# Blind Dereverberation Using Maximum Kurtosis Biology Essay

Echo in address, caused by room rei¬‚ections, is debatable specially for hands-free telephonic applications in a coni¬?ned infinite. The job is even terrible for hearing impaired people. Therefore blind speech dereverberation is an of import research country.

The undertaking is to take echo from the end product of a room, where the room impulse response, every bit good as the clean address signal is unknown. The method discussed herein maximizes the 4th order cumulant, referred to as Kurtosis, of the Linear Prediction ( LP ) remainder of the address to take echo from the debauched address.

## Foreword

This study is written during the i¬?rst semester of Master of Engineering with Thesis, specialisation in Signal and Speech Processing at the Dept. of Electrical and Computer Engineering, McGill University, Canada.

The study will cover analysis, execution, and trial of the maximal kurtosis based algorithm used to deconvolve room impulse response. Primary prosodies of the algorithm analysis, discussed herein, include the ability to deconvolve, convergence velocity, and the figure of needed generations. The execution of the algorithm is done on MATLAB R2009a in a 64-bit environment.In the study, the natural algorithm is denoted with log ; otherwise the base is stated. Throughout the study, the whole sequence of a signal will be denoted by a vector written with bold letters, i.e. ten, whereas x ( n ) will match to an component in that sequence. If both clip and vector indices are used the variable hj ( K ) is the j’th coei¬?cient at clip index K, where the bold face represents a vector.

Literature mentions are represented with Numberss in IEEE format, e.g. [ figure ] , and a the full list of mentions is found in the References subdivision.The study besides includes the MATLAB execution of the algorithm. 1

## Introduction

Sound moving ridges travel as wave forms, which are so rei¬‚ected by assorted surfaces, and objects in the room ; such rei¬‚ected multipath signals form a delayed and attenuated feedback of the beginning signal to the sink/Mic. Such a feedback is referred to as echo, and causes debasement of the address intelligibility.

## 1.1 Motivation and Problem Statement

Speech echo, assorted with environmental noise, is regarded as one of the primary issue in the address capturing in a coni¬?ned infinite, for illustration, concern oi¬?ces.

Normally, degraded ( linear or reverberant ) address is processed presuming that the debasement has long term stationary features relative to speech ; many methods of address sweetening have been proposed based on this construct. Unfortunately, due to crisp alterations in spectrum within a address frame and across the frames, the ensuing processed address produces signii¬?cant hearable deformations. Such noise decrease is accomplished at the cost of quality. Thus it is required to look at the methods concentrating on features of address for sweetening of debauched address instead than the debasement itself.

Over the old ages, several methods of address dereverberation based on a simplii¬?ed distinct theoretical account of address production have been proposed. The basic theoretical account consists of an excitement beginning, and a time-varying vocal piece of land i¬?lter. Such as theoretical account can easy be modeled by an Auto-Regressive ( AR ) linear anticipation ( LP ) technique. The reverse LP i¬?lter gives the LP-residual, which is a close estimate of the excitement signal. The motive for this undertaking is the observation that in reverberant environments, the LP residuary contains2010/04/19the original urges followed by several other extremums due to multi-path rei¬‚ections.

Therefore, dereverberation can be achieved by modifying the spectral envelope and/or the excitement signal.

## 1.2 Approach

It has been through empirical observation established that, for clean sonant address, LP remainders have strong extremums matching to glottal pulsations, whereas for reverberated address such extremums are spreaded in clip [ 1 ] , in other words, LP remainder of reverberated address is a time-spread version of the comparatively more spiky LP remainder of clean address. Therefore, amplitude spread, in a debauched signal, can be seen as a echo metric. Recent researches have suggested to look at kurtosis, which is a grade of peakedness of a distribution, as a sensible step of echo [ 2, 3 ] . The end of this undertaking is to analyze an online gradient-ascent algorithm to maximise LP residuary Kurtosis, as proposed in [ 4 ] .

In such an effort, there will be more accent on the address – and sweetening for human intelligibility – than on the debasement during the sweetening. The undertaking will concentrate on individual mike apparatus for it is more practical every bit good as disputing. Furthermore, the scenario considered here is that of Blind Derevereberation, where neither the clean signal, nor the room impulse response ( RIR ) is known. This is the instance in most practical state of affairss.Based on the targeted application, the job of dereverberation can farther be divided into two major categories, viz.

dereverberation targeted Automatic Speech Recognition ( ASR ) systems, or dereverberation targeted at doing the signal more apprehensible to worlds. This work is chiefly targeted at the latter category. When we want to take the dereverberation for better human intelligibility we want to do the signal sound better while protecting the spectral distribution of formants ; it is better to go forth some echo than doing spectral deformation. However, when the mark is ASR, the end is to maximise the Signal-to-Noise ratio by taking every bit much echo as possible ; a nice address – in footings of human perceptual experience – is non aspired.

There have been a batch of work done in this country. Some of the interesting methods are presented in the following subdivision.

## 1.3 Related Literature

The RIR, in general, is non-minimum stage. A non-minimum stage i¬?lter is a mixture of a minimal stage i¬?lter, where all uniquenesss lie inside the unit circle, and a maximal stage i¬?lter, where all the uniquenesss lie outside the unit circle. Therefore, the inversion of a non-minimum stage i¬?lter will ensue in a i¬?lter which has poles outside the unit circle, such a i¬?lter can non be causal and stable at the same clip. Thus the attack available is to gauge a near-inverse RIR i¬?lter to call off the ei¬ˆect of room in the debauched address. For the same ground, 2nd order statistics can non be used to retrace a direct signal, and hence, higher order statistics, such as kurtosis, are required.

The thought of utilizing kurtosis to take echo from address was at i¬?rst proposed by Tanrikulu et. Al. in [ 3 ] , as Least-mean kurtosis. However, the writers did non work any address specii¬?c belongingss of the input signal.

Later, Gillespie et. Al. in [ 4 ] proposed an LMS-like gradient maximising algorithm that maximizes the kurtosis of the LP remainders of the address signal to the clean address. LP residuary has been used as an ei¬?cient metric for the echo in address, and many dii¬ˆerent algorithms has been proposed utilising LP remainder for reverberant address sweetening.

Writers in [ 1 ] , for illustration, have utilised an LP residuary weighting strategy which enhances the parts with high signal-to-reverberation ratio in a speech signal. Other methods of dereverberation include spectral minus, as used in [ 5 ] . In [ 6 ] , writers have proposed to utilize the CELP posti¬?lterfor dereverberation.

Chapter 2

## Undertaking Dei¬?nitions and Background

This chapter present a brief debut to widely used constructs in this study.

## 2.1 Room

In this subdivision the room and its belongingss are described. The room is described a the i¬?lter, g, between the beginning and sink i.e. talker and mike. The clean end product of the talker is the address, s, and the signal at the sink is the reverberated address ten.

The ei¬ˆect of ambient environment on address can be modeled as a whirl in clip of the address signal and the RIR [ 7 ] . Furthermore, the system can besides be modeled as incorporating HYPERLINK “ # LinkTarget_1069 ” linear noise [ 1 ] . This is illustrated in Fig. 2.1 and Eq. 2.

1.s a?’a†’ga?’a†’ tenFig. 2.1 Block diagram of speech whirl with room impulse response.

ten ( n ) = g ( n ) a?- s ( n ) + tungsten ( n ) ( 2.1 )Where, n is the clip index, and tungsten ( n ) is the linear noise.In this undertaking, dii¬ˆerent room theoretical accounts were used.

For many experiments, simplii¬?ed room i¬?lters were dei¬?ned utilizing the celebrated image-source method. However, the execution proposed by Lehamn and Johansson [ 8 ] , which promises to turn to the job of anoma lous tail decay in the original image-source method proposed by Allen and Berkley [ 9 ] , was used. Furthermore, existent life RIRs were downloaded from Aachen university ‘s Aachen2010/04/19Impulse Response database [ 10 ] , and convolved with clean speech signal to bring forth rever berated address.

## 2.2 Echo

When a individual is talking in a regular room, the hearers will non merely comprehend the direct address signal, but besides assorted multipath transcripts of it created by rei¬‚ections on the room walls and other objects.

The multipath signals are delayed and perchance attenuated as compared to the direct signal. This phenomenon is known as echo. A really simple scenario with merely one rei¬‚ective surface is illustrated in Fig. 2.2.

To undertake this debasement, it is of involvement to minimise the ei¬ˆect of the room.In clip sphere, such ei¬ˆects can be divided into early and late rei¬‚ections. Early rei¬‚ections can be dei¬?ned as i¬?rst 50-100 MS of the rei¬‚ection. Early rei¬‚ections are good for the address intelligibility for worlds, as they provide information related to the acoustic environment, such as, size of the room, and the place of the talker in the room. Fig.

2.3 illustrates the direct, early and late signals.

## 2.

3 Speech Production Model

The vocal piece of land can be modeled as an autoregressive ( AR ) procedure. The sonant sounds are generated when the input is given as quasi-periodic pulsations, besides referred to as the glottal pulsations. Unvoiced sounds are made when the input is white noise.

This simple source-i¬?lter theoretical account is illustrated in Fig. 2.4.

## 2.

4 Performance Prosodies

The selected prosodies for algorithm rating are calculation complexness, measured in the figure of used generations, spectrograph, and subjective quality steps such as, feedback from many hearers. Spectrogram gives ocular cues of formant spreads in clip because of echo. Both computational complexness and subjective quality are of import prosodies for an hearing assistance application, which has limited computational powers at its disposal. Therefore, it is of import that the algorithms are every bit ei¬ˆective as possible, and giving as clear end product as possible. Other of import prosodies are execution clip ( measured in seconds or clock rhythms ) and the sum of needed memory for plan and informations storage. The executing clip and memory demands will nevertheless non be analysed in this undertaking, but an estimation of how far the algorithms are from a existent clip application will be considered. Besides, mean-square mistake between the original and reconstructed signal is non used here, because the system is non driven to minimise the mean-square mistake, and minimal mean-square mistake does non needfully correspond to better sounding address.

## 2.

5 Higher Order Statisticss

The chief advantage of utilizing higher order statistics follows the hypothesis that the standard signal at the Mic, x ( n ) , can be considered as composed of a Gaussian distributed, and a non-Gaussian distributed constituent. One of import premise here is that the input clean address is non-Gaussian. A reverberated address signal is a multipath signal, and it is represented as leaden, delayed, and summed transcripts of the same signal.

Hence from cardinal bound theorem ( CLT ) – which states that the distribution of the amount of independent and indistinguishable distributed ( iid ) signals is about Gaussian – the ambient noise and echo added to the signal because of whirl with RIR, can be considered as being Gaussian distributed.All Gaussian distributed signals have higher order statistics equal to nothing. The thought is hence to set up a cost map that maximizes the higher order statistics of the reverberated signal, which entails that the processed signal should obtain a pdf that is non-Gaussian, that is, the room impulse response has been removed.In higher order statistics, we would desire to concentrate on the 3rd and 4th order cumulants. The n-th order cumulants cn of a random variable Ten are dei¬?ned by the cumulant bring forthing map, which is logarithm of the moment-generating map.Tennessee g ( T ) = log ( E [ vitamin E Texas ] ) = a?zI?n = Aµt + I?2 t2 + …

( 2.2 )n! 2n=1Cumulants are so given by derived functions at zero of g ( T ) . A more general dei¬?nition of the n-th order cumulant for a non-Gaussian stationary random procedure x ( K ) is given in [ 11, Eq.19 ] :ten xGcn ( I„1, I„2, ..

. ..I„na?’1 ) manganese ( I„1, I„2, .

.. .

.I„na?’1 ) a?’ manganese ( I„1, I„2, … .

.I„na?’1 ) ( 2.3 )Where, the parametric quantity mxnis the n-th order cardinal mean of x ( K ) , and mGnthe n-th orderminute of a Gaussian signal with mean and autocorrelation equal to those of x ( K ) . The I„ ‘sare dii¬ˆerent holds, and cxnis the n-th order cumulant of x ( K ) . It is of import to observe herethat the above equation is non valid for n = 2. The 2nd order cumulant is auto-covariance of x ( K ) . It is clear from Eq.

2.3 that if x ( K ) is Gaussian distributed, the cumulants will be zero. This prove that the higher order cumulants are non ai¬ˆected by the Gaussian noise. Finally, it is deserving adverting three normally used parametric quantities, which are dei¬?ned for zero hold, and zero mean ( or cardinal mean ) , i.e.

, have minutes equal to cumulants.22 ( ) ] = I?nxx( 0, 0 ) = E [ x 3 ( N ) ] = I?3ten( 0 ) = E [ tendegree Celsiuss2tendegree Celsiuss2( 2.4 )tendegree Celsiuss442a?’ ( 000 ) = E [ ( ) ] 3 ( I?xn, ,x4I?= tenis the kurtosis.) 22342Where I?isthevariance, I?istheskewness, and I?The3 ( I?xxtenx2importanttonoteasthekurtosisofanormallydistributedsignalequalsto3 ( I?widelyusedi¬‚avourofkurtosisisthe normalizedkurtosis, dei¬?nedas:ten) 2 factor is) 2.

A more4I?x

## ==

E [ x4 ( N ) ]a?’ 3I?x( 2.5 )22 ( I? ( I?xtenTherefore the normalized kurtosis of a usually distributed signal peers to zero. Kurtosis is a step of “ peakedness ” , i.e. , a signal with many big value in the center and little values at the dress suits has a positive kurtosis.This concludes the brief presentation of higher order statistics and this chapter. The developed constructs and dei¬?nitions will be utilized in the extroverted chapters.

) 2 ) 2Chapter 3

## Dereverberation

Having acquired sui¬?cient background in old chapters, we would look at the kurtosis based method of dereverberation in this chapter.

## 3.1 Linear Prediction of Speech

A Speech signal can be expressed as a additive combination of its past samples. Based on the source-i¬?lter theoretical account discussed in Section 2.

3, the clean address can be modeled as an end product of an all-pole procedure.Ps ( n ) = a?’ Alaskas ( n a?’ K ) + U ( n ) ( 3.1 )k=1where Alaska ‘s are the corresponding i¬?lter coei¬?cients, and u ( n ) is the glottal pulse excitement signal. Let ‘s state the predicted signal for the above address be E?s ( n ) , which can besides be modeled as an end product of an all-pole procedure.PsE? ( n ) = a?’ berkelium ( n a?’ K ) ( 3.2 )k=1where berkelium ‘s are the additive anticipation ( LP ) coei¬?cients.

Now, if the address signal were genuinely generated by an all-pole i¬?lter, Eq. 3.2 would be an exact anticipation of the address signal at all times, except the glottal excitement blink of an eyes, i.e.

,For ak = berkelium ; mistake in anticipation, vitamin E ( n ) = s ( n ) a?’ sE? ( n ) = u ( n ) ( 3.3 )2010/04/19This mistake in anticipation is refered to as LP remainder. It is apparent from Eq. 3.

3 that the LP residuary whitens the address signal, and – in ideal conditions – represents the excitement signal.In a similar manner, LP of the reverberant address can be written as,Pten ( n ) = a?’ hkx ( n a?’ K ) + ex ( n ) ( 3.4 )k=1where ex ( n ) is the LP remainder for the reverberant address. As echo chiefly ai¬ˆects the excitement signal, it can be removed by modifying the LP remainder in a mode to accomplish ex ( n ) = u ( n ) , and so the clean speech signal can be synthesized from the cleansed remainder.

## 3.2 Maximum Kurtosis based Dereverberation

In this subdivision the maximal kurtosis based blind dereverberation is discussed. The basic thought is to maximise the kurtosis of LP remainder of received reverberant signal to accomplish dereverberation. The construct stems from the fact that the LP remainder of a address signal closely approximate the glottal excitement signal, and therefore, it has quasi-periodic extremums. These extremums spread in clip if echo is present/increased, and therefore echo causes the LP remainder of address to go less spiky. Remember from Section 2.5 that kurtosis is a step of the peakedness of a signal.

Hence, the kurtosis of the LP remainder of a speech signal additions as the echo in address additions. An experimental cogent evidence of the same is presented subsequently in Section 4.1.In [ 4 ] Gillispie et Al. show an adaptative algorithm to maximise the kurtosis of LP remainders. In the steepest-ascent algorithm, the cost map is given as the normalized kurtosis, as in Eq. 2.5.

The block diagram for the algorithm is given in Fig. 3.1.The adaptative i¬?lter H ( n ) is controlled by the feedback map degree Fahrenheit ( n ) given by the chosen cost map ( described subsequently ) . And the i¬?ltered LP residuary E?y ( N ) so achieved is used to synthesise the dereverberated signal Y ( n ) . An of import premise is made here, that the forecaster coei¬?cients obtained from the LP analysis are unai¬ˆected by the echo, and can be used to synthesise the clean address from the i¬?ltered residuary. This may non be true ever.

Hence, a secondary attack would be to double the adaptative i¬?lter coei¬?cients to straight i¬?lter the reverberant signal to acquire the dereverberated address, asillustrated in Fig. 3.2.

To deduce the version equations, we want to maximise the kurtosis of E?y ( N ) , given byE [ E?y4 ( N ) ]J ( N ) = a?’ 3 ( 3.5 )E2 [ E?y2 ( N ) ] which constitutes our cost map. The gradient of J ( N ) with regard to current i¬?lter isI?J E [ E?y2 ] E?y2 a?’ E [ E?y4 ]= 4E?y xE?= degree Fahrenheit ( n ) xE? ( n ) ( 3.6 )I?h E3 [ E?y2 ]E [ E?y2 ] E?y2 a?’ E [ E?y4 ]and hence, degree Fahrenheit ( n ) = 4E?y ( 3.7 )E3 [ E?y2 ] where degree Fahrenheit ( n ) is the coveted feedback map used to command the i¬?lter update.

The update equation can be written as:H ( n +1 ) = H ( n ) + Aµf ( n ) xE? ( N ) ( 3.8 )where Aµ is the step-size. The expected values can be calculated recursively, as followers:E [ E?y 2 ( N ) ] = I?E [ E?y 2 ( n a?’ 1 ) ] + ( 1 a?’ I? ) E?y 2 ( N )( 3.9 )E [ E?y 4 ( N ) ] = I?E [ E?y 4 ( n a?’ 1 ) ] + ( 1 a?’ I? ) E?y 4 ( N )The parametric quantity I? is the weighing factor in the recursive update, and controls the smoothness of the minute estimations.

## 3.

3 Complexity of the Algorithm

In this subdivision, the calculation complexness of the algorithm is discussed. Before the analysis of the algorithm is made it is noted that this could be optimized, e.g. , by utilizing pre-calculations of frequently used variables, utilizing look-up tabular arraies, and optimising with respects to correspondence, because the algorithm utilize summing ups which can be calculated in analogue. Execution velocity is critical because the application is a hearing assistance, where existent clip executing is required. Using parallel calculation will assist increase the executing velocity signii¬?cantly.

It will, nevertheless, require a processor which is capable of executing the computations in analogue.The kurtosis maximization algorithm can be divided into four separate computations de i¬?ned in Eq. 3.7, 3.8, and 3.

9. Furthermore it is besides necessary to cipher the end product signal Y ( n ) of the i¬?lter one time per algorithm update. In the following the figure of generations required to calculate each of the equations is determined.The i¬?ltering resulting in Y ( n ) is dei¬?ned asY ( n ) = hT x ( 3.10 )The figure of lights-outs in the i¬?lter H ( n ) is equal to L and hence Eq.3.

10 requires L generations to be computed. The figure of needed add-ons is non used in this simple cost analysis.The i¬?lter update equation, given in Eq.3.8, requires one generation in grading ( mul tiplication by Aµ ) the feedback degree Fahrenheit ( n ) , and multiplying this consequence with the input vector x ( n ) requires Fifty generations because length of x ( n ) is L, therefore entire L + 1 calculations.The feedback map is given in Eq.3.

7. Squaring of E? y ( N ) requires one generation, and because the generation with the changeless 4 can be included into the measure size Aµ in Eq.3.8, the nominator can be calculated utilizing three generations. The denominator requires two generations, and because it is assumed that a division requires the same figure of rhythms as a generation, even though it is a unsmooth estimate, the entire figure of generations is six for this equation.The i¬?rst outlook operation, E [ E?y2 ( N ) ] dei¬?ned in Eq.3.

9 requires two generations, because the squaring of E?y has already been made in Eq.3.7, and the latter estimation E [ E?y2 ( N ) ] requires three generations, because E?y4 ( N ) = yE?2 ( n ) .yE?2 ( N ) , where E?y2 ( n ) is known.Hence, entire figure of computation required to one time update the i¬?lter = L + ( L + 1 ) + 6+2+3=2L + 12. Using the O-notation the complexness is O ( L ) .This concludes the chapter, and following we will look at some experiments and consequences.

## Chapter 4 Experiments and Consequences

In this chapter, experimental apparatus and assorted consequences are discussed.

## 4.1 Kurtosis and LP remainder of reverberant address

To verify that the kurtosis of the LP remainder of a speech signal lessenings with echo, a room environment was simulated, utilizing the algorithm proposed in [ 8 ] , with following inside informations.Dimensions: 4 A- 13 A- 4 in M3.Mic Position: At [ 2,2,2 ]Beginning Position: Traveling from [ 2,3,2 ] to [ 2,12,2 ]Echo clip, T60 = 0.4 seconds.A clean address of 8000 Hz trying frequence was convolved with the RIR. The kurtosis of the LP remainder of this end product was calculated, and plotted against the distance between beginning and mic, as depicted in Fig.

4.1. As the distance between he beginning and mic additions, the echo in the standard address additions, and the kurtosis of its residuary lessenings. This is apparent from the i¬?gure. It should be noted that one should anticipate similar consequences if the beginning was i¬?xed at [ 2,2,2 ] , and the mic was traveling. Furthermore, it can be seen from the i¬?gure that the kurtosis of LP remainder of clean address is really high as compared to that of the reverberated residuary, and that the kurtosis of existent signal is non really high.2010/04/19This little experiment establishes that the kurtosis of LP residuary lessenings with addition in echo.

## 4.2 Derverberation Experiments

In this subdivision, three dereverberation experiments are discussed, where a separate reverberant room impulse response is simulated for each experiment. For all the experiments below I? =0.9 was used. For LP residual a overacting window of size 256, and i¬?lter-tap length of 20 was used.

## 4.2.1 Experiment 1

In the i¬?rst experiment, a room of 4 A- 4 A- 4 metre regular hexahedron dimension was considered, with reverberant clip, T60 = 0.

7 seconds. A clean address sampled at 8000 Hz was taken to be arising from a beginning located at [ 2,2,2 ] , and the mike was situated as [ 2,3,2 ] . To understand the public presentation of the algorithm, wave forms of the signals, every bit good as LP remainders were plotted. Spectrogram was analysed utilizing the “ wave-surfer ” package.

Furthermore, many people were asked to rate the betterment in echo for subjective steps. The consequences are discussed below.The LP remainders of the clean every bit good as reverberant, and so the dereverberated end product were calculated. The wave forms are depicted in Fig. 4.2.To visualise the ei¬ˆect of echo in the address signal, the wave forms of the clean, reverberant, and processed address were plotted, as illustrated in Fig.

4.3.In all the i¬?gures above, the kurtosis of the several signal has besides been marked above its wave form. It is evident from the secret plans that reverberation spreads the signal energy in clip doing the LP residuary less peaky ; the kurtosis values of dii¬ˆerent LP remainders besides align with the consequences. It is besides apparent that the LP remainder of the i¬?ltered end product is much closer to that of the clean address, and the kurtosis value has besides increased.Spectrogram of all the three wave forms were plotted utilizing “ wave-surfer ” package.

The same are shown in Fig. 4.4. It can be seen in the i¬?gure how dii¬ˆerent formants are spread in clip in the reverberant address, and that the i¬?ltering procedure produces a much cleaner image for the dereverberant address.

Subjective Feedback: When listened to the reverberant and processed address, theend product was noticeably better than the input, in footings of signii¬?cant extenuation in echo.

## 4.2.

2 Experiment 2

In this experiment, the instance of blind dereverberation is tried. A reverberant address from ITU-T Wideband database was taken, for which no clean signal or room information was available ; the signal was sampled at 16000 Hz. To understand the public presentation of the algorithm, wave forms of the signals, every bit good as LP remainders were plotted ; and many people were asked to rate the betterment in echo for subjective steps. The consequences are discussed below.

The LP remainders of the reverberant, and so the dereverberated are depicted in Fig.On the same lines as of experiment -1, the wave forms of the reverberant, and pro cessed address were plotted, as illustrated in Fig. 4.

6.Again, the kurtosis of the several signal has besides been marked above its wave form. It is evident from the secret plans that the LP remainder of the i¬?ltered end product is more spiky ; the kurtosis values besides increase with lessening in echo.Subjective Feedback: When listened to the reverberant and processed address, the end product was noticeably better than the input, in footings of signii¬?cant extenuation in echo.4.5.

## 4.2.3 Experiment 3

In the aforesaid two experiments the algorithm was used as an oi¬„ine algorithm, that is, i¬?rst the i¬?nal set of i¬?lter coei¬?cients was calculated by allowing the simulation tally for whole length of the residuary signal, and so the reverberant address was i¬?ltered through the adaptative i¬?lter, utilizing the derived coei¬?cients. However, the primary usage of dereverberation algorithms are in real-time scenarios, and therefore, for this experiment the i¬?lter was applied on-the-i¬‚y to the reverberant address, and a gradual betterment in the quality of address was noticed. For the intent of the experiment, same clean address signal as in Experiment-1 was used here, but for echo a existent life RIR downloaded from Aachen Impulse Response database [ 10 ] was used.

To understand the public presentation of the algorithm, wave forms of the signals, every bit good as LP remainders were plotted. The consequences are discussed below.The LP remainders of the reverberant, and so the dereverberated end product are depicted in Fig. 4.7.On the same lines as of experiment -1, the wave forms of the reverberant, and pro cessed address were plotted, as illustrated in Fig. 4.

8.Again, the kurtosis of the several signal has besides been marked above its wave form. It is evident from the secret plans that the LP remainder of the i¬?ltered end product is more spiky ; the kurtosis values besides increase with lessening in echo.Subjective Feedback: When listened to the reverberant and processed address, the end product was noticeably better than the input, in footings of signii¬?cant extenuation in echo. One could hear gradual betterment in the signal quality, as the algorithm learns and adapts the i¬?lter coei¬?cients with clip ; here a gradual betterment in the quality of address was noticed.

## 4.3 Drumhead

It was proved that the kurtosis of LP remainder is a good step of echo in address.

Assorted experiments were used to formalize that the algorithm works good for man-made every bit good as existent life RIR. Finally experiment 3 proved the algorithm to be suited for existent clip scenarios.Chapter 5

## Discussion and Decision

In this undertaking maximal kurtosis based attacks to the blind address dereverberation job was analysed. The applications targeted in this study are hearing assistance, and hands-free telephone systems, with a individual mike apparatus. The method was tested on fake and existent life RIR ‘s with existent sonant address.The enforced algorithm is based on the work by Gillespie et al. , [ 4 ] , who presented a steepest-ascent solution for the job. The beginning signal ( the direct address ) , s, is assumed to be non-Gaussian distributed.

The room so causes the ascertained signal ( the reverberated address ) , x, to be corrupted by delayed and leaden versions of s, and introduces Gaussian distributed constituents. A Gaussian distributed signal has higher order cumulants equal to zero, and the attack is hence to maximise the kurtosis of the ascertained signal, such that the room impact on the beginning signal can be removed.In decision, an interesting method to blind speech dereverberation has been implemented and analysed in item. Adjustments have been made on carefully performed trials and the i¬?nal word is that the algorithm is able to signii¬?cantly cut down the unsought echo in address.

## Future Work

Writers in [ 12 ] claim that an norm over several spatially distributed mikes can supply potentially better consequences, therefore, it may be worthwhile to look into into multi-microphone apparatuss.

Time sphere execution is prone to decelerate or no convergence because of all discrepancy in the eigenvectors of autocorrelation matrices of the input signal. Alternate noise robust executions may be investigated to avoid this issue, such as the subband adaptative method promoted in [ 4 ] .