Speech Signals Enhancement Using LPC Analysis. based on Inverse Fourier Methods

Transcription

1 Contemorary Engineering Sciences, Vol., 009, no. 1, 1-15 Seech Signals Enhancement Using LPC Analysis based on Inverse Fourier Methods Mostafa Hydari, Mohammad Reza Karami Deartment of Comuter Engineering, Faculty of Engineering Noshirvani Institute of Technology P.O. Box: 844, Babol, Iran Ehsan Nadernejad Deartment of Comuter Engineering, Faculty of Engineering Mazandaran Institute of Technology, P.O. Box: 744, Babol, Iran Abstract This aer, rooses a new methods for seech Signal enhancement based on sectral subtraction, Inverse Fourier Transform. We use the Linear Predicative Coding (LPC), VAD analysis, and Voice/ Unvoice (V/UV) detector for noise estimation and extraction, then we comare the roosed method with the revious ones and are able to recover the seech signal much better than the revious methods. Also, good results have been achieved in the auditory tests. Keywords: Seech signals, Seech enhancement, Sectral subtraction, multiband sectral subtraction, Inverse Fourier Sectral Subtraction, LPC analysis; VAD; V/UV detector I. INTRODUCTION Noise reduction is an imortant issue in seech signal rocessing systems, like seech signals coding, seech recognition. Thus many methods have been roosed for noise reduction in seech signals, some of which are methods based on sectral subtraction (base & Multi-Band) [5, 6, 7, 8], adative filtering [11], Wavelet transform [10, 1, 13, 14, 15]. In the sectral subtraction methods, 3 conditions should be met; a. Noise must be additive. b. Noise and the signal must be uncorrelated. c. A canal must be accessible. Although the base sectral subtraction method is very simle and efficient, it adds a new noise named musical noise. For reducing this noise, the sectral subtraction method alying sectral floor and over-subtraction, can be used [6].

2 Mostafa Hydari, Mohammad Reza Karami and Ehsan Nader Nejad Later, was roosed the multi-band sectral subtraction method in [5]. In this method, the corruted seech signal is initially divided into several frequency bands, and then the sectral subtraction method is alied to each band. As mentioned before, in this aroach it is suosed that the signal and noise are uncorrelated, but actually thus assumtion really haens in seech signals. Hence, the inverse Fourier sectral subtraction method has been resent, which is the same as the sectral subtraction method, but here, the subtraction, is alied to the inverse Fourier transform. In this method, the roblem of the correlation between the signal and noise is solved to some extent. Also, there are some other methods like ceestral subtraction, wavelet transform [10, 1, 13, 14, 15] for noise reduction or elimination (de-noising). In this aer, first, we describe the base sectral subtraction, multi-band sectral subtraction, and inverse Fourier sectral subtraction methods, then we estimated the noise from the seech signal using the LPC analysis [1,, 3, 4]. At last, we aly the estimated noise to the sectral subtraction, multi-band sectral subtraction, and inverse Fourier sectral subtraction methods and we see a noticeable imrovement in these methods. II. Power Sectral Subtraction (PSS) We suose that the signal and noise are additive, so a corruted seech signal can be exressed as bellow: x ( n) = s( n) + n( n) where x(n) is the corruted seech signal, s (n) is the clean sectral signal, and n (n) is a random noise signal. According to the second assumtion, the signal and noise are uncorrelated, so we can write: [1] R n ( τ ) = D0δ ( τ ) () R s, n ( τ ) = 0 (3) Where D 0 is a constant, Rn (τ ) is the auto-correlation of the random noise signal, and R s, n ( τ ) is the cross-correlation function of the s and n signals. According to the relations above and by suosing that the s and n signals are stationary, we can write: Γ ( ω) = Γ ( ω) + Γ ( ω) (4) x s n Where Γ x, Γ s, Γn are Power Density Sectrum (PDS) of x, s, n, resectively. Following equation (4) by estimating the PDF of the random noise signal, the PDF of the clean seech signal can be estimated as exressed below: ˆ ( ω) = Γ ( ω) Γˆ ( ω) Γ (5) s x n (1)

3 Seech signals enhancement using LPC analysis 3 ˆ ˆ Where Γ s ( ω), Γn ( ω) are Estimations of the Γ s (ω), Γ n (ω) and Equations (4) and (5) are true only when the clean seech signal and the noise are stationary, but actually this is not always true. Since the clean seech signals are locally stationary in short-time frames, and additionally the assumtion that noise is stationary is more accetable in short time intervals, windowing is alied to the corruted seech signal. Then the sectral subtraction is alied to each frame by considering m as the window number, we have: x ( n; = s( n; + n( n; (6) R n ( τ ; = D0δ ( τ ) (7) R s, n ( τ ; = 0 (8) Where x ( n; is the windowed signal of the seech signal x (n). By calculating the PDF for both sides of eq. (6) we have: Γ s ( = Γx ( Γn ( (9) Also we know that [1]: * X ( X ( Γx ( ω ; = = N X ( N (10) Where: N is the window length (size) and X is the seech signal. The factor 1 N can be simly neglected, since X ( is the bigger than the denominator: Γ x ( ω ; = x( (11) The following relation can be achieved using the relations (11), (9): S( = X ( N( (1) Where X ( is the magnitude of Fourier transform for the windowed x(n); S( ω ; and N( ω ; are the magnitude of the Fourier transform for the windowed clean seech signal and windowed noise signal, resectively. As can be seen from the equation (1), to comuting the magnitude of the Fourier transform of the clean signal, we need the magnitude of the random noise; hence the random noise signal is estimated from the silence. There is no seech signal in the silence art. Now, for achieve the clean seech signal in the time domain, it is necessary to calculate the magnitude of the Fourier transform as well as it is hase, and by short time fast Fourier transform (st.fft) get the seech signal in time domain. In all ractical alications, the hase of the clean seech sign can be considered equal to the hase of the corruted seech signal [8]. ϕ = ϕ (13) S ( X (

4 4 Mostafa Hydari, Mohammad Reza Karami and Ehsan Nader Nejad This means that the effect of noise on the hase of the seech signals is not sensible for human ear. According to the equations (1), (13), the clean seech signal can be estimated as below: S( = S( ex iϕ S = X ( ( N( 1 ex iϕ S ( (14) Where S(, N( are the Fourier transform of the estimated clean signal and Fourier transform of the estimated noise signal, resectively. Noisy Windowing Seech FFT Phase Information Γ ( ; n ω Enhanced Seech Overla & Add IFFT 1 Fig1. diagram block of Power Sectral Subtraction (PSS) The above method is called the Power Sectral Subtraction (PSS) methods. Fig.1. because the second order of the magnitude of the Fourier transform, which indicates the ower of the signal, is being used; usually they use another ower factor other than, in the sectral subtraction method, the magnitude of which is achieved using otimizing techniques. The method mentioned above is called the general sectral subtraction (GSS) method. 1 a a a S( ω ; = X ( N( ex iϕ (15) S ( But, imortant roblem in the sectral subtraction method is the negative values of the Fourier transform of the clean signal. In order words, we can't certainly assume the Fourier transform of the clean seech signal in each of the relations (14) and (15), as a ositive value. There are two methods for correcting these negative values [1]: S( a) half-wave correction : S( ; = 0 if S( elsewhere > 0 ω (16) b) Full-wave correction :

5 Seech signals enhancement using LPC analysis 5 S ( ω ; m ) = abc S ( ω ; m ) (17) III. Inverse Fourier Sectral Subtraction (IFSS) In the sectral subtraction method [5, 6, 7, 8], it is assumed that the noise and the signal are uncorrelated. This condition can be met by alying the autocorrelation function to both sides of equation (1). Now, if the accuracy of the relation (4) or (9) is reduced, the accuracy of the un correlation between the signal and noise would become less consequently. In the inverse Fourier sectral subtraction method, subtraction is alied to the inverse Fourier transform of the magnitude of the Fourier transform of the corruted signal and the estimated noise signal. It can be evidently said that in the inverse Fourier subtraction method, the subtraction is erformed in the time domain in which the un correlation between the signal and noise has less accuracy. Because usually noise is added to the signal in the time domain where it's not certainly uncorrelated, but addition in the frequency domain needs uncorrelation. In this method, the estimated clean seech signal is calculated according to fig 3. Noisy Seech Windowing FFT IFFT Phase Information IFFT N( ω ; Enhanced Seech Overla & Add IFFT 1 FFT Fig3. diagram block of Inverse Fourier Subtraction V. Linear Predication Coefficient (LPC) Because in our roosed algorithm, LPC analysis [1,, 3] is used for noise estimation, in this section we describe this analysis. The LPC is one of the strongest tools in seech signal rocessing. The general idea of this analysis is that each samle of the seech sign can be exressed as a linear equation of revious inuts and oututs: s( n) = a s( n k) + bl u( n l) (4) k k = 1 l = 0 q Where a k and b l are the denominator and nominator of the filter, resectively, and u(n) is the initial signal which is an imulse burst for voice and is a string of

6 6 Mostafa Hydari, Mohammad Reza Karami and Ehsan Nader Nejad random noise for unvoice [1,,3,4]. The transform function of the system can be achieved by alying the Z transform to the equation (4): S ( z) H z) = = U ( z) 1 q b z l l= 0 k = 1 a l ( (5) z k k An all ole model is very good estimation for the transform function H (z) [1] for seech signals and can be exressed as: H ( z) = 1 1 k= 1 a z 1 = A( z) k (6) k For human s larynx, P is an integer number in the range of The imortant oint in comuting the LPC is that these coefficients can be directly driven from the seech signal for this reason and because of the deendence of the seech signal on times first, windowing is done the signal then the LPC coefficients, are calculated in short frames []. A: Noise Estimation According to the discussions above, each samle of the seech signal can comuted with a good accuracy just using P revious samles of that signal (without using their revious P samles) [1]: S( n) = ak s( n k) (7) k = 1 the error signal is actually the difference between the main seech signal and the seech signal estimate from P revious samles: e( n) = S( n) S( n) = S( n) ak S( n k) (8) k = 1 If we aly Z transform on both sides of the relation above we have: E( z) = S( z) 1 a k = 1 k z A( z) S( z) (9) k = x (n) a z 1 + a z + + a z e(n) Fig4. diagram block of calculation of error function Where, is the z transform of the error signal and has the E(z) characteristics of a noise, sine a linear filter searates the uncorrelated. Part of the signal the most of which is noise for roving this claim, it's enough to calculate the auto-correlation function of the signal (n) e.

7 Seech signals enhancement using LPC analysis 7 In fig.5, the auto-correlation of the error, signal which belongs to a seech signal from the Timit database, is lotted. As can be seen, the signal e(n) has the characteristics of noise, since it's auto-correlation signal is the same as the autocorrelation function of the random noise signal. In our roosed algorithm, we have used this signal for noise estimated that has resulted in a great imrovement in the SNR of the corruted seech signals (comared to the exiting methods). Fig5. auto-correlation function of the error signal. Although the signal e (n) is not the noise signal added to the clean seech signal, it has most it's characteristics. On the other hand, some of the uncorrelated signal related to the seech signal exists in the outut of the filter A (z), which is negligible comared to noise. B: Imroving the outut of filter A(z) using VAD, V/UV detector algorithms As mentioned above, in the sectral subtraction and inverse sectral subtraction it's assumed that the noise effect is the same for all of the signal range [5, 6, 7, 8]. But, in ractice, this situation sanely aaaa1 haens; Since in addition to the existence of different noise source, there is another fact that is the effect off noise on the seech signal deends on the frequency. This deending leads on the frequency [7]. This deendence leads us to the act that the effect of noise on voice and unvoice signals is not the same. So, we are trying to find a method that by searating the voice and unvoice frames, get a higher accuracy in studying this different effect of noise. Also, since in our roosed methods, we want to use LPC analysis for noise estimation, it's imortant to know that the estimated noise in the voice frames is nearer to the actual noise comared with the unvoice frames. Fig.6 shows the reresentation of the amount of this error for voice and unvoice signals versus the number of the filter oles H(z).

8 8 Mostafa Hydari, Mohammad Reza Karami and Ehsan Nader Nejad Error unvoice voice Fig6. The other fact is that a silence frame only consists of noise. When this frame asses through the filter A(z), it becomes weaker so it must be multilied by the gain of an amlifier and for reducing the amount of error in unvoice signals, the estimated noise should the amount of error in unvoice signals, the estimated noise should be weakened. N( ω ; = γ N( (30) According to the discussions above, γ is different for the voice and unvoice frames. VI. Inverse Fourier Subtraction using LPC, VAD, and V/UV Detector Analysis (LPIFSS) As can be seen in fig., in the inverse Fourier sectral subtraction method, like the sectral subtraction [5,6,7,8], we need an estimation of noise that uses the silence art of the corruted seech signal. Usually the first frame of the seech signal is considered as the silence art of the signal. In this method it's suosed that: 1- First frame of the corruted signal with noise belong to the signal. - The effect of noise should be the same in all the signal range. To imrove the method above, it's suggested that instead of directly alying the estimated noise of the silence art of the signal to the algorithm, it's better to ass it through A(z) first, and then consider the outut of the filter as noise an alying it to the inverse Fourier sectral subtraction algorithm, Because the outut of this filter is nearer to noise rather than first estimation of noise. On the other hand (also), for solving roblem of the changing effect of noise in the corruted seech signal rang, we calculate the estimated noise of the each frame from the nearest silence frame. To have, the most likelihood between the estimated on the actual noise, it's recommended to average the estimated Fourier transform:

9 Seech signals enhancement using LPC analysis 9 m 1 N ( ω ; = N ( ω ; (34) m ω = 1 a s( n; = IFFT{{ FFT[ IFFT{ X ( ω ; } a 1 a (35) γ IFFT{ N ( ω ; } ] }ex{ iϕ }} s( ω ; m k j ) VI. Exerimental Result In this art, want to comare the roose methods with the revious ones. For this reason, first in chart 1 the PSS, GSS and LPSS methods have been comared with each other for SNR= 0, 5, 10 db (noise of the white Gaussian noise tye) to show the ability of the roose noise estimation method for imroving the SNR of the seech signals, in all the SNR rang, from low to good. Chart1, show the ower of the LPSS method in noise reduction. As mentioned earlier in the revious methods, usually the first frame is used as the silence art; the weakness of this method becomes obvious when the first frame is not silence. Chart comares the LPSS method with PSS and GSS methods for seech signals from the TIMIT database and shows the riority of roosed noise estimation method for these kinds of signals. Chart1. Comarison of the PSS, IFSS and LPIFSS with SNR 0, 5, 10 db ( noise is WGN tye)

10 10 Mostafa Hydari, Mohammad Reza Karami and Ehsan Nader Nejad Chart, comare LPSS method with IFSS methods when the first frame is not silent Next, we have alied, PSS, IFSS and LPIFSS on (to) 50 corruted seech signal (noise of the WGN tye) from the TIMIT database with the initial SNR of 10 db and the average outut SNRs have been showed in chart (3). As can be seen, alying the roosed noise estimation method on each of the methods, results in an enhanced SNR of outut. For a deeer study on the roosed methods and comaring them with the revious ones, the clean and corruted seech signals with SNR = 10 db in cooeration with their imroved signals using the GSS, IFSS, LPSS and LPIFSS methods have been shown in fig (8) and their sectrum have been lotted in fig (9). Chart3. comare of the outut SNR in roosed and existing methods with the initial SNR of 10 db

11 Seech signals enhancement using LPC analysis 11 Fig8. enhancement results for seech corruted by WGN a) Clean seech signal b) Noisy Seech ( SNR=10) c) enhancement seech by PSS (SNR=1.68) d) enhance seech by IFFS ( SNR=13.7db) e) enhanced seech by LPIFSS (SNR = 14.6 )

12 1 Mostafa Hydari, Mohammad Reza Karami and Ehsan Nader Nejad Fig9. Sectrogram for seech corruted by WGN a) Clean Seech signal b) Noisy Seech (SNR=10) c) Enhanced seech by PSS (SNR=1.68) d) enhance seech by IFSS (SNR 13.7) e) enhanced seech by LPIFSS (SNR =14.6) VII. Mean Oinion Score (MOS) Auditory Test U to now (has been), the SNR of the enhanced seech signal used for the comarison between the roosed methods and the revious ones. Now we wanted to comare them qualitatively and thus we use the auditory test [14]. We have alied 10 seech signals from the TIMITS database with the initial SNR of 10 db, on the conventional and roosed algorithm, suosing that the noise is of WGN tye, and have asked 6 eole (3 women and 3 men in a wide age rang ) To score the enhanced signals. The results are shown in table 1 [14]. The average of their scores for these 10 seech signals (60 tries for each initial) SNR as shown in chart 4.

13 Seech signals enhancement using LPC analysis 13 Table1. MOS Auditory Test, Five-oint scales for quality and imairment, and associated scores [16] Score Imairment 5(Excellent) Imercetible 4 (Good) (Just) Percetible but not annoying 3 (Fair) Percetible and slightly annoying (Poor) Annoying but not objectionable 1 (Bad) Very annoying (Objectionable) Chart 4. comare roosed and existing methods by MOS test VIII. Conclusions In this aer, we roosed a new method for seech signal enhancement based on inverse Fourier transform sectral subtraction. By studying these seech imroving methods, we have shown their weakness in the accurate estimation of noise. For solving this roblem, the idea of using the LPC analysis for noise estimation was roosed. By studying these methods, we understood that in all the methods, there's a need for noise estimation or some of its arameters. As a result, we tried to find a method which is able to give a better and more accurate estimation of noise. In the LPC analysis, we are looking for a filter and a model for the larynx that has all the larynx characteristics and by alying noise to it's inut, we get seech signal at it outut. So, if we aly the seech signal to the inverse model (filter), we must get noise signal at its outut. Since, the un correlate art of the noise seech signal aears at the filter outut that because of the filter linearity, most of it is noise. We have alied this noise in the seech signal enhancement and used it to imrove the method above. Next, we tried to imrove this estimated noise and we have used VAD and V/UV detector algorithms. After imroving the revious methods, we resented a method for seech signals that doesn't need and estimation of noise or it's arameters.

14 14 Mostafa Hydari, Mohammad Reza Karami and Ehsan Nader Nejad By comaring the roosed and the exiting methods, we have seen that the roosed methods imroved the SNR of the enhanced signals as well as showing a better resonse in the MOS test. References [1] J. R. Deller, J. H. L. Hansen, J.G. roakis, Discrete-time rocessing of seech signals. nd edition, IEEE ress, 000. [] L. R. Rabiner, R. W. Schafer. Digital rocessing of seech signals. Prentice Hall, [3] J. Tierney A study of LPC analysis of seech in additive noise, IEEE trans. Acoust. Seech and signal rocess, ASSP-8,4, : (Aug.1980). [4] M.r. Sambur, N.s. Jayant LPC analysis/synthesis from seech inuts containing guantizing noise or additive white noise, IEEE Trans. Acoust. Seech and signal rocess. ASSP-4, 6, : (Dec.1976). [5] S. Kamath P. Loizou, A Multi-band sectral subtraction method for Enhancing seech corruted by colored noise, roceedings of ICASSP-00, Orlando, FL, May 00. [6] M. Berouti, R. Schwartz, J. Makhoul, Enhancement of seech corruted by acoustic noise, roc. IEEE ICASSP, Washington DC, Aril 1979, [7] Y. Ghanbari, M. R. Karami, B. Amelifard, Imroved multi-band sectral subtraction method for seech enhancement, Proceedings of the 6 th ISTED International conference SIGNAL AND IMAGE PROCESSING, :5-30, Agust 3-5, 004, Honolulu, Hawaii, USA. [8] S. F. Boll, Suression of acoustic noise in seech using sectral subtraction, IEEE Trans. On Acoust. Seech & signal rocessing, vol. ASSP-7, Aril 1979, : [9] P. S. Whitehead, D.V. Andeson, M. A. Clements, Adative acoustic noise suression for seech enhancement, IEEE International Conference on Multimedia & Exo., July 003. [10] D. L. Donoho, De-noising by soft-thresholding, IEEE Transactions on Information Theory, vol. 41, No. 3, May 1995, : [11] K. Y. Lee, B. G. Lee, S. Ann, Adative filtering for seech enhancement in colored noise, IEEE Trans. On Signal Processing Letters, Vol. 4, October 1997, : [1] Ing Yann Soon, Soo Ngee Koh, Chai Liat Yeo, Wavelet for Seech Denoising, TENCON 97, Brisbane, Australia, 1997, : [13] H.Sheikhzadeh, H. R. Abutalebi, An Imroved Wavelet-Based Seech Enhancement System, in roc. 7 th Euroean Conference on Seech Communication and Technology (EuroSeech), Aalborg, Denmark, Se. 001.

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