SPEECH ENHANCEMENT BASED ON ITERATIVE WIENER FILTER USING COMPLEX SPEECH ANALYSIS

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1 SPEECH ENHANCEMENT BASED ON TERATVE WENER FLTER USNG COMPLEX SPEECH ANALYSS Keiichi Funaki Computing & Networking Center, Univ. o the Ryukyus Senbaru, Nishihara, Okinawa, 93-3, Japan phone: +(8) , ax: +(8) , unaki@cc.u-ryukyu.ac.jp ABSTRACT Recently, applications o speech coding and speech recognition have been exploding; or example, cellular phones and car navigation systems in an automobile. Since these are commonly used in noisy environment, noise reduction method, viz., speech enhancement is required as a pre-processor or speech coding and recognition. terative Wiener ilter (WF) method has been adopted as the speech enhancement that estimates speech and noise power spectra using analysis iteratively. n this paper, we propose an improved method or Wiener ilter algorithm by introducing the complex speech analysis instead o the conventional analysis. The complex speech analysis can estimate more accurate spectrum in low requencies, thus it is expected that it can perorm better or the WF especially or babble noise or car internal noise that contains much energy in low requencies. The objective evaluation has been perormed or speech signal corrupted by white Gaussian, pink noise, babble noise or car internal noise by means o spectral distance. The results demonstrate that the proposed method can perorm better or babble or car internal noise than the conventional real-valued method.. NTRODUCTON n these days, the speech enhancement plays an important roll to improve the perormance o the speech coding and speech recognition as cellular phone or the car navigation system are being widely used more and more. These systems are oten used in noisy environment. Thereore, the quality o speech coding or the perormance o speech recognition is deteriorated due to the surrounding noise. n order to avoid the deterioration, technology that removes noise rom the noisy speech viz., speech enhancement is strongly desired. Especially, speech enhancement is an important actor or speech coding to keep the quality even under noisy environment. 3GPP (The 3rd Generation Partnership Project) thus provides the minimum perormance requirement and the evaluation procedure or AMR-NB[]. Several speech enhancement methods such as [] have already satisied the requirement. Moreover, speech enhancement is being sincerely demanded or wide band speech coding such as [3] since the additive noise in wide band speech can be percepted. Traditional approaches or speech enhancement have been proposed rom the end o 97 s to 98 s [4],[5],[6]. Spectrum subtraction (SS) method [4] is widely adopted since it can be implemented easily and it can realize some degree o eect. However, the SS generates unpleasant artiicial sound called musical noise so that it is not suitable or speech coding. Wiener ilter method has been proposed by J.S.Lim[6], and the method designs the optimal ilter minimizing the mean squared error (MSE) in the requency domain. The musical noise is reduced by the Wiener ilter method than the SS method. accurate power spectrum or clean speech and accurate power spectrum o additive noise can be estimated, the Wiener ilter can be designed accurately. However, the power spectrum o clean speech cannot be observed directly. Thereore, the iterative Wiener ilter (WF) method is adopted to estimate the power spectrum more accurately. First, the power spectrum or noise is estimated in silent segment o speech and the speech power spectrum is estimated by analysis or noisy speech. Next, the Wiener ilter is designed by using the estimated spectra and speech enhancement is carried out by iltering the noisy speech with the Wiener ilter to obtain the enhanced speech. Next, analysis is operated or the enhanced speech and the Wiener ilter is designed again and the ilter is operated or the noisy speech to obtain enhanced speech. These procedures are repeated to obtain more accurate speech power spectrum and to design more optimal Wiener ilter. However, it is known that the spectrum o the enhanced speech is distorted ater several iterations and the optimal number o iteration cannot be determined[7],[8]. On the other hand, the complex speech analysis methods have already been proposed or an analytic signal [9],[],[]. An analytic signal is a complex signal having an observed signal in real part and a Hilbert transormed signal or the observed signal in imaginary part. Since the analytic signal provides the spectrum only on positive requencies, the signals can be decimated by a actor o with no degradation. As a result, the complex speech analysis oers attractive eatures, or example, more accurate spectral estimation in low requencies. The remarkable eature is easible to design more appropriate Wiener ilter in the WF and it may lead to higher perormance o speech enhancement especially or the additive noise whose energy is concentrated in low requencies, or example, babble noise or car internal noise. n this paper, we propose an improved WF method by adopting the MMSE based time-varying complex AR (TV- CAR) speech analysis[] instead o analysis. The TV- CAR speech analysis introduces the TV-CAR speech model, in which the AR model parameters are represented by complex basis expansion. The reminder o this paper is organized as ollows. We will explain the TV-CAR speech analysis in Section and will explain the iterative Wiener ilter method and the proposed algorithm in Section 3. The beneit o complex speech analysis will be explained in Section 4. We will explain the experiments evaluating the perormance or additive white Gaussian, pink, babble, or car internal noise in Section 5.

2 . TV-CAR SPEECH ANALYSS. Analytic speech signal Target signal o the time-varying complex AR (TV-CAR) method is an analytic signal that is complex-valued signal deined by y c (t)= y(t)+ j y H(t) () where y c (t), y(t), and y H (t) denote an analytic signal at time t, an observed signal at time t, and a Hilbert transormed signal or the observed signal, respectively. Since analytic signals provide the spectra only over the range o (,π), analytic signals can be decimated by a actor o two. The term o / is multiplied in order to adjust the power o an analytic signal with that o the observed one. Note that superscript c denotes complex value in this paper.. Time-Varying Complex AR (TV-CAR) model Conventional model is deined as Y (z )= + i= a i z i () where a i and are i-th order coeicient and order, respectively. Since the conventional model cannot express the time-varying spectrum, analysis cannot extract the time-varying spectral eatures rom speech signal. n order to represent the time-varying eatures, the TV-CAR model employs a complex basis expansion shown as a c L i (t)= g c i,l l c (t) (3) l= where a c i (t),,l,gc i,l and l c (t) are taken to be i-th complex AR coeicient at time t, AR order, inite order o complex basis expansion, complex parameter, and a complex-valued basis unction, respectively. By substituting Eq.(3) into Eq.(), one can obtain the ollowing transer unction. Y TVCAR (z ) = = + + i= a c i (t)z i L i= l= The input-output relation is deined as y c (t) = = i= a c i (t)y c (t i)+u c (t) L i= l= g c i,l c l (t)z i (4) g c i,l c l (t)yc (t i)+u c (t) (5) where u c (t) and y c (t) are taken to be complex-valued input and analytic speech signal, respectively. n the TV-CAR model, the complex AR coeicient is modeled by a inite number o arbitrary complex basis. Note that Eq.(3) parameterizes the AR coeicient trajectories that continuously change as a unction o time so that the time-varying analysis is easible to estimate continuous time-varying speech spectrum. n addition, as mentioned above, the complexvalued analysis acilitates accurate spectral estimation in the low requencies, as a result, the TV-CAR analysis allows or more accurate spectral estimation in low requencies and since more optimal Wiener ilter can be designed, it assigns better perormance on speech enhancement. Eq.(5) can be represented by vector-matrix notation as ȳ = Φ θ + ū θ T = [ḡ T,ḡT,,ḡT l,,ḡt L ] ḡ T l = [g c,l,gc,l,,gc i,l,,gc,l ] ȳ T = [y c (),y c ( + ),y c ( + ),,y c (N )] ū T = [u c (),u c ( + ),u c ( + ),,u c (N )] Φ = [ D, D,, D l,, D L ] D l = [ d,l,, d i,l,, d,l ] d i,l = [y c ( i) l c ( + i) l c ( + ),,y c (N i) c l (N )]T (6) where N is analysis interval, ȳ is (N,) column vector whose elements are analytic speech signal, θ is (L,) column vector whose elements are complex parameters, Φ is (N,L ) matrix whose elements are weighted analytic speech signal by the complex basis. Superscript T denotes transposition..3 MMSE-based algorithm[] MSE criterion is deined as r = [r c (),r c ( + ),,r c (N )] T = ȳ + Φ ˆθ (7) r c (t) = y c (t)+ L i= l= ĝ c i,l c l (t)yc (t i) (8) E = r H r =(ȳ + Φ ˆθ) H (ȳ + Φ ˆθ) (9) where ĝ c i,l is the estimated complex parameter, r c (t) is an equation error, or complex AR residual and E is Mean Squared Error (MSE) or the equation error. To obtain optimal complex AR coeicients, we minimize the MSE criterion. Minimizing the MSE criterion o Eq.(9) with respect to the complex parameter leads to the ollowing MMSE algorithm. ( Φ H Φ ) ˆθ = Φ H ȳ () Superscript H denotes Hermitian transposition. Ater solving the linear equation o Eq.(), we can get the complex AR parameter at time t (a c (t)) by calculating the Eq.(3) with the estimated complex parameter ĝ c i,l.

3 3. WENER FLTER ALGORTHM 3. Wiener ilter Assuming that the clean speech s(t) degraded by an additive noise w(t), the noisy speech x(t) is deined by x(t)=s(t)+w(t). () Wiener ilter is an optimal ilter that minimizes the Mean Squared Error (MSE) criterion. n the case o Eq.(), the ilter can be deined by S(ω)=H(ω)X(ω) () where ω is the requency index, S(ω), X(ω), and H(ω) are the discrete Fourier transorm o the clean speech, the transorm o noisy speech and transer unction o Wiener ilter, respectively. The MSE can be deined as ollows. The Wiener ilter can be derived by H(ω)= P ss (ω) P ss (ω)+p ww (ω) (3) where P ss (ω) and P ww (ω) are power spectrum o speech, s(t) and that or noise, w(t), respectively. From Eq.() and (3), the enhanced speech is estimated in the requency domain by S(ω) = P ss (ω) X(ω) (4) P ss (ω)+p ww (ω) The enhanced speech can be obtained by inverse FFT or S(ω) and OLA (OverLap Add) procedure is carried out in the time domain between adjacent rames to avoid click sound. 3. terative Wiener Filter (WF) algorithm[6][8] The perormance o the Wiener ilter depends on the accuracy o speech power spectral estimation, P ss (ω). t is possible to make the estimated spectrum close to the true one by repeating the Wiener ilter processing. Figure shows the block diagram o the iterative Wiener ilter algorithm. The two kinds o power spectra can be estimated by analysis as ollows. Noise power spectrum, P ww (ω) are estimated in the irst non-speech section. Speech power spectrum, P ss (ω) is estimated by analysis or input noisy speech, x(n). By the Wiener iltering and nverse FFT operation, enhanced speech is estimated and then it is analyzed in order to estimate more accurate speech power spectrum, P ss (ω) by means o analysis and the Wiener ilter is operated again. The iterative procedure is repeated to obtain more clean speech. 3.3 Proposed Method The proposed method employs the estimated two spectra, P ss (ω) and P ww (ω) estimated by the TV-CAR speech analysis[] instead o analysis. The two spectra can be estimated as P ss (ω) = P ww (ω) = + + L i= l= L i= l= G s ĝ s c i,l c l (t)e jiω (5) G w ĝ w c i,l c l (t)e jiω. (6) ĝ c s i,l is estimated by Eq.() rom analytic speech or the enhanced speech at previous iteration (input speech at irst iteration) and G s is energy o the corresponding residual. ĝ c w i,l is estimated by Eq.() rom analytic speech or the input speech and G w is energy o the corresponding residual. Note that these two power spectra provide only one side o spectrum, thus, mirroring is operated to apply to Eq.(3). As mentioned above, complex speech analysis can estimate more accurate speech spectrum in low requencies. t is expected that the eature leads to higher perormance o the WF algorithm. n this paper, time-invariant complex speech analysis (L = ), is equivalent to complex analysis, is adopted. Figure : Block diagram o the WF algorithm 4. BENEFT OF COMPLEX SPEECH ANALYSS Figure shows example o the estimated speech spectra by complex speech analysis or analytic signal[] and conventional analysis or speech signal. Figure : Estimated Spectra with complex and conventional analysis n Figure, let side denote the estimated spectra. Upper is or real-valued analysis. Lower is or complexvalued analysis. Blue line means estimated spectrum by analysis and green line means estimated DFT spectrum. Right side means estimated poles rom the estimated AR ilter. One can observe that the complex analysis can estimate more accurate spectrum in low requencies whereas the estimation accuracy is down in high requencies. Since speech

4 spectrum provides much energy in low requencies, it is expected that the high spectral estimation accuracy in low requencies makes it possible to improve the perormance on the WF. 5. EXPERMENTS We have already carried out the experiments to compare the perormance o the proposed method (TV-CAR) or analytic speech with that or the conventional one ( method) or observed speech by means o objective evaluation o Cepstral distance (). Since the WF is based on iltering in the requency domain, spectral distance such as cepstral distance is appropriate measure or objective evaluation. Table shows the experimental conditions. Sampling rates were 6KHz or 8KHz. Additive noises were white Gauss noise, pink noise, babble noise or car internal noise[]. Noise levels were -5,, 5, or [db]. n the TV-CAR speech analysis, L is set to be one, thus the TV- CAR speech analysis is equivalent to non-time varying, complex analysis. Figures 3 and 4 show the experimental results. Figure 3 means the results or 8KHz o speech. Figure 4 means the results or 6KHz o speech. n these igures, (),(),(3) and (4) means s or additive white Gauss noise, those or additive pink noise, those or or additive babble noise, and those or additive car internal noise, respectively. n these igures, X-axis means noise level (,, 5,, -5 [db]) and Y-axis means. denotes the s by means o the conventional method with analysis. denotes the s by means o the proposed method with complex analysis. The results demonstrate that the proposed method can perorm better than the conventional one or additive pink, babble or car internal noise whereas the proposed method does not perorm better or additive white Gauss noise. The reason why the proposed method can perorm better or additive pink, babble or car internal noise is as ollows. The complex speech analysis can estimate more accurate speech spectrum in low requencies or these noises whose energy is concentrated in low requencies. Table Experimental Conditions Speech data Male sentences Female sentences ATR database set B Sampling 8KHz/6bit 6KHz/6bit Window Length m Shit Length ms FFT 4 samples analysis =4, L=(time-invariant) Pre-emphasis None Complex analysis =7, L=(time-invariant) Pre-emphasis None Noise () White Gauss noise () Pink noise[] (3) Babble noise[] (4) Car internal noise[] Noise Level,,5,,-5[dB] Cepstral Distance () Cepstral Distance Window Length [msec] Shit Length [msec] order 6/3 or 8/6KHz Cepstral order 6/3 or 8/6KHz 6. CONCLUSONS n this paper, we have proposed the improved iterative Wiener ilter (WF) algorithm based on the TV-CAR speech analysis in a single channel system. The perormance has already been evaluated by means o cepstral distance () not only or 8KHz but also or 6KHz sampled speech signal corrupted by additive white Gauss, pink, babble or car internal noise. According to an inormal listening test and objective evaluation o, the proposed method outperorms conventional WF or additive pink, babble or car internal noise that contains much energy in low requencies. Future study is as ollows.. mprove the noise estimation. ntroduce robust TV-CAR speech analysis based on ELS method[3] 3. ntroduce the time-varying speech analysis (L = ). REFERENCES [] Minimum Perormance Requirements or Noise Suppressor Application to the AMR Speech Encoder, 3GPP TS 6.77 V8..,Apr.. [] M.Kato,et.al., Noise Suppression with High Speech Quality Based on Weighted Noise Estimation and MMSE STSA, ECE Trans. Vol.E85-A. No.7, July. [3] TU-T Recommendation G.7., Wideband coding o speech at around 6 kbit/s using Adaptive Multi-Rate Wideband (AMR-WB), Jul.,3. [4] S.F.Boll, Suppression o acoustic noise in speech using spectral subtraction, EEE Trans., ASSP-7, pp.3-,979. [5] Y.Ephraim and D.Malah, Speech enhancement using minimum mean-square error log-spectral amplitude estimator, EEE Trans., ASSP-33, pp , 985. [6] J.S.Lim and A.V.Oppenheim, All-pole modeling o degraded speech, EEE Trans., ASSP-6, pp.97-, 978. [7] H.L.Hansen and M.A.Clements, Constrained iterative speech enhancement with application to speech recognition, EEE Trans. Signal Processing, vol.39, pp , April 99. [8] P.C.Loizou, Speech Enhancement, Theory and Practice, CRC Press, 7. [9] S.M.Kay, Maximum entropy spectral estimation using the analytic signal, EEE Trans. ASSP-6, pp , 98. [] T.Shimamura and S.Takahashi, Complex linear prediction method based on positive requency domain, ECE Trans., Vol.J7-A, pp , 989. (in Japanese) [] K.Funaki, et.al., On a time-varying complex speech analysis, Proc. EUSPCO-98, Rhodes, Greece, Sep [] NOSE-X9, noise.html [3] K.Funaki, A time-varying complex AR speech analysis based on GLS and ELS method, Proc. EUROSPEECH-, Alborg, Denmark, Sep..

5 () s or additive white Gauss noise (8KHz) () s or additive white Gauss noise (6KHz) () s or additive Pink noise (8KHz) () s or additive Pink noise (6KHz) (3) s or additive Babble noise (8KHz) (3) s or additive Babble noise (6KHz) (4) s or additive Car nternal noise (8KHz) Figure 3: s or 8KHz speech 5 5 (4) s or additive Car nternal noise (6KHz) Figure 4: s or 6KHz speech