A Robust Noise Spectral Estimation Algorithm for Speech Enhancement in Voice Devices

Transcription

1 Louisiana State University LSU Digital Coons LSU Master's Theses Graduate School 005 A Robust oise Spectral Estiation Algorith for Speech Enhanceent in Voice Devices Brett Joseph Chessher Louisiana State University and Agricultural and Mechanical College bchess@lsu.edu Follow this and additional wors at: Part of the Electrical and Coputer Engineering Coons Recoended Citation Chessher Brett Joseph "A Robust oise Spectral Estiation Algorith for Speech Enhanceent in Voice Devices" (005. LSU Master's Theses This Thesis is brought to you for free and open access by the Graduate School at LSU Digital Coons. It has been accepted for inclusion in LSU Master's Theses by an authorized graduate school editor of LSU Digital Coons. For ore inforation please contact gradetd@lsu.edu.

2 A ROBUST OISE SPECTRAL ESTIMATIO ALGORITHM FOR SPEECH EHACEMET I VOICE DEVICES A Thesis Subitted to the Graduate Faculty of the Louisiana State University and Agricultural and Mechanical College In partial fulfillent of the Requireents for the degree of Master of Science in Electrical Engineering in The Departent of Electrical and Coputer Engineering by Brett Joseph Chessher B.S. University of Southern Mississippi 00 Deceber 005

3 ACKOWLEDGMETS There are any people besides yself that are greatly responsible for the copletion of this thesis. I would lie to give thans to y special friends Allie Kristin Jaie John Kristy Jennifer and Estephen for their copanionship support and patience throughout the past nine onths of this research. Secondly I would lie to give a special thans to Dr. Hsiao-Chun Wu Daren Launey Waheeduddin Syed and Saeer Herlear for their guidance support and otivation. It has been ore than a pleasure to wor along the side of all of the during y years as a graduate student for the Electrical and Coputer Engineering departent. It is easy to depart fro reality and becoe iodest later in life with titles and achieveents. However it is the foundation that aes a person. I would lie to than both Forrest and ancy Chessher who is y father and other respectively for their guidance and nurture throughout y life. I also than y elder and twin brother Pete and Mie for their life copanionship. My dedication and hard wor is a direct influence fro y upbringing. God has truly blessed e with a great childhood and faily life. I than all the faculty ebers of the College of Science and Technology at the University of Southern Mississippi for providing e with a strong acadeic foundation especially Prof. Randy Buchanan Prof. Cecil Harrison Prof. Johnsey Mr. Todd Adas Mr. Dan Kohn and Prof. Joseph Kolibal. I would also lie to than y lifelong friends I have ade during y undergraduate years in the state of Mississippi including Greg McLelland Michael Watson Gabe Radau Dan Garcia David Dawins Todd Fisher Matt Reed and the rest of the 3-- Crew. ii

4 Last but not least a very special thans goes to y aunt Brenda (anny Uncle Paul ancy Jaes and Caeron for the good ties during y years living in Baton Rouge. My uncle is no longer with us on Earth and therefore this thesis and the nine long onths of research is dedicated to Paul Cleve Bourque (Uncle Paul. It was his thoughts that always ept y otivation strong. iii

5 TABLE OF COTETS ACKOWLEDGMETS...ii LIST OF TABLES...vi LIST OF FIGURES...vii ABSTRACT...ix CHAPTER. FUDAMETAL SPEECH AALYSIS.... Motivation.... Short-Tie Fourier Transfor....3 Windowing Effect....4 Haing Window Short-Tie Fourier Analysis of a Speech Signal with Haing Windowing...7 CHAPTER. ITRODUCTIO OF OISE SPECTRAL SUPPRESSIO...9. Fundaentals of oise Suppression Methods...9. oise Spectral Subtraction Bayesian Methods for oise Suppression...9 CHAPTER 3. EISTIG OISE SPECTRAL ESTIMATIO METHODS FOR BAYESIA OISE SUPPRESSIO Introduction The Ipact of the A Priori Signal-to-oise Ratio Voice Activity Detection for oise Frae Labeling Conventional oise Spectral Estiation Methods Coparative Studies of Conventional oise Spectral Estiation Methods...8 CHAPTER 4. OVEL ROBUST OISE SPECTRAL ESTIMATIO Introduction Forulation of Robust oise Spectral Estiator Optial Adaptive Recursion Coefficients Flowchart...37 CHAPTER 5. SIMULATIO AD RESULTS Siulation Procedures and Measures Siulation Results...4 CHAPTER 6. COCLUSIO...48 REFERECES...49 iv

6 APPEDI: DERIVATIO OF THE OPTIMAL ADAPTIVE RECURSIO COEFFICIETS...5 VITA...53 v

7 LIST OF TABLES Table 5. R-SR of the Speech fro Male Speaer...4 Table 5. R-SR of the Speech fro Feale Speaer...43 Table 5.3 R-SR of the Speech fro Male Speaer...44 Table 5.4 R-SR of the Speech fro Feale Speaer...45 Table 5.5 R-SR of the Speech fro Feale Speaer vi

8 LIST OF FIGURES Figure. Magnitude Spectru of a 60Hz Sine Wave Using a Rectangular Window...3 Figure. Magnitude Spectru of a 6.5Hz Sine Wave Using a Rectangular Window...4 Figure. 3 A Haing Window Consisting of 400 Saples...5 Figure. 4 Frequency Analysis of a 6.5Hz Sine Wave Using a Haing Window...5 Figure. 5 Coparison of the Spectral Energy between the Rectangular Window and Haing Window...6 Figure.6 Magnitude Spectru of a Clean Speech Signal Using the Short-Tie Fourier Analysis...8 Figure. Speech Enhanceent Using a oise Suppression Filter...0 Figure. oise Suppression Filter Gain Curves of a Magnitude Spectral Subtraction Filter...6 Figure. 3 oise Suppression Filter Gain Curves of a Power Spectral Subtraction Filter...7 Figure. 4 The Short-tie Spectral Magnitude of an Enhanced Speech Using the Magnitude Spectral Subtraction...8 Figure. 5 Musical oise Resulting fro the Magnitude Spectral Subtraction...8 Figure 3. A Priori SR Estiate Versus ISR Estiate in a Coparative Study...5 Figure 3. Enhanced Speech and Estiated oise Spectra Using the Moving φ = Average and the Single-Pole Recursion ( Figure 3. 3 Enhanced Speech and Estiated oise Spectra Using the Moving φ = Average and the Single-Pole Recursion ( Figure 3. 4 Enhanced Speech and Estiated oise Spectra Using the Moving φ = Average and the Single-Pole Recursion ( vii

9 Figure 3. 5 Enhanced Speech and Estiated oise Spectra Using the Moving Average and the Single-Pole Recursion in the Presence of Jet oise φ = ( Figure 4. Flowchart of the Proposed Robust oise Spectral Estiation Algorith...38 viii

10 ABSTRACT In this thesis a new robust noise spectral estiation algorith is proposed for the purpose of single-icrophone speech enhanceent. This algorith can generate the optial noise spectral estiates in the Miniu Mean Square Error (MMSE sense based on the speech statistics in the noisy environents. Copared to the well-adopted conventional noise spectral estiation ethod using the single-pole recursion our proposed schee is ore reliable since the recursion coefficients are adaptable and optial in the MMSE therein. We also propose a new accurate Resulting Signal-to-oise Ratio (R-SR estiator as a quality easure to benchar the existing noise spectral estiation techniques. This new R-SR estiator can be applied to quantify not only the residual noise but also the speech distortion and therefore it can well serve as the overall speech quality easure after the noise suppression. We conduct the experients to evaluate the perforance of the noise suppression using our robust noise spectral estiation algorith and copare it with those of two ajor existing noise spectral estiation ethods. Through nuerous siulations we have shown that our noise suppression technique significantly outperfors the conventional ethods in both stationary and nonstationary noise environents. ix

11 CHAPTER. FUDAMETAL SPEECH AALYSIS. Motivation Speech processing has drawn a lot of research interest for ore than half a century. owadays the inforation technology has occupied a significant portion of daily life and hence the voice activated devices are in high deand. However the speech signals are sensitive to the bacground noise which would severely degrade the speech quality and the corresponding intelligibility. Therefore the robust speech enhanceent techniques either using the icrophone arrays or the single icrophone are always desirable. In this thesis we investigate a new robust noise spectral estiation algorith and its application for the speech enhanceent based on a single icrophone.. Short-Tie Fourier Transfor Speech recognition and speech enhanceent are the two ajor speech technological deands. evertheless the speech analysis is siilar for both speech applications. Typically speech signals are observed in the short-tie intervals where the signals are segented into very short slots and each slot or frae is to be processed independently. Usually a window function is used to define the frae length. The Short-Tie Fourier Transfor (STFT is the well-adopted speech analysis tool which is defined by Equation. []. In Equation. i( represents the last saple of the frae. The window πn ( h( n x( i( n exp j = 0... = = n 0 (. where h(n 0 = 0 0 n otherwise

12 x(n Speech signal in the tie doain ( The th discrete frequency coponent (bin of speech in the th frae i( Tie index corresponding to the th frae Window size size typically ranges between3 and 56 for speech signals sapled at 8Hz []. This is equivalent to the tie interval ranging between 4 and 3 sec..3 Windowing Effect The window function is used not only to partition a speech signal or tie series into short-tie fraes but also to preserve the spectral inforation. Spectral inforation fro one frequency ban ay lea into the adjacent frequency bans after the analog-todigital conversion and the Digital Fourier Transfor (DFT are perfored []. This is often referred to as the Fast Fourier Transfor (FFT leaage []. A typical exaple of FFT leaage can be found in the sinusoidal signal spectral analysis. A sinusoid is everlast in tie but only a hundred or thousand saples can be collected via a digital coputer. The sapled wavefor can be deeed as the rectangular-windowed sinusoidal sequence (h(n = for 0 n - and h(n = 0 for n< 0 U n > in Equation.. and this is equivalent to the convolution between the frequency response of the sinusoid and the corresponding Sinc function in the frequency doain. Thus the spectru of the windowed sinusoid which is an ipulse in the frequency doain convolved with the sinc function ay lead to the FFT leaage in the adjacent frequency bans. Figure. shows the agnitude spectru of a 60Hz sine wave sapled at a frequency of 8Hz using a rectangular window of 400 saples. The dotted points along A frequency ban is the analog frequency apped to a discrete frequency bin in the digital Fourier transfor.

13 Spectral Magnitude Figure Frequency in Hertz Magnitude Spectru of a 60Hz Sine Wave Using a Rectangular Window the dashed line for a Dirac-delta lie ipulse sequence in the frequency doain. where the FFT leaage is insignificant in this case. As depicted in Figure. if the sine wave possesses the frequency of 6.5Hz and is sapled at 8Hz using the sae rectangular window the FFT leaage becoes obvious where the significant spectral side lobes are leaed into the frequency bans close to 6.5Hz..4 Haing Window The aforeentioned FFT leaage can be greatly itigated using other window functions. A widely used window function for speech processing is the Haing window which is shown in Figure.3. The agnitude spectru for the 6.5Hz sine wave 3

14 Spectral Magnitude Figure Frequency in Hertz Magnitude Spectru of a 6.5Hz Sine Wave Using a Rectangular Window is depicted in Figure.4 using the Haing window of 400 saples. This spectru still shows soe FFT leaage which appears in the three nearest frequency bins. It is also noted that the spectral agnitude in the ain lobe is lower than that in Figure.. This phenoenon can be explained by investigating the frequency response of both rectangular and Haing windows as shown in Figure.5. According to Figure.5 the rectangular window consists of ore DC spectral energy (at very low frequency as a atter of fact that the rectangular window function is constant. It is obvious that the transition bandwidth (the difference between the null-to-null bandwidth and the 3dB bandwidth of the Haing window spectru is rather larger than that of the rectangular 4

15 0.8 Aplitude Figure Saple Index A Haing Window Consisting of 400 Saples Spectral Magnitude Figure Frequency in Hertz Frequency Analysis of a 6.5Hz Sine Wave Using a Haing Window 5

16 80 60 Rectangular Haing Spectral Energy (db Figure Saple Index Coparison of the Spectral Energy between the Rectangular Window and Haing Window window spectru. Hence the spectral bandwidth of the windowed sine wave in Figure. is less than that in Figure.4. However Figure. consists of larger ripples due to the FFT leaage since the rectangular window spectru has the larger side lobes as shown in Figure.5. Consequently Haing window is superior to the rectangular window for ost speech applications. The Haing window is defined in Equation. [3]. h ( n πn cos 0 n =. (. 0 otherwise 6

17 .5 Short-Tie Fourier Analysis of a Speech Signal with Haing Windowing Usually the window function is advanced to generate the successive speech fraes with the 50% overlap of frae length fro one to next. The purpose of this overlapping technique is to provide soother statistical transitions. However this overlapping operation has to be taen into consideration when the signal reconstruction is carried out where the overlap-and-add ethod is to be used to reconstruct the signal. For the speech analysis the STFT using the Haing window and the overlapping technique is applied to create a agnitude spectru with respect to both tie and frequency. As an illustration a signal consisting of an 8sec clean speech phrase One three five six speech. was produced by a ale speaer. The signal was sapled at 8Hz. The STFT is undertaen with frae length 56 and 50% overlapping. Thus each frae consists of a 3sec segent of the speech phrase. The resulting STFT agnitude spectru is shown in Figure.6. 7

18 5 Magnitude Frequency in Hertz 0 0 Tie in seconds Figure.6 Magnitude Spectru of a Clean Speech Signal Using the Short-Tie Fourier Analysis 8

19 CHAPTER. ITRODUCTIO OF OISE SPECTRAL SUPPRESSIO. Fundaentals of oise Suppression Methods The ain single-icrophone speech enhanceent approach naely noise suppression relies on the robust noise spectral estiation. In this chapter we discuss the fundaentals of the existing noise suppression ethods. The suppression of noise for speech enhanceent has been a challenging research topic for decades. During these years nuerous noise suppression ethods have been developed according to the welladopted additive noise odel which is shown in Equation.. The noise suppression x = s + n (. where x oisy speech signal s Clean speech signal n oise signal ethods derived fro this additive noise odel can be classified into two different categories naely spectral subtraction ethods and the Bayesian ethods. Spectral subtraction ethods are easily ipleented by taing advantage of the additive noise odel where the noise estiates are siply subtracted fro the raw data. Bayesian ethods are derived by iniizing a distortion easure based on an underlying noise statistical odel. Epirically the Bayesian noise suppression ethods outperfor the noise spectral subtraction ethods. However noise spectral subtraction ethods are very coputationally efficient and robust over the nonstationary noise. For convenience it is usual to characterize a noise suppressor as a filter. Due to the difficulty of estiating the phase of clean speech the phase of the noisy speech signal is 9

20 siply assued to be identical to that of the clean speech. Heuristically this assuption leads to the proising results and is still currently adopted in practice especially for single-icrophone applications [4]. In addition it has been shown in [5] that the precise phase estiation is not iportant for speech enhanceent. The typical approach for speech enhanceent using a noise suppression filter is illustrated in Figure.. According to Figure. the speech signal x(n is the discrete-tie speech sequence; then the short-tie agnitude spectru ( exp { [ ( ]} and the short-tie phase spectru jθ both are calculated for every frae and every frequency bin. The noise suppression filter H( needs to be adapted to produce the clean speech estiates ( S for every frae and every frequency bin. Finally the enhanced speech signal ( n s in the th frae can be obtained by taing the inverse digital Fourier transfor (IDFT of the product spectru ( exp{ j [ ( ]} S θ. x(n STFT abs( ( H( Ŝ( phase exp { jθ [ ( ]} IDFT ŝ(n Figure. Speech Enhanceent Using a oise Suppression Filter. oise Spectral Subtraction.. Magnitude Spectral Subtraction Aong the early pioneers Steven F. Boll applied the additive noise odel to design a agnitude spectral subtraction algorith for speech enhanceent [6]. Boll s spectral 0

21 subtraction ethod was developed under the following two assuptions: the noise is either acoustically or digitally added to the speech signal and the noise environent is locally stationary or slowly tie-varying. According to [6] if the slowly tie-varying nonstationary noise is considered a voice activity detector (VAD ust be used to deterine the speech pauses in the signal for updating the noise estiates. We assued that the VAD is reliable and thus it is not a focus of this thesis. The initial noise estiate ( 0 is deterined by averaging the agnitude spectra over several beginning fraes collectively of the speech signal. The individual noise spectral estiates are coputed in each frae and each frequency bin according to Equation.. Modifying Equation. we can define the agnitude spectral subtraction filter ( S ( exp jθ [ ( ] ( ( ( ( H MSS as Equation.3. = (. Estiated clean speech spectral aplitude oisy speech spectral aplitude oise spectral estiate of the th discrete frequency ban where S ( ( ( [ ( ] H MSS θ Phase of noisy speech spectru ( ( = (.3 ( where S( = ( H ( MSS Occasionally ( > ( H( < 0 and hence S ( = ( H( < 0 will lead to an ipossible speech agnitude spectru. Thus Equation. has to be odified as Equation.4 to include an additional constraint. A half-wave odulation technique was proposed in [6] to avoid the aforeentioned proble which is described

22 in Equation.5. S H { 0} exp jθ [ ( ] ( ax ( ( ( = (.4 ( H ( ( + H ( H MSS MSS = HW = (.5 where ( 0 H HW... Power Spectral Subtraction Shortly after Boll s agnitude spectral subtraction ethod was introduced a power spectral subtraction ethod was launched by M. Berouti [7]. Power spectral subtraction is very siilar to agnitude spectral subtraction; the only difference is the forer spectral subtraction is perfored in the power spectru instead of the agnitude spectru [7]. The power spectral subtraction is expressed in Equation.6. The S ( = ( ( exp( jθ [ ( ] ( ( 0 othewise > 0 (.6 siilarity between agnitude and power spectral subtraction ethods is obvious according to Equations.4 and.6. Berouti claied that his agnitude spectral subtraction schee could reduce the annoying artifacts nown as usical noise in the enhanced speech signal while the original agnitude spectral subtraction ethod could not solve this proble [7]. Berouti proposed a solution to reduce usical noise by odifying the power spectral subtraction forula in Equation.6. A positive noise floor paraeter c was introduced to increase the lower liit fro zero. The significance of this noise floor paraeter will also be discussed in the next section. A coplete description of

23 3 ( ( ( [ ] ( ( ( ( ( > = otherwise c c j S ( exp θ Berouti s power spectral subtraction ethod is suarized in Equation.7. The Berouti s noise suppression filter ( H PSS is expressed in Equation.8. (.7 where c oise floor paraeter ( c Spectral noise floor ( ( ( ( ( ( > = = otherwise c c H H PSS ( ( ( ( (.8..3 Coparative Studies of Spectral Subtraction Methods Both agnitude and power spectral subtraction ethods can be expressed using the general clean speech spectral estiation forula given by Equation.9. In Equation.9 the over-subtraction paraeter β (β produces an overestiate of the noise spectral estiate. A noise floor paraeter c (usually c<< is also included in this equation which sets the lower liit of the enhanced speech [7]. The over-subtraction paraeter β ( ( ( [ ] ( ( ( ( ( > = otherwise c c j S ( exp α α α α α α α β θ β (.9

24 4 where { } = α β Over-subtraction paraeter c oise floor paraeter is usually adjusted via trial-and-error to result with superior speech quality [7]. The effect of the over-subtraction paraeter on the noise suppression filter can be shown by coparing the noise suppression filter gain curve for different values of β with respect to the actual signal-to-noise ratio (SR. To forulate the noise suppression filter gain we divide each ter in Equation.9 by ( α to for Equation.0. We then define ( ( ( ( ( ( ( ( ( ( > = otherwise c c S α α α α α α α β β (.0 the ( ( ( S SR ( ( ( ( ( ( + = + = SR S. By substituting ( ( ( + = SR into Equation.0 we obtain Equation.. The overall signal-to-noise ratio is coputed as = S SR ( ( where ( S and ( are the actual clean speech and pure noise agnitude spectra respectively. ( ( ( ( [ ] ( + > + + = otherwise SR c c SR SR S α α α α β β. (.

25 Thus a general forula analogous to Equation. can be drawn to forulate the noise suppression filter gain G ( SR. β G( SR = SR + α c SR + α α [ SR + ] α β > c otherwise (. In Figures. and.3 the noise suppression filter gain curves for different values of β are illustrated for the agnitude and power spectral subtraction ethods respectively. The noise floor paraeter c was set at 0 for Figure. and for Figure.3 to depict the gain curves. This is due to the fact that the noise floor paraeter was proposed in [7] for the power spectral subtraction. The paraeter β plays a significant role in the reduction of the residual noise which is the noise reaining in the enhanced speech signal. A larger β value is desirable if the average noise spectral energy is significantly lower than the average speech spectral energy because the filter gain will decrease at a faster rate as the SR which will lead to less residual noise during the unvoiced intervals. Siilarly a saller β value is desirable if the average noise spectral energy is close to or larger than the average speech spectral energy because the filter gain will decrease slowly as the SR which will lead to less speech attenuation within low-energy voiced durations. A fixed value of β would hinder the robustness of the noise spectral subtraction ethods in adverse noise environents. It was entioned in [7] that 3 β 5 when using the power spectral subtraction ethod. However in this thesis we use the agnitude spectral subtraction ethod with β = since the a priori SR 5

26 G(SR in db Figure. -50 β = β =.5 β =.5 β = SR (db oise Suppression Filter Gain Curves of a Magnitude Spectral Subtraction Filter inforation is not available and the noise suppression filter perforance can only rely on the robustness of the adopted noise spectral estiation technique. The noise floor paraeter c is significant in the reduction of usical noise which is a type of residual noise that sounds lie different onotones rapidly changing in both tie and frequency. An exaple of usical noise is shown in Figures.4 and.5. In Figure.4 the agnitude spectral subtraction was applied with a noise floor paraeter c = 0 to suppress the additive white noise fro a speech signal of a 5dB SR. The speech phrase One three five six speech. was sapled at 8Hz and processed with a Haing window of 56 saples and 50% overlapping in this exaple. Figure.5 shows a 6

27 G(SR in db Figure β = 3 β = 3.5 β = 4 β = SR (db oise Suppression Filter Gain Curves of a Power Spectral Subtraction Filter snapshot of the first 0.5sec of the speech phrase in the frequency range of 0 to 600Hz. In this figure the residual noise peas of significant agnitude are apparent around 500Hz at 0.sec and 00Hz at 0.sec. The ajor peas such as these create the spurious onotone sounds defined as usical noise. The spectral agnitudes of the utterance in Figure.4 are uch larger than those of the usical noise in Figure.5 and hence the occurrence of the usical noise ight be deeed to be insignificant. However this is often isleading since the utterances are coposed by vowels and consonants [8]. The vowels contribute the ajor spectral energy perceived in Figure.4 while the consonants especially the fricatives can contribute very sall spectral energy at the level 7

28 0 5 Magnitude 0 5 Figure Frequency in Hertz Tie in seconds The Short-tie Spectral Magnitude of an Enhanced Speech Using the Magnitude Spectral Subtraction Magnitude Frequency in Hertz Tie in seconds 0.5 Figure. 5 Musical oise Resulting fro the Magnitude Spectral Subtraction 8

29 close to usical noise. Therefore those fricatives can be ased by the usical noise and the utterance intelligibility is deteriorated accordingly. It was shown in [7] that the usical noise was itigated using the power spectral subtraction ethod given by Equation.7. This reduction of usical noise results fro the adjustable noise floor paraeter. As stated in Equation.7 and shown in Figure.3 the noisy speech signal is greatly attenuated if the agnitude spectru of the raw data is close to the noise spectral estiate. Although this would cause a reduction in the usical noise during the speech pauses ostly usical noise would often reain within the speech portions. Due to the lac of robustness agnitude and power spectral subtraction ethods are inferior for the reduction of usical noise to Bayesian noise suppression ethods which will be discussed in the next section..3 Bayesian Methods for oise Suppression.3. Miniu Mean Square Error Estiation of the Short-Tie Spectral Aplitude One of the ost widely studied Bayesian noise suppression ethods is the Miniu Mean Square Error Estiation of the Short-Tie Spectral Aplitude (MMSE-STSA which was proposed by Yariv Ephrai and David Malah [9]. In the MMSE-STSA ethod the MMSE estiate of the short-tie clean speech spectral agnitude within a single frae is deterined where the noisy speech agnitude spectru is assued to be corrupted by additive white Gaussian noise (AWG. The coplete description of the MMSE-STSA schee is beyond the scope of this thesis; however the resulting enhanced speech estiate and filter expression are shown in Equations.3 and.4 respectively. 9

30 0 ( ( ( [ ] ( ( exp j H S θ = (.3 ( + + = = ( ( ( ( ( ( exp ( ( ( 0 I I H H STSA υ υ υ υ υ γ υ π (.4 where = ( ( ( γ A posteriori SR ( ( ( ( γ ξ ξ υ + = + = 0 ( ( ax ( ( ( ( S λ λ ξ A priori SR for 0 λ. ( ( = π π 0 cos exp cos ( dy y z n y z I n Modified Bessel function of the first ind Equation.4 introduces two iportant functions that are still widely used in odern speech enhanceent ethods. The functions ( γ and ( ξ are defined as the a posteriori and a priori SR estiates respectively [0]. It has been deonstrated in [] and [] the a priori SR estiate ( ξ aids in the reduction of usical noise because it perfors as a soothing function of the a posteriori SR estiate ( γ which is the ratio of the noisy speech spectral energy and the estiated noise spectral energy. According to Equation.4 the MMSE-STSA noise suppression filter ( H STSA is a function of both a posteriori and a priori SR estiates. Thus ( H STSA relies on the previous frae s clean speech spectral estiate along with the noise spectral estiate. It is noted that the functions of the a posteriori and a priori SR estiates in Equation.4

31 both include a noise spectral estiate update. It is assued that a VAD is used to update the noise estiates during a speech pause as entioned in Section... The particular function defined in Equation.4 for the a priori SR estiate is nown as the Decision Directed estiation approach [9] in which the best results were achieved in ters of the residual noise reduction for λ = However odern research has been perfored to odify or iprove the Decision Directed estiation approach by aing λ as an adaptive paraeter [3] [4] [5] [6]..3. Miniu Mean Square Error Estiation of the Log-Spectral Aplitude One year after introducing the MMSE-STSA Ephrai and Malah proposed another noise suppression ethod called the Miniu Mean Square Error Estiation of the Log- Spectral Aplitude (MMSE-LSA [7]. Through the inforal listening test in [7] the sound quality resulting fro the MMSE-LSA ethod was superior to that fro the MMSE-STSA ethod due to further residual noise reduction. The MMSE-LSA filter function also involves less coputational coplexity than the MMSE-STSA filter. The filter function of the MMSE-LSA including only a single exponential integral is defined by Equation.5. H ξ ( = LSA = exp + ξ ( υ ( ( H (.3.3 Wiener Filtering e t t dt (.5 Due to its proising results siplicity and efficiency the Wiener filter is probably the ost applicable noise suppression filter today. The Wiener filter is derived fro the MMSE of the clean speech estiate in the tie doain. Siilar to the MMSE-STSA and

32 MMSE-LSA filters the odern Wiener filter is also a function of the a priori SR estiate. In fact the Decision Directed estiation approach is coonly applied in the Wiener filtering to deterine the a priori SR estiate []. The Wiener filter is defined in Equation.6 [] []: H ξ ( = Wiener = (.6 + ξ ( ( H (.3.4 Coparative Studies of Bayesian oise Suppression Methods Since the nuerical evaluation of the odified Bessel function of the first ind is involved in the MMSE-STSA noise suppression filter as given by Equation.4 and the nuerical integration is also required in the MMSE-LSA filter as given by Equation.5 the corresponding coputational coplexities are rather high. Therefore we adopt the Wiener filter in this thesis for the feasible practical ipleentation. The Wiener filter is actually a classical Bayesian noise suppression ethod that originally was a function of the a posteriori SR estiate. It [Wiener filter] was later odified using the a priori SR estiate defined in [0].

33 CHAPTER 3. EISTIG OISE SPECTRAL ESTIMATIO METHODS FOR BAYESIA OISE SUPPRESSIO 3. Introduction In Chapter the Bayesian noise suppression ethods all involved a function of the a priori SR estiate. The a priori SR estiate is a function of the clean speech spectral energy estiate according to the Decision Directed estiation ethod given by Equation.4. Since the clean speech spectral energy estiate is related to the accuracy of the noise spectral energy estiate a robust noise spectral estiation technique would lead to a ore accurate clean speech energy estiate as well as a ore accurate a priori SR estiate which would give rise to a ore accurate noise spectral estiate update in the future. Our research goal is to design a reliable noise spectral estiation ethod with the aide of the VAD and the proposed technique can be integrated with any existing VAD algorith in practice. In this chapter two coonly used noise spectral estiation ethods for speech processing will be discussed. Such two spectral estiation ethods involve the oving average and the single pole recursion. 3. The Ipact of the A Priori Signal-to-oise Ratio The a priori SR estiation is crucial in the Wiener filtering. The a priori SR estiate ξ ( is given by Equation 3. using the Decision Directed estiation ethod proposed in [9]. It was also deonstrated in [] and [] that the ore accurate the S( ξ ( = λ + ( λ ax{ γ ( 0} (3. ( 3

34 ( where a posteriori SR estiate is defined as γ ( ( a priori SR estiate the less usical noise in the enhanced speech spectru. As previously discussed in Chapter the residual noise reduction relies on a robust noise suppression filter with the accurate noise spectral estiation. Figure 3. illustrates the apriori SR estiates for the first 0.5sec of the phrase One three five six speech where only ξ ( 5 is plotted and the speech signal is ebedded in the additive white Gaussian noise with a 5dB SR. Since the first 0.5sec of this phrase consists of no speech therefore the spectral energy shown is the pure noise energy which corresponds to the solid line in the botto graph of Figure 3. whereas the dashed line indicates the noise spectral estiates. In the top graph of Figure 3. the solid line represents the a priori SR estiates and the dotted line represents the instantaneous SR estiates. The instantaneous SR (ISR estiate is equivalent to the a posteriori SR estiate inus or γ ( 5. Since the noise spectral energy estiate is significantly lower than the actual noise spectral energy a significant aount of residual noise will reain in the enhanced speech after the noise suppression. It was shown in Chapter the noise suppression filter gain decreases with the a priori SR estiate. As a result a significant aount of energy fro the actual noise spectral peas would reain in the enhanced speech spectru. This is the cause for the production of usical noise. The a priori SR estiates behave lie a soothing function for the ISR. Since the a priori SR estiates change very little in coparison to the ISR estiates there will be less shorttie drastic variations in the noise suppression filter gain and it leads to the usical noise 4

35 00 0 ISR SR apriori SR (db Actual oise oise Estiate Energy Figure Tie in seconds A Priori SR Estiate Versus ISR Estiate in a Coparative Study itigation. As a result the enhanced speech signal will sound closer to a uniforly attenuated version of the original noise during the speech pauses. Consequently the sound quality fro a Bayesian noise suppressor using the a priori SR estiation is found to be ore pleasant []. 3.3 Voice Activity Detection for oise Frae Labeling This thesis only concentrates on the noise spectral estiation ethods dependent on the VAD. The general purpose of a VAD will be briefly discussed in this section. In Chapter the Short-Tie Fourier Transfor (STFT was introduced to segent the noisy speech signal into fraes using an arbitrary window function. A VAD is used to deterine if the current frae consists of both noise and speech or just pure noise. The 5

36 general rule of a typical VAD is defined in Equation 3.. In Equation 3. a logical is confired if the current frae is found to contain speech energy. Thus the fraes labeled as a logical 0 are used for the noise spectral estiation. Conventional noise spectral estiation ethods will be described in the following sections. In these sections it is assued that the current frae is classified as a logical 0 by the VAD. L where ( ν [ ( ] ν ( ν T µ = (3. 0 T [ ] < µ L Logical function dependant on the input arguent T [ ] Transfor or apping function µ Threshold defined to deterine the logical output 3.4 Conventional oise Spectral Estiation Methods 3.4. The Moving Average In section 3. the noise spectral estiation technique used to calculate the noise energy in Figure 3. was the oving average. The oving average shown in Equation 3.3 also nown as the arithetic ean is basically an average noise spectru over the recent past fraes. It is the siplest noise spectral estiate. However the oving ν M ( ( ν = l l= 0 (3.3 M average ethod cannot be well adapted to the nonstationary environent since this ethod is effective ostly in stationary noise environents. In addition the nuber of required fraes M for the accurate noise estiates should be sufficiently large. If M is considerably sall the resulting noise spectral estiate would easily be doinated and 6

37 biased by an abrupt noise pea. In the exaple of Figure 3. M 50 is required for the noise spectral estiation which is equivalent to the first 0.784sec of the signal. The tie duration of 0.784sec is too long for the stationary assuption of any noise in reality. Though it is not the ost popular noise spectral estiation technique due to the lac of robustness the oving average schee is soeties used as a soothing function to reduce spectral artifacts arising fro the noise suppression [6]. In [6] Boll applied a 3- saple oving average estiator i.e. M = 3 to estiate the noise spectru and reduce the usical noise Single-Pole Recursion Single-pole recursion is the ost widely used noise spectral estiator for speech processing []. As shown in Equation 3.4 the single-pole recursion can be characterized a first-order low-pass filter where φ R( 0. The single-pole recursion ethod can better ν ν ( φ ( + ( φ ( ν = (3.4 trac the nonstationary noise statistics than the oving average schee because it weighs the recent past ore heavily than the distant past where the weight of a historical noise spectral estiate decays asφ n and n is the nuber of updates after that estiate []. According to Equation 3.4 the requireent of the storage device is uch less stringent than the oving average estiator too. In the past few years there have been soe odifications of the single-pole recursion estiator (Equation 3.4 [8] [9] to include the attac and decay coefficients. In Equation 3.5 φ a and φ d are denoted as such attac and decay coefficients respectively. 7

38 This technique nown as two-sided single-pole recursion was developed to eliinate the transient phenoena in the presence of VAD errors []. Thus a saller weight would ν ν ( φ ( + ( φ ( ν = (3.5 φ a where φ φ b for φ > φ. ν ( ( = ν a b ν ( < ( ν be placed on the current frae if its frae energy is greater than the ost recent update of the noise spectral estiate. This estiation ethod was created to reduce the stationary noise and would not perfor well in the nonstationary environents. Thus the two-sided single-pole recursion is not prevalent for the speech applications in adverse environents. 3.5 Coparative Studies of Conventional oise Spectral Estiation Methods In this section the oving average and single-pole recursion ethods will be investigated for different noise scenarios to gain ore insights. In the single-pole n recursion φ 0 as φ 0 at a given n. It eans that the better tracing capability of the noise spectral estiator can be perceived asφ 0. In Figure 3. both oving average and single-pole recursion were used to estiate the noise spectra for the sae signal in the exaple of Figure 3. except with additive babble (speech-lie noise. The coefficient φ for the single-pole recursion estiation is 0.5 for this exaple. Figure 3. shows the enhanced speech spectral energy estiate fro the Wiener filtering in the top 8

39 Energy Actual Speech Energy Moving Average Estiate S-P Recursive Estiate Energy Actual oise Moving Average S-P Recursive Figure Tie in seconds Enhanced Speech and Estiated oise Spectra Using the Moving φ = 0.5 Average and the Single-Pole Recursion ( plot and the estiated noise spectral energy in the botto plot for the 5 th DFT frequency bin. In the botto plot it is shown that the single-pole recursion ethod perfored very well in tracing the tie-varying noise spectru. However the single-pole recursion estiate was uch less accurate than the oving average estiate during the voice region. The VAD detected the speech activities slightly before.4sec and the noise spectral energy estiate reains unchanged until the next speech pause. Since the VAD detected speech energy within low noise energy durations the speech spectral estiate using the single-pole recursion ethod consisted of ore residual noise during the speech onset. It is also shown in Figure 3. that the residual noise energy appearing in the 9

40 Energy Actual Speech Energy Moving Average Estiate S-P Recursive Estiate Energy Actual oise Moving Average S-P Recursive Figure Tie in seconds Enhanced Speech and Estiated oise Spectra Using the Moving φ = 0.9 Average and the Single-Pole Recursion ( enhanced speech energy is insignificant for both ethods during the noise fraes (0 to.4 sec. This is because the Wiener noise suppression filter is a function of the a priori SR; thus the noise energy during the unvoiced periods would be greatly attenuated. However the noise spectral estiates during the voice periods are of ost interest because the residual noise eerges fro those periods. In Figure 3.3 the sae experient was conducted usingφ = 0. 9 which is a typical value suitable for all inds of noise. Apparently the noise spectral estiate fro the single-pole recursion ethod is ore accurate using φ = 0. 9 than that using φ = 0. 5 but not as accurate as that using the oving average schee according to Figures 3. and 30

41 Energy Actual Speech Energy Moving Average Estiate S-P Recursive Estiate Energy Actual oise Moving Average S-P Recursive Figure Tie in seconds Enhanced Speech and Estiated oise Spectra Using the Moving φ = 0.98 Average and the Single-Pole Recursion ( 3.3. We further increase φ to 0.98 to generate Figure 3.4 for the sae experient and show that the enhanced speech spectral energies are very siilar for both ethods. However a recursion coefficient of 0.98 ay be too high for other noise scenarios because a weight of only 0.0 is placed on the current noise frae during the noise spectral estiate updates. Seeingly the advantage of the oving average schee over the single-pole recursion ethod has been illustrated in the previous exaples. In addition it has been shown in Figures and 3.4 that the oving average schee produced a rather accurate noise spectral energy estiate although the babble noise is considered 3

42 nonstationary therein. evertheless it was entioned earlier that the oving average schee lacs robustness in the nonstationary noise environents. As a atter of fact only the first sec of the speech signal in a single DFT frequency bin was inspected and the noise environent did not change drastically in such a short tie. The oving average ethod wors well in short-tie only if sufficient noise fraes are available during speech pauses for updating the noise spectral estiate in a slowly changing noise environent. A practical exaple of a drastic change in the noise bacground is a obile phone conversation or a speech recording in a relatively quiet area with a jet flying above. If the jet is passing quicly the noise arising fro the jet will be in bursts. An exaple to illustrate this phenoenon is shown in Figure 3.5. Figure 3.5 shows the oving average and single-pole recursion noise spectral estiates for the speech pause between the words One and Three of the 45 th DFT frequency bin. At the beginning of this speech pause around the sec instant the fading sound of a fast-oving jet was siulated. In the 45 th DFT frequency bin it is shown that the single-pole recursion ethod better traced the nonstationary noise spectru and produced a ore accurate speech spectral energy estiate for the voiced duration between.6 and 3.sec. The noise spectral estiate was produced fro the oving average ethod during the speech pause fro sec to.5sec as shown in Figure 3.5 while the single-pole recursion estiate was carried out as a continuation fro the initial noise frae. In the exaples illustrated by Figures it is obvious that the single-pole recursion ethod with a fixed recursion coefficient is not robust for different noise environents. It was also illustrated in Figure 3.5 that the oving average ethod is not 3

43 Energy Actual Speech Energy Moving Average Estiate S-P Recursive Estiate Energy Actual oise Moving Average S-P Recursive Figure Tie in seconds Enhanced Speech and Estiated oise Spectra Using the Moving Average and the Single-Pole Recursion in the Presence of Jet oise φ = 0.90 ( robust in the highly nonstationary noise environents either. In Chapter 4 a robust noise spectral estiation algorith will be proposed which eploys both oving average and single-pole recursion ethods; a novel technique to deterine the optial adaptive recursion coefficient in the MMSE sense for better noise spectral tracing capability will also be introduced thereupon. 33

44 CHAPTER 4. OVEL ROBUST OISE SPECTRAL ESTIMATIO 4.. Introduction We propose a new robust noise spectral estiation ethod in this chapter. Our noise spectral estiation technique is optial in the MMSE sense and can be easily eployed with any existing VAD. This chapter begins with a brief description of our algorith and ends with the detailed flowchart. The sections are organized as followed: 4. Forulation of Robust oise Spectral Estiator 4.3 Optial Adaptive Recursion Coefficients and 4.4 Flowchart. 4. Forulation of Robust oise Spectral Estiator It was presented in the previous chapter that both oving average and single-pole recursion ethods are not robust. As shown in the exaples of Chapter 3 the noise spectral estiates during voice regions using the single-pole recursion were sensitive to the recursion coefficient φ. It was also shown that the long-ter noise spectral estiation using the oving average ethod ay produce an inaccurate estiate in adverse noise conditions due to the unifor weighting of the data. However according to Figure 3. the oving average schee led to an accurate noise spectral estiate for nonstationary noise in short-tie; it ight lead to less accurate estiates than the single-pole recursion ethod in soe cases as shown in Figure 3.5. Thus it is believed that a ore accurate estiate in adverse noise conditions can be achieved by decoposing the noisy speech signal into short-tie segents in which the noise spectral estiates are averaged in each individual segent and then the single-pole recursion ethod is eployed between the averaged estiates cross the successive segents thereafter. 34

45 Our proposed robust noise spectral estiation ethod dynaically creates short-tie speech segents by collecting a sufficient nuber of both noise and speech fraes in the progress of the noisy speech signal. In each segent the oving average estiator is utilized to produce a segental noise spectral estiate dependent only on the noise fraes. Once such a segental noise spectral estiate is obtained the single-pole recursion ethod is utilized between the current and previous segents to deterine the noise spectral estiate of that current segent. The recursion coefficient is adaptive for each DFT frequency bin to weigh the individual segental noise spectral estiates and generate the ultiate noise spectral estiate for the further noise suppression. Such adaptive recursion coefficients are optial in the MMSE sense which will be discussed in the next section. Our novel robust noise spectral estiator is forulated in Equation 4. below. ν [ ] ( φ ( ( ν ν ( φ ( = (4. opt + opt ν where ( Ultiate robust noise spectral estiate of the th frequency bin and ν ( ( the th segent Moving average estiate of the th frequency bin and the th segent φ opt Optial adaptive recursion coefficient of the th frequency bin and the th segent 4.3 Optial Adaptive Recursion Coefficients As entioned earlier the recursion coefficient is adapted for each DFT frequency bin independently. It is believed that an adaptive recursion coefficient for each frequency bin will greatly iprove the conventional single-pole recursion ethod over different nonstationary noise environents for two reasons. First a ore accurate noise spectral 35

46 36 estiate can be achieved by heavily weighing the previous segental noise spectral estiate in the stationary noise conditions. Second the nonstationary noise ay possess the stationary spectra in a certain frequency bins. Thus the different adaptive recursion coefficients should be pursued for different DFT frequency bins for the optiality. We apply the MMSE criterion ( = ν is chosen in Equation 4. accordingly and derive the optial adaptive recursion coefficients as given by Equation 4.. The derivation of ( ( ( ρ ψ φ opt = (4. where ( S Enhanced speech spectral estiate of the th frequency bin and th segent ( { } ( ( { } ( ( { } ( ( { } ( ( ( { } ( ( ( { } ( ( ( ( 4 ( ψ S E S E S E S E E E ( ( ( ( 4 4 ( ρ +. Equation 4. is provided in the Appendix. Since = ν the noise spectral estiate is given by Equation 4.3. The clean speech spectral estiate ( S of the current segent can be approxiated using any of the noise suppression ethods described in Chapter. ( ( ( ( ( ( φ φ opt opt + = (4.3 However it was found that the noise spectral subtraction provided a relatively accurate speech spectral estiate regardless of the usical noise artifacts reaining in the enhanced speech spectru. Only a rough approxiation is necessary at this point since

47 the interediate noise spectral estiate ( is not for the purpose of speech enhanceent. Besides the noise spectral subtraction is very coputationally efficient. Therefore the noise spectral subtraction is adopted to generate the clean speech spectral estiate. Due to the errors in the clean speech spectral estiates S ( occasionally φ opt ( < 0 or φopt ( >. Therefore φ opt ( has to be liited to [ 0] defined in Equation 4.4. ( 0 φopt ( 0 φopt ( < 0 φ ( > R and it is φ opt φopt ( = (4.4 opt 4.4 Flowchart Our novel robust noise spectral estiation ethod is illustrated in the flowchart of Figure 4.. It is assued that the tie-doain noisy speech signal has already been digitally sapled for n = In the flowchart p denotes the speech frae index and r the noise frae index. The constant integers P and R denote the iniu nuber of speech and noise fraes respectively required to for an eligible segent. Thus the segent length is dynaically varying. Once an eligible segent is fored the noise spectral suppression is perfored on that segent and the frae counter is reset to start collecting new fraes for the next segent. 37