Correlogram is an important representation for periodic signals. It is widely used in pitch estimation and source separation. For these applications, major problems of correlogram are its low resolution and redundant information. This paper proposes a voiced speech segregation system based on a newly introduced concept called dynamic harmonic function (DHF). In the proposed system, conventional correlograms are further processed by replacing the autocorrelation function (ACF) with DHF. The advantages of DHF are: 1) peak's width is adjustable by controlling the variance of the Gaussian function and 2) the invalid peaks of ACF, not at the pitch period, tend to be suppressed. Based on DHF, pitch detection and effective source segregation algorithms are proposed. Our system is systematically evaluated and compared with the correlogram-based system. Both the signal-to-noise ratio results and the perceptual evaluation of speech quality scores show that the proposed system yields substantially better performance.
In realistic environment, speech is often corrupted by acoustic interference. Meanwhile, many applications have bad performance when handling the noisy speech. Therefore, noise reduction or speech enhancement is meaningful for systems such as speech recognition and hearing aids. Numerous speech enhancement algorithms have been proposed in the literature . The methods, such as independent component analysis  or beam forming , require multiple sensors. However, this requirement is not applicable for many applications such as telecommunication. Spectrum subtraction  and subspace analysis  proposed for monaural speech enhancement usually make strong assumptions on acoustic interference. Therefore, these methods are limited to some special environments. Segregating speech from one monaural recording has proven to be very challenging. At present, it is still an open problem in realistic environments.
Compared with the limited performance of speech enhancement algorithms, human listeners with normal hearing are capable of dealing with sound intrusions, even in monaural condition. According to Bregman , a human's auditory system segregates a target sound from interference through a process called auditory scene analysis (ASA) which has two parts: (1) sound signal decomposition and (2) components grouping. Bregman considered that the components organization included sequential organization on time series and simultaneous organization on frequency series. To simulate ASA inspired a novel field, computational auditory scene analysis (CASA) , which has obtained more and more attention. Compared with other general methods, CASA can be applied under single channel input, and it has no strong assumption on the prior knowledge of noise.
A large proportion of sounds have harmonic structure, such as vowels and music tone. The most distinct characteristic is that these sounds consist of fundamental harmonic () and several overtones which are called harmonic series. A good deal of evidence suggest that harmonics tend to be perceived as a single sound. The phenomenon is called the "harmonicity" principle in ASA. Pitch and harmonic structure provide an efficient mechanism for voiced speech segregation in CASA systems [8, 9]. Continuous variation of pitch is good for sequential grouping, and harmonic structure is suitable for simultaneous grouping. Licklider  proposed that pitch could be extracted from nerve firing patterns by a running autocorrelation function performed on the activity of individual fibers. Licklider's theory was implemented by the scholars (e.g., [11–14]). Meddis and Hewitt  implemented a similar computer model for harmonics perception. Specifically, their model firstly simulated the mechanical filtering of basilar membrane to decompose the signal and then the mechanism of neural transduction at hair cell. Their important innovation was to conduct the autocorrelation to model the neural firing rate analysis of human being. These banks of autocorrelation functions (ACF) were called correlograms which provide a simple way to pitch estimation and source separation. For pitch estimation, previous research  showed that peaks of summary correlograms indicate the pitch periods. According to the experiment results, Meddis and Hewitt argued that many phenomena about pitch perception could be explained with their model including the missing fundamental, ambiguous pitch, the pitch of interrupted noise, inharmonic components, and the dominant region of pitch. For source separation, the method as in  is to directly check that whether the pitch period is close to the peak of correlograms. By these advantages of correlogram, it is widely used in pitch detection  and speech separation algorithms [8, 9, 15].
However, there are some unsatisfactory facts. One was pointed out that the peak corresponding to the pitch period for a pure tone is rather wide . It leads to low resolution for the pitch extraction since mutual overlap between voices weakens their pitch cues. Some methods were proposed to obtain narrow peaks, such as "narrowed" ACF  and generalized correlation function . Another problem is redundant information caused by the "invalid" peaks of ACF. In fact, we care more about the peak of ACF at the pitch period when using correlogram to estimate pitch and separate sound sources. For example, algorithm  used the maximum peak of summary correlogram to indicate the pitch period. However, competitive peaks at multiples of pitch period may leads to subharmonic errors. To overcome the drawbacks, the first thing is to make the peaks narrower, and the second is to remove or suppress the peaks which are not at the pitch periods. We propose a novel feature called dynamic harmonic function to solve these two problems. The basic idea of DHF is shown in the next section.
The rest of the paper is organized as follows. We firstly present the basic idea behind DHF in Section 2. Section 3 gives an overview of our model and specific description. Our system is systematically evaluated and compared with the Hu and Wang model for speech segregation in Section 4, followed by the discussion in Section 5 and the conclusion in Section 6.
2. Basic Idea of DHF
DHF is defined as a Gaussian mixture function. Gaussian means equal to the peak position of ACF which carries periodic information about the original signal in a certain frequency range. The peak width can be narrowed by adjusting the Gaussian variance. Meanwhile, the Gaussian mixture coefficient controls the peak height of DHF. The problem is how to estimate the mixture coefficients. The basic idea is as follows.
Voiced speech generally has a harmonic structure including continuously numbered harmonics. Therefore, one could verify a pitch hypothesis based on whether or not there is a continuously numbered harmonics corresponding to this pitch. For example, when its neighbor harmonics appear at 400 Hz or 800 Hz, harmonic at 600 Hz is regarded as the third harmonic of the complex tone whose pitch is 200 Hz, such as case A in Figure 1. In this case, the pitch period is at the third peak position of ACF of frequency region around 600 Hz. While in case B, the pitch period is at the second peak position. Based on this idea, Gaussian mixture function tends to give a high peak at a pitch period hypothesis if its neighbor harmonics appear. It implies that the shape of guassian mixture function of a harmonic does not only depend on the frequency of harmonic itself but also the neighbor harmonics around. Therefore, we call it dynamic harmonic function.
Figure 1. Frequency component perception.
3. System Overview
The proposed model contains six modules shown in Figure 2. In front-end processing stage, signal is decomposed into small units along time and frequency. Each unit is called T-F unit. After that, the features of each unit are extracted, such as normalized ACF, normalized envelope ACF proposed in previous studies , and newly introduced carrier to envelope energy ratio. In the second stage, DHF in each unit is computed. According to different characteristic, the units are first classified into two categories: (1) resolved T-F unit dominated by a single harmonic and (2) unresolved T-F unit dominated by multiple harmonics. The computations of DHF for resolved and unresolved T-F unit are different. More details can be seen in Section 3.2. In the pitch estimation stage, pitch of target speech is extracted based on DHFs. Before that, the resolved T-F units are merged into segments firstly. Segmentation has been performed in previous CASA systems. A segment is a larger component of an auditory scene than a T-F unit and captures an acoustic component of a single source. An auditory segment is composed of a spatially continuous region of T-F units. Therefore, computational segment is formed according to time continuity and cross-channel correlation. It is reasonable to expect that high correlation shows the adjacent channels dominated by same source. However, frequencies of target and intrusion are often overlapped and it leads to the computational segments being dominated by different sources. In our model, we expect a segment to be dominated by the same harmonic of the same source. Hence, we employed another unit feature called harmonic order to split the segments into relative small ones. Its benefit is shown in following subsection. Harmonic order represents the unit dominated by which harmonic of the sound. During the unit labeling stage, T-F unit is labeled as target or intrusion according to the estimated pitch and DHF. In the fifth stage, T-F units are segregated into foreground and background based on segmentation. Finally, the T-F units in foreground synthesize the separated speech.
Figure 2. Schematic diagram of the proposed multistage system.
3.1. Front-End Processing
3.1.1. Signal Decomposition
At first, an input signal is decomposed by 128-channel gammatone filterbank  whose center frequencies are quasilogarithmically spaced from 80 Hz to 5 kHz and bandwidths are set according to equivalent rectangle bandwidth (ERB). The gammatone filterbank simulates the characteristic of basilar membrane of the cochlea. Then, the outputs of filterbank are transited into neural firing rate by hair cell model . The same processing is employed in [9, 15]. Amplitude modulation (AM) is important for channels dominated by multiple harmonics. Psychoacoustic experiments have demonstrated that amplitude modulation or beat rate is perceived in a critical band within which harmonic partials are unresolved . The AM in channels are obtained by performing Hilbert transform on gammatone filter output and then by filtering the squared Hilbert envelope by a filter with passband (50 Hz, 550 Hz). In the following part, gammatone filter output, hair cell output, and amplitude modulation at channel are represented by , , and , respectively.
Then, time frequency (T-F) units are formed with 10 ms offset and 20 ms window in each channel. Let denote a T-F unit for frequency channel and time frame . The T-F units will be segregated into foreground and background according to their features.
3.1.2. Feature Extraction
Previous researches have shown that the correlogram is an effective mid-level auditory representation for pitch estimation and source segregation. Thus, the normalized correlogram and the normalized envelope correlogram are computed here. For T-F unit , they are computed as the following equations which are same as in :
where lag , shiftcorresponds to 10 ms and window length .
One knows that the peak position of ACF reflects the period or its multiple of the signal. is a proper feature to segregate the T-F units dominated by a single harmonic. However, it is not suitable for the T-F units dominated by several harmonics because of the peaks' fluctuation, as shown in Figure 3(b). In this case, is employed for segregation whose first peak position usually corresponds to pitch period. In order to remove the peaks at integer multiples of the pitch period, the normalized envelope ACF is further processed into "enhanced" envelope ACF as shown in Figure 3(d). Specifically, is half rectified and expended in time by factor and subtracted from clipped , and again, the result is half rectified. Iteration is performed by to cancel spurious peaks in possible pitch range. The computation is similar with the one in .
Figure 3. (a) is channel response dominated by multiple harmonics; (b) is the ACF of the channel; (c) is the envelope ACF of the channel; (d) is the "enhanced" envelope ACF of the channel and the vertical line in (d) is the corresponding pitch period.
Since we use different features to segregate the T-F units dominated by a single harmonic and the ones dominated by several harmonics, it is important to classify the T-F units correctly according to their different characteristics. In order to narrate facility, we define the resolved T-F unit as the one dominated by a single harmonic and the unresolved T-F unit as the one dominated by multiple harmonics. In fact, the fluctuation of envelope is relative severe in unresolved T-F units because of the amplitude modulation. Figure 4 shows the filter response and its envelope in resolved T-F unit (Figure 4(a)) and in unresolved T-F unit (Figure 4(b)). Here, a feature—carrier to envelope energy ratio, proposed in our previous work , is employed to classify the units into resolved and unresolved ones. If the is larger than a threshold, the T-F unit is regarded as resolved one and vice versa. For T-F unit , its computation is given by
Figure 4. Filter response (the solid line) and its envelope (the dash line). (a) At channel 20 with center frequency 242 Hz. (b) At channel 100 with center frequency 2573 Hz.
In a unit , severe fluctuation of envelope leads to being small. Hence, we regard as unresolved if or else as resolved. Here, the according to the experiments.
As demonstrated in , cross-channel correlation measures the similarity between the responses of two adjacent filter channels and indicates whether the filters are responding to the same sound component or not. It is important for subsequent segmentation. Hence, the cross-channel correlation and cross-channel correlation of envelopes are calculated as
where, and are zero-mean and unity-variance versions of and .
3.2. Dynamic Harmonic Function
DHF is defined by a one-dimensional Gaussian mixture function as in formula (6) which indicates the probability of lag being the pitch period. We intend to use the variances of Gaussian function to narrow the peaks' width and the mixture coefficients to suppress the "invalid" peaks. In the following part, we show how to calculate the parameters of DHF. Although the representations of DHF are identical, calculations of the parameters are different for resolved and unresolved units
where, lag (same as in ACF); is the number of peaks of ACF.
In formula (6), there are four parameters component number, Gaussian means, Gaussian variances, and Gaussian mixture coefficients to be computed. The component number equals to the number of peaks of ACF. Mean of the th Gaussian function is set to the position of the th peak of ACF. Gaussian variances are used to control the peak width of DHF which are determined later. The following part will show the estimation method of the mixture coefficients.
For the DHF of a T-F unit, we want to give a higher peak at the pitch period if it is dominated by voiced sound, which means a larger mixture coefficient for the corresponding Gaussian function. Therefore, our work is to estimated pitch period at each T-F unit. Let us see an example at first. The input signal is a complex tone with Hz and all the amplitude of harmonics are equal. Figures 5(a)–5(c) show the ACFs of correlogram at channel 10, 30 and 45 with center frequency 148 Hz, 360 Hz, and 612 Hz, respectively. And Figure 5(d) shows the enhanced envelope ACF at channel 100 with center frequency 2573 Hz. Obviously, channel 30 is dominated by the second harmonic of complex tone. However, it is not indicated by ACF because its peaks have equal amplitude. In fact, without information of the other channels, there are several interpretations for channel 30 according to ACF. For example, the channel could be dominated by the second harmonic where Hz or by forth harmonic where Hz. In DHF, we expect that the second mixture coefficient of DHF could be larger than others. Analysis above implies that the computation of mixture coefficient has to combine the information of other channels. According to analysis above, the mixture coefficient of DHF for resolved T-F unit is computed as follows:
where, is the mean of the th Gaussian function;. Formula (8) shows the pseudopossibility of dominated by the th harmonic of the sound with pitch period at . And (9) shows the possibility of the th harmonic with hypothesis pitch period appearing at frame
Figure 5. (a) ACF at channel 10 whose center frequency (cf) is 148 Hz; (b) ACF at channel 30 whose cf is 360 Hz; (c) ACF at channel 45 whose cf is 612 Hz; (d) enhanced envelope ACF at channel 100 whose cf is 2573 Hz; Input signal is a complex tone with Hz; The vertical dash line shows the pitch period.
Formula (10) shows that the th mixture coefficient depends on the appearance of the th or th harmonic. As seen in Figure 5, the second mixture coefficient of DHF in (b) is large, because there are channels (a) and (c) dominated by the first and the third harmonic of the complex tone whose pitch period is 5.0 ms. While the forth mixture coefficient is small, because no channels were dominated by the third or the fifth harmonic whose frequencies are 300 Hz and 500 Hz, respectively.
From formula (8)–(10), it can be seen that a mixture coefficient of DHF does not depend on its all related harmonics but only two neighbours. One reason is to simplify the algorithm. The other is that previous psychoacoustic experiments  showed that the nearest related harmonics have the strongest effect for the harmonic fusion. During the experiments, scholars used a stimulus in which a rich tone with 10 harmonics wav alternated with a pure tone and checked if the harmonic of rich tone could be captured by the pure tone. It was found that a harmonic was easier to capture out of the complex tone when neighboring harmonics were removed. According to the results, one of conclusions is "the greater the frequency separation between a harmonic and its nearest frequency neighbors, the easier it was to capture it out of the complex tone."
For unresolved T-F unit, computation of the mixture coefficients is different from resolved. One reason is that unresolved T-F unit is dominated by several harmonics at the same time. Hence, the peak order of its ACF does not reflect the harmonic order accurately. Another reason is that the resolution of gammatone filter is relative low in high-frequency region and the continuously numbered harmonic-structure cannot be found in correlograms. Fortunately, the peak of enhanced envelope ACF tends to appear around pitch period, as shown in Figure 5(d). It implies that the mixture coefficient should be large if the mean of Gaussian function is close to the peak of enhanced envelope ACF. Therefore, the mixture coefficient equals to the amplitude of enhanced envelope ACF at the mean of Gaussian function, as in
where is the enhanced envelope ACF; is the th peak's position of ACF.
In order to estimate the pitch, we also define the summary DHF at frame as formula (12) which is important for pitch estimation
Figure 6 shows the comparison of correlogram and DHFs. It can be seen that (1) peaks in DHFs are less in ACFs, (2) the peaks at the pitch period are properly preserved, and (3) the peaks in summary DHF are narrower than in summary correlogram. Figure 7 shows the periodogram (a time series of summary correlogram) comparison. The input signal is male utterance, "where were you away a year, Roy" mixed by a female utterance. For conventional periodogram (a), pitch information of two sources is mixed together and it is hard to separate directly whereas it is clear in DHF periodogram (b).
Figure 6. Auditory features. The input signal is complex tone with Hz. (a) correlogram at frame for the clean female speech (channel 1–80 is ACFs, channel 81–128 is envelope ACFs). The summary correlogram is shown in bottom panel; (b) corresponding dynamic harmonic functions. The summary dynamic harmonic function is shown in bottom panel. The variance of DHF is 2.0.
Figure 7. -axis is frame, -axis is lag; (a) Conventional periodogram (channel 1–80 is ACF, channel 81–128 is envelope ACF); (b) Dynamic harmonic function periodogram. The input signal is male speech mixed with female speech.
3.3. Pitch Estimation
Pitch estimation in noisy environment is closely related to sound separation. If, on one hand, the mixed sound is separated, the pitch of each sound can be obtained relatively easily. On the other hand, pitch is a very efficient grouping cue for sound separation and widely used in previous systems [8, 9, 15]. In the Hu and Wang model, a continuous pitch estimation method is proposed based on correlogram in which the T-F units are merged into segments according to cross-channel correlation and time continuity. Each segment is expected to be dominated by a single voiced sound. At first, they employed the longest segment as a criterion to initially separate the segments into foreground and background. And then, the pitch contour is formed using units in foreground and followed by sequential linear interpolation, more details can be found in .
It is obvious that initial separation plays an important role for pitch estimation. Although result of the simple decision could be adjusted in the following stage through iterative estimation and linear interpolation so as to give an acceptable prediction of pitch contour, it yet does not satisfy the requirements of the segregation and may also deliver some segments which are dominated by the intrusions into the foreground. This will certainly affect the accuracy of the result of pitch.
As a matter of fact, the pitch period is reflected by the ACF of each harmonic. The problem is that ACF has multiple peaks pitch estimation could be simple that if we find the longest segment which is dominated not only by the same source but also by the same harmonic and also know the harmonic order. It only needs to summate the corresponding peaks on each frame and regard the position of the maximum peak as pitch period. This process avoids source separation and pitch interpolation. Under the instruction of above analysis, we try (1) to find the longest segment and (2) to estimate the harmonic order. In this subsection, we will solve these two problems based on DHFs.
In previous systems [9, 15], the segments are formed by cross-channel correlation and time continuity of T-F units. The motivation is that high-cross-channel correlations indicate adjacent channels dominated by the same harmonic and voiced sections have continuity on time scale. However, some of the formed segments are dominated by different sources or multiple harmonics. Figure 8(a) shows the segments which are generated by cross-channel correlation and time continuity. The input signal is a voiced speech mixed by click noise. The black region is dominated by speech and the gray region is dominated by click noise. It is obvious that click noise has no harmonic structure and unit at higher channels is dominated by multiple harmonics. Hence, we expect that each segment is dominated by a single harmonic of the same source. Therefore, to use these segments directly is not proper. Here, we add other two features of T-F unit for segmentation. One is carrier-to-envelope energy ratio which is computed by formula (3) and the other is unit harmonic order.
Figure 8. Segmentation comparison. The input signal is a voiced speech mixed by click noise. (a) Segments formed by cross-channel correlation and time continuity. The black region is dominated by speech and the gray region is dominated by click noise. (b) Segments formed by cross-channel correlation, time continuity and carrier-to-envelope energy ratio.
3.3.1. Initial Segmentation
As mentioned in Section 3.2, T-F units are classified into resolved and unresolved by carrier-to-envelope energy ratio. Each resolved T-F unit is dominated by a single harmonic. In addition, because the passbands of adjacent channels have significant overlap, a resolved harmonic usually activates adjacent channels, which leads to high-cross-channel correlations. Thus, only resolved T-F units with sufficiently high-cross-channel correlations are considered. More specifically, resolved unit is selected for consideration if , chosen to be little lower than in . Selected neighboring units are iteratively merged into segments. Finally, segments shorter than 30 ms are removed, since they unlikely arise from target speech. Figure 8(b) shows a result of segmentation for the same signal in Figure 8(a).
3.3.2. Harmonic Order Computation
For a resolved T-F unit , harmonic order indicates the unit dominated by which harmonic. Although DHF suppress some of peaks compared with ACF, there are still multiple invalid peaks especially at the fraction of pitch period, as seen in Figure 6(b). We still cannot decide the harmonic order by DHF. Fortunately, those peaks at the fractional pitch period are suppressed in summary DHF. Hence, the computation combines the DHF and summary DHF as
From the above algorithm, we can see that the harmonic order of a resolved unit depends on single frame. Due to the noise's interference, estimations of harmonic order of some units are unreliable. Therefore, we extend the estimation by segmentation. Firstly, the initial segments further splits according to harmonic order of resolved T-F unit. These newly formed segments include small segments (shorter than 50 ms) and large segments (longer than 50 ms). Secondly, the connected small segments are merged together. For those units in the rest small segments, they are absorbed by neighboring segments. Finally, the harmonic order of each unit is recomputed by formula (14). For units in segment , the harmonic orders are in accordance with segment harmonic order
Here, all the variances of DHFs are 2.0 for computation of summary DHF. The results are not significantly affected when the variances are in range [2, 4]. Too large values will cause the mutual influence by peaks of different sources. But too small values are also improper for describing the peaks' vibration of the units which are dominated by target speech.
3.3.3. Pitch Contour Tracking
For voiced speech, the first several harmonics have more energy than others, which are relative robust to noisy. Here, we only use the longest segment to estimate the pitch contour. With the harmonic order, it is quite easy to estimate pitch depending only on the longest segment. The algorithm is as follows:
(1)summate the th peak of DHF of T-F units in the longest segment at each frame where is the harmonic order of T-F unit,
(2)normalize the maximum value of summation at each frame to 1,
(3)find all the peaks of summation as pitch period candidates at each frame,
(4)track the pitch contour within candidates by dynamic programming,
where is the summation at frame , is the th peak of , the weight .
Figures 9(a) and 9(b) illustrate the summary DHF (only with the peak corresponding to harmonic order) in longest segment and pitch contour. As shown in figure, the pitch contour is roughly given by summary DHF. The dynamic programming corrects some errors during the pitch tracking. Figure 9(b) shows the estimated pitch contour matches that of the clean speech very well at most of the frames.
Figure 9. Result of pitch for the mixture of speech and cocktail party. (a) Summary of dynamic harmonic function (only with the peak corresponding to harmonic order) within longest segment. (b) Estimated pitch contour, marked by "o" and the solid line is the pitch contour obtained from clean speech before mixing.
3.4. Unit Labeling
The pitch computed above is used to label the T-F units according to whether target speech dominates the unit responses or not. Mechanism of the Hu and Wang model is to test that the pitch period is close to the maximum peak of ACF. It is because that for the units dominated by target speech, there should be a peak around the pitch period. The method employed here is similar but with some differences.
For resolved T-F units, the maximum peak of DHF tends to appear at the pitch period as presented in previous section. We can label a unit as target speech if is close to the maximum peak of DHF. However, computation method of DHF is influenced by noise. To obtain the robust results, the method has some changes. For the resolved T-F unit in segment (generated in Section 3.3), if its nearest peak to the pitch period equals to the harmonic order and satisfies (16), it is labeled as target or else as intrusion
where ; is estimated pitch period at frame ; the variance for .
For an unresolved T-F unit, we cannot use the same labeling method as resolved T-F unit because it is dominated by multiple harmonics. As analysis before, the peaks of envelope ACF tend to appear at the pitch period. Thus, DHF of unresolved unit shows a large peak at the pitch period. The labeling method is changed into (17). In (17), it is to compare the pseudo-probabilities at and at the most possible pitch period in unit. If its ratio is larger than the threshold threshold, the unresolved T-F unit is labeled as target or else as intrusion
where ; the variance .
The variance of DHF in each unit depends on the first peak's position . It leads to the peak width of DHF close to ACF. And the threshold is according to our experiment results.
3.5. Segregation Based on Segment
In this stage, units are segregated based on segmentation. Previous studies showed that it is more robust. Our method here is very similar with the Hu and Wang model .
3.5.1. Resolved Segment Grouping
For a resolved segment generated in Section 3.3, it is segregated into foreground if more than half of its units are marked as target, or else it is segregated into background . The spectra of target and intrusion often overlap, and as a result, some resolved segments contain units dominated by target as well as those dominated by intrusion. The is further divided according to the unit label. The target units and intrusion units in merged into segments according to frequency and time continuity. The segment retained in which is made up of target units and larger than 50 ms. And the segment are added to , if it is made up of intrusion units and larger than 50 ms. The rest smaller segments are removed.
3.5.2. Unresolved Segment Grouping
The unresolved segment is formed by target unresolved T-F units with frequency and time continuity. The segments larger than 30 ms are retained. The rest of the units in small segments are merged into large segment iteratively. At last, the unresolved units in large segments are grouped into , and the rest are grouped into . This processing part is similar with the Hu and Wang model.
Finally, the units in foreground are resynthesised into wave form by the method in . Figure 10 shows the waveforms as an example. It shows the clean speech in Figure 10(a), mixture (mixed by cocktail party noise) in Figure 10(b) and segregated speech by proposed system in Figure 10(c). As can be seen, the segregated speech resembles the major parts of clean speech.
Figure 10. Waveforms. (a) clean speech; (b) mixture of clean speech and cocktail party noise; (c) segregated speech by the proposed method.
4. Evaluation and Results
Proposed model is evaluated on a corpus of 100 mixtures composed of ten voiced utterances mixed with ten different kinds of intrusions collected by Cooke . In the dataset, ten voiced utterances have continuous pitch nearly throughout whole duration. The intrusions are ten different kinds of sounds including N0, 1 kHz pure tone; N1, white noise; N2, noise bursts; N3, "cocktail party" noise; N4, rock music; N5, siren; N6, trill telephone; N7, female speech; N8, male speech; and N9, another female speech. Ten voiced utterances are regarded as targets. Frequency sampling rate of the corpus is 16 kHz.
There are two main reasons for using this dataset. The first is that the proposed system focuses on primitive driven  separation, and it is possible for system to obtain the pitch from same source without schema driven principles. The other reason is that the dataset has been widely used in evaluate CASA-based separation systems [8, 9, 15] which facilitates the comparison.
The objective evaluation criterion is signal to noise ratio (SNR) of original and distorted signal after segregation. Although SNR is used as a conventional method for system evaluation, it is not always consistent with the voice quality. Perceptual evaluation of speech quality (ITU-T P.862 PESQ, 2001) is employed as another objective evaluation criterion. The ITU-T P.862 is an intrusive objective speech quality assessment algorithm. Since the original speech before mixing is available, it is convenient to apply the ITU-T P.862 algorithm to obtain the intrusive speech quality evaluation result of the separated speech.
SNR is measured in decibel and computed by following equation. The results are listed in Table 1
where is original voiced speech and is the synthesized waveform by segregation systems.
Table 1. SNR Results. (Mixture: Original degraded speech; Hu-Wang: Hu and Wang model; Proposed: Proposed model; TP Hu-Wang: true pitch-based Hu and Wang model; TP proposed: true pitch-based proposed model; IBM: Ideal binary mask)
The proposed system is compared with the Hu and Wang model. Meanwhile, we also show the performance of ideal binary mask (IBM) which is obtained by calculating local SNR in each T-F unit and selecting units (SNR > 0 dB) as the target. The SNR results of IBM are the upper limit of all CASA-based systems which employ "binary mask". Table 1 gives the variety of SNR in which each value represents the average SNR of one kind intrusion mixed with ten target utterances and the last column shows the average SNR over all intrusions. As shown in Table 1, proposed system improves SNR for every intrusion and gets 13.01 dB improvement of overall mean against unprocessed mixture. Compared with results of the Hu and Wang model, proposed model enhances the separation results about 1.48 dB for overall mean. The highest enhancement of SNR happens on the mixtures of N2 and is about 3.50 dB higher than the Hu and Wang model. Other larger improvements (more than 1.0 dB) are obtained for harmonic sound (N4, N5, N7, N8, and N9) or tone-like sound (N0 and N6). While less improvements are obtained for broadband noises (e.g., N1 and N3).
To further compare the pitch detection algorithm and T-F unit grouping method separately, we replace the estimated pitch with true pitch (obtained on clean speech) for both the Hu and Wang model and proposed system. From Table 1, we can see that true pitch makes the Hu and Wang model enhance the SNR for 0.56 dB (from 11.12 dB to 11.68 dB). But the enhancement is tiny about 0.07 dB for the true pitch-based proposed system. And the only noticeable improvement is on N3 about 0.46 dB. The overall mean of SNR of the true pitch-based proposed system is about 1.00 dB higher than that of true pitch-based Hu and Wang model.
Although conventional SNR is widely used, it does not reflect the related perceptual effects, such as auditory masking. As computational goal of CASA , IBM directly corresponds to the auditory masking phenomenon. Recent psychoacoustic experiments have demonstrated that target speech reconstructed from the IBM can dramatically improve the intelligibility of speech masked by different types of noise, even in very noisy conditions . Li and Wang  also systematically compared the performance of IBM and ideal ratio masks (IRM) and the results showed that IBM is optimal as computational goal in terms of SNR gain. Considering the advantages of IBM, we compute the SNR and PESQ score using the speeches reconstructed from IBM as the ground truth instead of clean speeches.
Figure 11 shows that the SNR of the proposed system are much higher than unprocessed mixtures of all kinds of intrusions. Compared to the performance of the Hu and Wang model, the SNR of the proposed system has significant improvement for all kinds of intrusions except for N3 and N4 with small drops. To further obtain the voice quality of segregated speech, PESQ is employed as a measurement. Figure 12 shows the PESQ scores of IBM against unprocessed mixtures (white bars), segregated speeches from proposed system (gray bars) and from the Hu and Wang model (black bars) on ten kinds of intrusions. As Figure 12 showing, the segregated speeches from proposed system obtain higher PESQ scores on all ten kinds of intrusions (especially on N2, N7, N8, and N9) than unprocessed mixtures and the outputs of the Hu and Wang model.
Figure 11. SNR results using IBM as the ground truth. White bars show the results from unprocessed mixtures, black bars those from the Hu and Wang model, and gray bars those from proposed system.
Figure 12. PESQ results using IBM as the ground truth. White bars show the results from unprocessed mixtures, black bars those from the Hu and Wang model, and gray bars those from proposed system.
Comparing the results of the Hu and Wang model, the most SNR gain about 4 dB is obtained in N0 (pure tone) By analyzing the segregated speeches, we found that the Hu and Wang model groups many target units into the background. It is mainly because some segments include both target units and interference units. These kinds of segments are divided into small ones by harmonic order in our system. Therefore, it leads to the significant SNR gain. For N2 (click noise), the SNR gain also due to the segmentation (see Figure 8). The difference is that the Hu and Wang model groups many interference units into foreground. It should be noticed that the gains of PESQ scores on these two noises are different, about 0.1 on N0 and 0.5 on N2, comparing with the Hu and Wang model. It implies that the second error, grouping intrusion units into foreground, has a greater impact on speech perceptual quality.
Figure 13 shows the spectrograms of mixture of male and female speech in (a), processed by IBM in (b), processed by the Hu and Wang model (c), and processed by proposed model (d). In Figure 13, we can see that the result of proposed model is closer to that of IBM. However, the result of the Hu and Wang model has residual female speech.
Figure 13. Spectrogram comparison: (a) mixture; (b) results of IBM; (c) results of the Hu and Wang model; (d) results of proposed model. The input signal is male speech mixed with female speech.
In sound separation, the application concerns about whether a unit is dominated by a resolved harmonic or by unresolved harmonics. Previous research showed that this process is very important. Resolved and unresolved harmonics are relative concepts which depend on the distance of harmonics and also the resolution of gammatone filterbank. Therefore, the decision of unit cannot be made by its channel frequency. A reasonable decision is to check the filter response in unit. As in previous research , cross-channel correlation is used which measures the similarity between the responses of two adjacent filters, indicates whether the filters are responding to the same sound component. However, it is not reliable for some units especially in high frequency region (as shown in Figure 8(a)). Hence, we use a more direct measurement, carrier to envelope energy ratio, to help classifying the units.
ACF reflects the period information of the signal in a unit. According to the "harmonicity" principle, each peak position could be a pitch period. However, only one of them corresponds to the true pitch period. DHF tends to reduce the peaks by the fact that voiced speeches have continuous numbered harmonics. In noisy environment, it will lead to errors when both neighbors of a harmonic are masked at the same time. However, we found that these cases are relative less.
Pitch detection is another key stage for sound separation. Our algorithm uses only the longest resolved segment for pitch detection. Based on this process, it is relative easy for pitch tracking which is a difficult problem. It should be pointed out that robustness of the system may reduce when the interfering sounds dominate frequency regions for resolved harmonics. However, resolved harmonics have larger energy than unresolved ones. They are more robust to noise. In addition, it should be pointed out that DHF is generated based on the idea of continuous numbered harmonics. For sounds without this feature, DHF is improper
In this paper, we propose the dynamic harmonic functions which derive from conventional correlograms. DHF has the uniform representation for both resolved and unresolved units. Based on DHF, the pitch detection algorithm and T-F unit grouping strategy are proposed. Results show that proposed algorithm improves the SNRs for variety kinds of noises over the Hu and Wang model.
This work was supported in part by the China National Nature Science Foundation (no. 60675026, no. 60121302, and no. 90820011), the 863 China National High Technology Development Projects (no. 20060101Z4073, no. 2006AA01Z194), and the National Grand Fundamental Research 973 Program of China (no. 2004CB318105).
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