suitable for this problem since they have been shown to model successfully the statistics of spectral vectors of both speech [18, 23] and audio signals . The Karhunen Loeve transform (KLT) is adopted for the LSFs decorrelation. KLT is especially fit for GMM-modeled parameters since it is the optimal transform for Gaussian signals in a minimum-distortion sense. Using GMMs, each LSF vector is assigned to one of the Gaussian classes using some classification measure, thus is considered as approximately Gaussian and can be best decorrelated using the KLT.
4.1. Fixed Rate Coding
4.2. Variable Rate Coding
where is the allocated bits to the th component of the th cluster and is the th eigenvalue of cluster . In our implementation we rounded in the nearest integer number for more accurate bit allocation.
To summarize, the procedure for coding the LSF vectors of each frequency band is as follows.
4.2.1. Cluster Quantization
the vector's components are passed through a nonuniform quantizer (compressor, uniform quantizer, expander);
4.2.2. Overall Quantization
For our experiments, we use microphone signals obtained from a US orchestra hall by placing 16 microphones at various locations throughout the hall. (Provided by Professor Kyriakakis of the University of Southern California.) Our objective is to indicate that the model and the coding method we propose result in a good-quality recording with low datarate requirements. For this purpose, we use two of these microphone signals, where one of the microphones mainly captures the male voices of the chorus of the orchestra, while the other one mainly captures the female voices. These recordings are very easy to distinguish acoustically. In Section 5.2, some additional sound signals are used for examining the scenario when the reference signal might be a sum of the various spot recordings. The efficiency of the proposed algorithm is tested via objective and subjective tests.
5.1. Modeling Performance
In this section, we show that the use of the proposed method results in a modeled signal that is objectively and subjectively very close to the original recording. For this purpose, we use the two microphone recordings of the male and female voices of the chorus, as mentioned. The objective is to resynthesize one of these recordings using its corresponding low-dimensional model coefficients along with the residual of the other recording.
From initial listening tests, it has been clear that using a number of bands around 8 for our model produced high-quality resynthesis without loss of the objective of the initial recording. For example, we have been able to resynthesize the male voices recording based on the residual from the female voices. On the other hand, without the use of a filterbank, the resulting quality of the resynthesized signal greatly deteriorated with an introduction of a large degree of crosstalk to the recording. In order to show this objectively, we measured the distance between the residual signals of the two recordings, using the normalized mutual information as a distance measure. The intuitive claim, as explained in Section 3, is that decreasing the distance of the two residuals will increase the quality of the resynthesized recording. Our listening tests indicated that increasing the number of subbands in our model, and consequently improving the model accuracy, resulted in much better quality of the resynthesized signals. While several measures were tested, the normalized mutual information proved to be very consistent in this sense.
for which it can be shown that . The NMI obtains its minimum value when and are statistically independent and its maximum value when . The NMI does not constitute a metric since it lacks symmetry, however it is invariant to amplitude differences , which is very important when comparing audio waveforms.
The NMI values in Figure 5 are median values of the segmental NMI between the power spectra of the two residual signals using an analysis window of 6 milliseconds. The residual signals are obtained using an overlap-add procedure so that they can be compared using the same analysis window. Our claim, that using a subband analysis with a small LP order for each band will produce much better modeling results than using a high LP order for the full frequency band, is justified by the results shown. For the full band analysis, we obtain an NMI value of 0.0956 while for an 8-band filterbank the median NMI is 0.5720 (40th order wavelet filters). In Figure 5 we plot the median NMI for different orders of the Daubechies filters. We can see that increasing the filter order results in slightly better results. Intuitively this was expected; an increase in the filter order results in better separation of the different bands, which is important since we model each subband signal independently of the others. In a similar experiment, we compared the residual signals in the time domain and found that the median NMI doubles when using the 8-band system when compared to the full-band case. The results for both the frequency and time domains are similar regardless of the analysis window length for obtaining the NMI segmental values. When increasing the window size, the NMI drops, which is expected since more data are compared. The decrease is similar for the various numbers of bands we tested.
In order to test the performance of our method in terms of crosstalk , we also employed subjective (listening) tests, in which a total of 17 listeners participated (individually, using good-quality headphones—Sennheiser HD 650). We used the two concert hall recordings from the same performance as mentioned earlier (one capturing the male voices and one capturing the female voices of the chorus). We chose three parts of the performance (about 10 seconds each, referred to as Signals 1–3 here) where both parts of the chorus are active so that the two different microphone signals can be easily distinguished. For each signal we designed an ABX test, where A and B correspond to the male and female chorus recording (in random order), while each listener was asked to classify X as being closer to A or B regarding as to whether the male or female voices prevail in the recording.
For this test, as well as all the listening tests employed for the results of this manuscript (both ABX and DCR tests explained in the following paragraphs), the sound level of all waveforms was normalized so that they sound as having equal level (or else the loudness level could have affected the results). This normalization was achieved by dividing each signal with its maximum absolute value, and in practice this procedure proved to be sufficient for all signals to sound as having the same sound level; the reader is referred to the authors' website mentioned in Section 5.2 for listening to the audio waveforms that were used in the listening tests. For both the ABX and DCR tests, a simple computer-based graphical user interface (GUI) was designed for the convenience of the listeners. The GUI consisted of a series of three buttons for the ABX test (two buttons for the DCR test), each button triad (or dyad for the DCR test) corresponding to the same part of a music recording. By clicking to a button in the screen using the mouse, the listener could listen to the corresponding audio file. As is common in these tests, the listener was encouraged to listen to audio clips as many times as desired and in any order preferred.
Results from the ABX listening tests, for measuring the crosstalk introduced by the proposed model.
5.2. Donwmix Subjective Tests
In this section, the focus is on testing whether resynthesis of the various spot signals from a downmix sum signal is a viable scenario. This is important in cases when spot signals do not contain common content, which is often the case in studio recordings. As in the previous section, we are again interested to test the amount of crosstalk that is introduced, and whether there are implications regarding the quality of the resynthesized signals. It is expected that it will be more difficult to resynthesize good-quality spot signals from the sum signal compared to the reference signal that was used in the previous section since the sum signal will contain frequency components which were not at all present in some spot signals. Also, crosstalk will be more audible in separate track recordings.
(viii)male speech, and
Signals (i)–(v) are excerpts from the EBU SQAM (Sound Quality Assessment Material) test disc and were obtained from (http://sound.media.mit.edu/mpeg4/audio/sqam/). These are stereo recordings, and only one of the 2 channels was used in our experiments. Signals (vi)-(vii) are a courtesy of rock band "Orange Moon." Signals (viii)-(ix) were obtained from the VOICES corpus (http://www.cslu.ogi.edu/corpora/voices/), available by OGIs CSLU . All signals are 16-bit 44.1 kHz signals, except from the speech signals which are 22 kHz signals. The modeling parameters used for the experiments of this section correspond to the parameters of ABX-1 test of the previous section, which gave the best objective and subjective results, with the exception of LP order per band which was 16 (instead of 8). In the speech files, though, due to the use of different sampling rate, only 4 subbands were used (instead of 8).
bass plus soprano,
(2)guitar plus rock singer,
(3)harpsichord plus violin,
(4)female plus male speech,
(5)trumpet plus violin,
(6)violin plus guitar, and
(7)violin plus harpsichord.
These seven signals correspond one-to-one to the Tests (1)–(7) in the ABX resuls, and to Signals (1)–(7) in the DCR results.
The instrument that is referred first in the above list is the instrument that we wanted to resynthesize from the sum signal. In the ABX test, each listener was presented with the original two instrument recordings that were used to obtain the sum signal as signals A and B (in random order), as well as the resynthesized signal (Signal X), and was asked to associate X with A or B depending on which instrument prevails in the recording. In the DCR tests, each listener was asked to grade the resynthesized signal compared to the original recording that we wanted to obtain (regardless to whether the listener recognized that this was indeed successful in the ABX test). The audio files that were used in these tests can be found in (http://www.ics.forth.gr/~mouchtar/originals/tests.html), which includes the classical music recording of the previous section. These sound files include the separate recordings as well as the sum signal.
The results of the ABX test are given in Table 2. The ABX results clearly show that the amount of crosstalk is small, when considering which instrument prevails in the resynthesized recording, which is a very encouraging result. The total ABX score for all files is 97%. Figure 7 shows the DCR results for the seven test signals. Each listener was asked to grade the resynthesized signal with respect to the original signal we want to model. From the results of the figure we can make the following conclusions.
As expected, when attempting to resynthesize the violin using a sum with the harpsichord, the DCR result is very low. On the other hand, when attempting to obtain the harpsichord from the same sum signal, the DCR result is much better. This is due to the fact that percussive sounds cannot be adequately modeled by their spectral envelope, and significant information remains in the residual. Thus it is a difficult task to diminish the percussive signal when resynthesizing another spot signal, but the opposite is not as hard.
The same conclusion holds for the vocals and the guitar signals, but to a lesser degree, given that in our tests the guitar has a percussive nature but not to the same degree as the harpsichord.
Results from the ABX listening tests, for measuring the crosstalk introduced by the proposed model using the sum reference signal.
Given the SQAM waveforms, we also derived some test audio files for illustrating some interesting aspects of the proposed modeling approach. One subject of interest is to show that the residual signal of the reference channel is needed for good-quality synthesis, as opposed to using a synthetic error signal such as white noise or a randomly chosen segment from the actual error signal of the target signal. As is true for speech signals as well, white noise cannot be used as an error signal for synthesizing high-quality audio signals. In fact, in speech processing the problem of producing the best model error signal for achieving best audio quality has been an important issue both in text-to-speech synthesis (TTS) and speech coding alike. This problem is even more important in music applications as the one examined in the text, where quality is of extreme importance. It is thus necessary to note the fact that using white noise as model error, even with the correct energy scaling for each time frame, will not produce high-quality synthesis in our application, nor in speech synthesis and coding. The same is true for more carefully designed synthetic error signals (e.g., for speech an impulse train can be generated based on the estimated pitch, although this in practice is not possible for polyphonic music). The reason is that the whitening process is not perfect and important information remains in the error signal. This information cannot be approximated by white noise or any other synthetic signal but can be approximated by a similar error signal (obtained from the reference signal). The general practice in the speech processing domain is to use the error from actually recorded speech signals (e.g., phonemes, as in concatenative speech synthesis). Similarly in our case, the error signal is not synthesized but it is obtained from actually recorded signals (the reference recording), and this is possible only for the case that we examine here, that is, for various spot signals of a multichannel recording, which have similar content. If the various spot signals were not correlated, the proposed method would fail (unless a downmix signal was derived as a reference signal), since the model error signals must be very similar in order to use one error signal for synthesizing all spot signals.
The other issue that we wish to illustrate at this point using the SQAM waveforms is that the creation of a downmix signal is necessary for the case when the reference and target signals become uncorrelated. For simplification, let us consider one reference and one spot signal. The proposed method assumes that the two microphone signals have similar content, in the sense that the microphones capture the same instruments with different weights (e.g., one microphone captures mostly the male voices of the chorus but the female voices are also present in the recording, and vice versa for the other microphone). In principle, the whitening process of removing the AR spectrum (improved by multiresolution analysis) will result in two error signals with the same content. This, as explained in the manuscript, is due to the fact that the two error signals will contain the same frequencies (harmonics) with equal amplitude (due to whitening). This concept is central in the proposed method. When the reference and target signals are not correlated, or are weakly correlated, the proposed method will result in poor quality (the two error signals will contain different harmonics even in the ideal case of perfect whitening).
In order to show examples of the resulting audio quality that is obtained in the above described cases, we have derived the audio waveforms that can be found in our previously mentioned website, in subdirectory named "Incorrect Error Synthesis Examples." In these test audio files, we have included an experiment where we use the violin and trumpet recordings from the SQAM dataset. Our objective is to resynthesize the trumpet signal using only its multiband AR spectrum and (i) white noise scaled using the correctly extracted variance (i.e., obtained from the corresponding subband and time frame of the trumpet error signal), (ii) from a randomly selected frame of the trumpet signal (different one for each subband), again scaled with the "correct" variance of each frame, and (iii) using the error signal from the violin recording. The above experiments were derived so that we can verify our claims regarding the fact (a) that random noise or an irrelevant error signal cannot produce high-audio quality (experiments (i) and (ii)) and (b) that the downmix process is necessary for introducing correlation between the reference and target signals. The listener can easily verify these claims by comparing the resynthesis result from the downmix signal which can be found in the aforementioned link ("Trumpet-violin" subdirectory).
As a general conclusion, resynthesis from a sum signal is a more challenging task than from a signal which originally contains common information with all spot signals (as is the case in USCs classical music recordings). However, as we also note later in Section 5.3, the DCR results obtained do not necessarily indicate the quality of the resynthesized signals alone. The fact that in the resynthesized signals there is an amount of crosstalk which is not present in the original recording affects the DCR tests, although the actual audio quality of the signal might not be distorted. This can be seen if we compare the results of this section with the results of Section 5.1. As opposed to Section 5.1, in this section, the actual separate recordings were available and were used for testing. Consequently, the ABX results obtained for the sum scenario were much better since it is easier to identify the target recording than in Section 5.1. On the other hand, since now the original recordings contain separate instruments, in the DCR test the effect of crosstalk is much more evident and is considered more important by the listeners than in Section 5.1. In other words, the DCR results in this section are more related with the crosstalk issue rather than the resulting quality. We invite the reader to judge on the performance of the proposed model by visiting our aforementioned website.
5.3. Coding Results
Regarding the coding scheme proposed, our initial listening tests indicated that the final quantized version is acoustically close in quality compared to the recorded signal, for bitrates as low as 5 kbps. Again, it is mentioned that the objective in this paper is to obtain subjective results above 3.0 grade, which can be considered a good performance for low bitrate coding applications. First, we give some objective results using the LSD measure. The audio data used for the LSD results correspond to about 1 minute of the male and female chorus classical music recordings that have been used in Section 5.1. Classical music signals 1–3 that were used in the listening tests of Section 5.1 (and are used for the listening tests of this section as well) are part of this 1 minute testing dataset. The sampling rate for the audio data is 44.1 kHz; we divide the frequency range into 8 octave subbands using th order Daubechies wavelet filters. The model parameters are those that gave the best quality in the modeling (objective and subjective) results of the previous section, that is, 8th order LP, 256 samples frame with 75% overlapping.
Before proceeding to the description of the results, we give some details regarding the GMM training procedure. A training audio dataset of about 136 000 LSF vectors (approximately 3 minutes of audio) was used to estimate the parameters of a 16-class GMM. The training database consists of recordings of the same performance as the data we encode (but a different part of the recording than the one used for testing). In practice, it may not be possible to obtain a training set that corresponds to the same data that are coded. In these cases, it is possible to use a training database which contains a large number of music recordings, which translates into a large degree of variability in the LSF parameters. It is also possible to use only a subset of the large database which is closer in content to the content that will be coded.
For obtaining this LSF vector training dataset, we applied to the audio data the same wavelet-based filterbank that is used for the modeling/encoding procedure (8-bands, critical subsampling, same window length in samples for each band). In this manner, we collected all the subband vectors into one set of 136 000 LSF vectors; with this set we trained a single GMM that was used for decorrelating all subband vectors during the coding procedure. While this approach was followed in this paper, it is important to note that a problem arises regarding the lack of training vectors in the lower subbands. More specifically, under these model parameters, the number of vectors in the th band is double the number of vectors in the th and so forth. Consequently, the training dataset contains more vectors from—and is thus more accurate for—the higher-frequency bands than the lower-frequency bands. In turn, during coding, the lower bands demand more bits/frame for achieving the same LSD with the higher-frequency bands. On the other hand, this does not significantly increase the total bitrate since the critical subsampling results in far less data in the lower bands. Nevertheless, we attempted to resolve this issue by using the same frame rate in millisecond (varying in samples) for each band during training, which results in the same number of training vectors per band. We trained a model using the vectors from all bands as one training set. We also trained a different model, by creating 8 training sets (different GMM for each band), given that in this case there are enough vectors in all subbands for training a different GMM per band. Both of these latter approaches produced much higher LSD than our initial approach, mostly in the lower-frequency bands. This can be possibly attributed to the fact that the training and testing conditions are different (in our case the analysis/synthesis frame rate for each band). In turn, this results in a mismatch between the training and testing vectors, which is evident in terms of LSD.
The log spectral distortion for various bit rates (variable rate coding scheme). For the 5 kbps case, the actual number of bits/frame used for each band can be found on Table 4.
An example of the total bits that were assigned in each band for variable rate coding, corresponding to the 5 kbp s case of Table 3, and the associated LSD.
We should note that the LSD values given in all the tables of this section offer an objective performance measure which is not trivial to correlate with the acoustic tests that follow later in this section. This is in contrast to speech coding, where it is generally accepted that an average LSD value of 1 dB (combined with less than 2% of LSD values in the region 2–4 dB) will result in speech of high perceptual quality. In our case, there are two issues that prohibit at this point such a generalization. These are (i) the fact that LSF coding for audio signals has not been used in the past for good-quality audio coding, and consequently extensive tests are required and (ii) the use of filterbanks, which raises the issue that for the same average (over all subbands) LSD value, we can achieve a wide range of LSD values per band. The latter remains an open question for our future research, that is, to determine how the LSD per band measure that we use correlates with subjective quality. From our tests, it has been clear that the listeners have different tolerance in the coding error for each subband, which is related to psychoacoustic principles. In our future research, we intend to examine whether a minimum LSD value per band can be derived, similarly to the aforementioned principles in speech coding research.
In order to test the performance of the coding procedure, we conducted DCR-based listening tests, using the aforementioned (in Section 5.1) 5-grade scaling procedure. Twenty-two volunteers listened to three sound clips (originally recorded versus coded classical music Signals 1–3 similarly to Section 5.1). In this case, the coded signals were obtained using the best modeling parameters (8-level db40 wavelet-based), while coded using the variable rate coding scheme with 16 GMM classes. Regarding the bits/frame used for each band, we encoded the audio signals using the following bitrates: (i) 5 kbps with varying bits/frame for each band, (ii) 10 kbps with varying bits/frame for each band, (iii) 15 kbps using 22 bits/frame for each band, and (iv) 20 kbps with 29 bits/frame for each band. The choice of these four bitrate values, for each of the three sound clips mentioned, resulted in a total of 12 DCR tests. The signals 1–3 that were used in the listening tests are part of the 1-minute audio signals that were used to derive the LSD values in this paper.
At this point, it is of interest to mention that for the results described in this paper, the residual signal is derived from a PCM coded recording, using 16 bits/sample and a 44.1 kHz sampling rate. In practice, as mentioned, the coding scheme we propose is based on coding a single audio channel (from which the residual is derived) and using side information in the order of 5 kbps for each of the remaining microphone recordings. The single audio channel can be encoded using any monophonic coding scheme, such as perceptual audio coders. In informal listening tests, we used the residual of an MP3 coded signal with 64 kbps rate, for resynthesizing Signals 1–3 using 5 kbps bitrate. The resulting perceptual quality was similar to the quality of the signals used in the listening tests of Figure 8.
We proposed a multiresolution source/filter model for immersive audio applications, which can lead to good quality (above 3.0 perceptual grade compared to the original) low bitrate coding. More specifically, we showed that it is possible to encode the multiple microphone signals of a multichannel audio recording into a single audio channel, and additional information in the order of 5 kbps for each microphone signal. The approach followed is focused towards encoding the microphone signals before those are mixed into the final multichannel mix and is thus suitable for immersive applications such as remote mixing and distributed musicians' collaboration. Our objective and subjective results demonstrate that our algorithm offers a viable approach for very low bitrate audio coding, with audio quality that is acceptable for many practical applications.
The authors wish to thank the listening tests volunteers, Christos Tzagkarakis for helping organize the listening tests, Andre Holzapfel and his rock group "Orange Moon" for providing the rock music test files, and Professor Kyriakakis of the University of Southern California for providing the classical music test files as well as for his overall support of the project. This work has been cofunded by a Marie Curie Transfer of Knowledge (TOK) Grant within the 6th European Community Framework Program and by the European Social Fund and Greek Government National Resources.
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