Equalization of Audio Channels A Practical Approach for Speech Communication. Nils Westerlund

Transcription

1 Equalization of Audio Channels A Practical Approach for Speech Communication Nils Westerlund November, 2

2 Abstract Many occupations of today requires the usage of personal preservative equipment such as a mask to protect the employee from dangerous substances or the usage of a pair of ear-muffs to damp high sound pressure levels. The goal of this Master thesis is to investigate the possibility of placing a microphone for communication purposes inside such a preservative mask as well as the possibility of placing the microphone inside a persons auditory meatus and perform a digital channel equalization on the speech path in question in order to enhance the speech intelligibility. Subjective listening tests indicates that the speech quality and intelligibility can be considerably improved using some of the methods described in this thesis.

3 Acknowledgements I would like to express my gratitude to Dr. Mattias Dahl for his support and extraordinary ability to explain complex systems and relationships in an understandable way. I would also like to express my appreciation to Svenska EMC- Lab in Karlskrona for letting me use their semi-damped room for measurement purposes.

4 Contents 1 Channel Equalization An Introduction Non-Adaptive Methods Adaptive Channel Equalization Equalization of Mask Channel Gathering of Measurement Data Coherence Function Channel Equalization using tfe Adaptive Channel Equalization The LMS Algorithm The NLMS Algorithm The LLMS Algorithm The RLS Algorithm Minimum-Phase Approach Results of Mask Channel Equalization Equalization of Mouth-Ear Channel Gathering of Measurement Data Coherence Function of Mouth-Ear Channel Channel Equalization Using tfe Adaptive Channel Equalization The LMS Algorithm Results of mouth-ear channel equalization Identification of True Mouth-Ear Channel Basic Approach Conclusions Further Work A MatLab functions 37 A.1 LMS Algorithm A.2 NLMS Algorithm A.3 LLMS Algorithm A.4 RLS Algorithm A.5 Minimum-Phase Filter Design A.6 Coherence and Transfer Function A.7 Estimate of True Channel

5 Chapter 1 Channel Equalization An Introduction x(n) h(n) y(n) X(z) H(z) Y(z) Figure 1.1: System with input and output signals and the corresponding system in z-domain. A linear time-invariant system h(n) takes input signal x(n) and produces an output signal y(n) which is the convolution of x(n) and the unit sample response h(n) of the system, see fig The input, output and system is assumed to be real and only real signals will be considered in this thesis. The convolution described above can be written as y(n) = x(n) h(n) (1.1) where the convolution operation is denoted by an asterisk. In z-domain, the convolution represents a multiplication given by Y (z) = X(z)H(z) (1.2) where Y (z) is the z-transform of the output y(n), X(z) is the z-transform of the input x(n) and H(z) is the z-transform of the unit sample response h(n) of the system. In many practical applications there is a need to correct the distortion caused by the channel and in this way recover the original signal x(n). In this thesis, this corrective operation will be called channel equalization. 2

6 1.1 Non-Adaptive Methods A cascade connection of a system h(n) and its inverse h I (n) is illustrated in fig Suppose the distorting system has an impulse response h(n) and let Identity system x(n) h(n) y(n) h (n) I d(n) = x(n) Figure 1.2: System h(n) cascaded with its inverse system h I (n) results in an identity system. h I (n) denote the impulse response of the inverse system. We can then write d(n) = x(n) h(n) h I (n) = x(n) (1.3) where d(n) is the desired signal, i.e. the original input signal x(n). This implies that h(n) h I (n) = δ(n) (1.4) where δ(n) is a unit impulse. In z-domain, (1.4) becomes Thus, the transfer function for the inverse system is H(z)H I (z) = 1 (1.5) H I (z) = 1 H(z) (1.6) Note that the zeros of H(z) becomes the poles of the inverse system and vice versa. If the characteristics of the system is unknown, it is often necessary to excite the system with a known input signal, observe the output, compare it with the input and then determine the characteristics of the system. This operation is called system identification [1]. If we obtain an output signal y(n) from a system h(n) excited with a known input signal x(n), we could of course use the z-transforms of y(n) and x(n) to form H(z) = Y (z) X(z) (1.7) However, this is an analytical example and the transfer function H(z) is most likely infinite in duration. A more practical approach is based on a correlation method. The crosscorrelation of the signals x(n) and y(n) is given by r xy (l) = n= x(n)y(n l), l =, ±1, ±2,... (1.8) 3

7 The index l is the lag parameter 1 and the subscripts xy on the crosscorrelation sequence r xy (l) indicate the sequences being correlated. If the roles of x(n) and y(n) is reversed, we obtain Thus, r yx (l) = n= y(n)x(n l), l =, ±1, ±2,... (1.9) r xy (l) = r yx ( l) (1.1) Note the similarities between the computation of the crosscorrelation of two sequences and the convolution of two sequences. Hence, if the sequence x(n) and the folded sequence y( n) is provided as inputs to a convolution algorithm, the convolution yields the crosscorrelation r xy (l), i.e. r xy (l) = x(l) y( l) (1.11) In the special case when x(n) = y(n) the operation results in the autocorrelation of x(n), r xx (l). Recall that y(n) = x(n) h(n). The insertion of this expression for y(n) into (1.11) yields r xy (l) = h( l) r xx (l) (1.12) In z-domain, (1.12) becomes P xy (z) = H (z)p xx (z) (1.13) where H (z) is the complex conjugate of H(z) and P xx is the power spectral density of x(n). The transfer function for the identified system is then H (z) = P xy(z) P xx (z) (1.14) where P xy (z) is the cross spectral density between x(n) and y(n). If r xy (l) is replaced by r yx ( l) in (1.12), the complex conjugate in (1.14) is eliminated and we obtain the following estimate of the transfer function: H(z) = P yx(z) P xx (z) (1.15) The MatLab 2 function tfe 3 uses this method to estimate a transfer function of the system in question [4]. In later sections it will be clear that this method is both straightforward and powerful when identifying a given system. 1.2 Adaptive Channel Equalization Another trail to equalize a channel is to use adaptive algorithms. There are a vast amount of application areas for adaptive algorithms and the mathematical theory is quite complex and reaches beyond the scope of this thesis. Therefore, 1 Also commonly referred to as (time) shift parameter 2 MatLab is a trademark of The MathWorks, Inc. 3 Transfer Function Estimate 4

8 in this section, only a brief description of the basic principles of adaptive filtering will be given [2]. A block diagram of an adaptive filter is shown in fig It consists of a shift-varying filter and an adaptive algorithm for updating the filter coefficients. The goal of adaptive FIR-filters, is to find the Wiener filter w(n) that minimizes d(n) x(n) Adaptive filter d(n) Adaptive algorithm e(n) Figure 1.3: Basic structure for an adaptive filter. the mean-square error ξ(n) = E{ d(n) ˆd(n) 2 } = E{ e(n) 2 } (1.16) where E{ } is the expected value and ˆd(n) is the estimate of the desired signal d(n). We know that if x(n) and d(n) are jointly wide-sense stationary processes, the filter coefficients that minimize the mean-square error ξ(n) are found by solving the Wiener-Hopf equations [2] R xx w = r dx (1.17) where R xx denotes the autocorrelation matrix of x(n), w denotes the vector containing filter coefficients and r dx denotes the crosscorrelation vector of d(n) and x(n). The calculation of the Wiener-Hopf equations is a complex mathematical operation including an inversion of the autocorrelation matrix R xx. If the input signal or the desired signal is nonstationary, this operation would have to be performed iteratively. Instead, the requirement that w(n) should minimize the mean-square error at each time n can be relaxed and a coefficient update equation of the form w(n + 1) = w(n) + w(n) (1.18) can be used. In this equation w(n) is a correction that is applied to the filter coefficients w(n) at time n to form a new set of coefficients, w(n + 1), at time n+1. Equation (1.18) is the heart of all adaptive algorithms used in this thesis. 4 Since the error function ξ(n) is a quadratic function, its curve can be viewed as a bowl with the minimum error at the bottom of this bowl. The idea of 4 Except for the RLS algorithm described in section

9 adaptive filters is to find the optimal vector w(n) by taking small steps towards the minimum error. The update equation for this vector is w(n + 1) = w(n) µ ξ(n) (1.19) where µ is the step size and ξ(n) is the gradient vector of ξ(n). Note that the steps are taken in the negative direction of the gradient vector since this vector points in the direction of steepest ascent. The gradient can be directly estimated by the product of e(n) and x(n). Introducing this estimate in (1.19) yields w(n + 1) = w(n) + µe(n)x(n) (1.2) which is the well known Least Mean Squares (LMS) algorithm. Further developments of this algorithm includes Normalized LMS (NLMS) and Leaky LMS (LLMS). All of these algorithms will be evaluated in later sections of this thesis [2]. In fig. 1.4, a block scheme that can be used for adaptive channel equalization is shown. The original signal s(n) is passed through some sort of system (a channel) that distorts the input signal and this distorted signal is then used as input to the adaptive algorithm. The output signal ˆd(n) from the adaptive causal filter is subtracted from the desired signal d(n) and the result forms the error e(n). The error is the second input signal to the adaptive algorithm. If the system is considered as a non-trivial system, it will not only affect the spectral characteristics of the input signal but also introduce a delay on the same 5. This is the reason why the delay is so important. Another important property is that if the channel to be equalized is causal, the equalizing filter will be non-causal if no delay of the filtered signal x(n) is acceptable. However, only causal Finite Impulse Response (FIR) adaptive filters will be used in this thesis and these filters will indeed introduce a delay on the signal. Also note that an FIR filter of course only can approximate an Infinite Impulse Response (IIR) filter with a certain precision if such a filter is needed for an optimal solution [3]. 5 That is, if the impulse response of the system is more complex than a zero-centered unit sample. 6

10 Delay d(n) Input signal s(n) Channel x(n) Adaptive filter d(n) e(n) Adaptive algorithm Figure 1.4: Basic structure for an adaptive channel equalizer. 7

11 Chapter 2 Equalization of Mask Channel In this chapter, a protective mask is studied. The goal was to equalize the distortion of human speech caused by this mask. In order to collect the necessary data to perfom this study, a measurement setup was assembled in order to record data on site. 2.1 Gathering of Measurement Data The gathering of measurement data was made with the help of a test dummy head 1, two DAT-recorders 2 and a signal analyzer 3. The test dummy used, was constructed specially for audio measurements and was equipped with a loudspeaker placed in its mouth. A microphone was mounted on the inside of the mask and the mask was then attached to the test dummy head, see fig To damp disturbing environmental noise, the complete arrangement was placed behind particle boards covered with insulation wool. The signal analyzer was used to generate noise bandlimited to 12.8 khz and one of the DAT-recorders, the SV38 model, was used to record noise and speech sequences while the other was used for playback of speech sequences. The sampling frequency was 48 khz with a resolution of 16 bits and the information on the DAT-tapes was then stored as wav-files using the software CoolEdit 2. The wav-files was finally read by MatLab for further processing. A block scheme of the complete setup is shown in fig The first action taken, was to reduce the amount of data by sampling rate conversion. Using the MatLab function decimate, the sampling frequency was reduced in two steps: First from 48 khz to 24 khz and then from 24 khz to 12 khz. Hence, the amount of data was reduced to one fourth. For a detailed description of how decimate works, see [5]. 1 Head Acoustic 2 Sony TCD-D8 and Panasonic SV38 3 Hewlett-Packard 3657A 8

12 Figure 2.1: (a) Test dummy head equipped with a loudspeaker in its mouth. The microphone is placed inside the mask. (b) Placement of the microphone in the mask. Figure 2.2: Block scheme of the complete measuring setup. 2.2 Coherence Function A powerful tool for investigating the properties of input-output signals, is the coherence function. If P xx and P yy are the power spectral densities of input signal x(n) and output signal y(n) respectively, and P xy is the cross spectrum of the input and output signal, the coherence function C xy can be calculated as C xy = P xy 2 P xx P yy (2.1) A coherence function equal to one, means that a perfectly linear and noise-free system is being measured. Thus, a coherence function gives a direct measure of the quality of the estimated frequency response. In appendix A.6 a MatLab function that calculates the coherence function is listed. 9

13 The coherence function C xy of the mask is shown in fig The length of the FFTs (Fast Fourier Transform) used for calculating C xy was Frequency [Hz] Figure 2.3: The coherence function C xy of the mask. The input signal was flat bandlimited noise sequence with variance σ 2 = 1 (FFT-length 248). 2.3 Channel Equalization using tfe First, the impulse response of the system was estimated using the MatLab function tfe. For a detailed description of how this function works, see [4]. A short resum of the theory behind tfe is given in section 1.1. An alternative function, custom made by the author, is listed in appendix A.6. The data was divided into non-overlapping sections and then windowed by a Hanning window. The magnitude squared of the Discrete Fourier Transforms (DFT) of the input noise sections were averaged to form P xx. The products of the DFTs of the input and output noise sections were averaged to form P xy. A one-sided spectrum is returned by tfe and in order to perform an Inverse FFT (IFFT), the spectrum has to be converted to a two-sided spectrum. This spectrum can then be used as input to the MatLab function ifft and in this way the corresponding impulse response for the transfer function can be calculated. For a detailed description of the MatLab function ifft, see [5] The channel transfer function and impulse response for different filter lengths are shown in fig Calculating a channel equalizing filter for the mask using tfe is easily done simply by switching the input parameters. That is, if the tfe function call to estimate a channel is Txy=tfe(inputNoise, outputnoise), the function call to estimate an equalizing filter to the same channel would be Txy inv=tfe(outputnoise, inputnoise). The result of this operation is shown in fig Adaptive Channel Equalization The MatLab function tfe calculates the transfer function using brute force. However, an alternative approach is the usage of adaptive methods. In this section an investigation based on LMS, NLMS, LLMS and RLS (Recursive Least Squares) adaptive FIR filters will take place. 1

14 L=5 L=11 L=256 L= Filter taps Frequency [Hz] Figure 2.4: The left column shows impulse responses for the mask. The filters were calculated using the correlation method. The filter lengths are L=5, L=11, L=256 and L=512. The right column shows the corresponding transfer functions. The transfer functions were calculated using the MatLab function freqz [5] The LMS Algorithm The first adaptive algorithm used for channel equalization was the LMS algorithm according to w(n + 1) = w(n) + µe(n)x(n) (2.2) An implementation of the LMS algorithm is listed in appendix A.1 Step size The correct choice of the step size µ is of great importance when using the LMS algorithm or other LMS-based algorithms. Using (2.3), the maximum step size can easily be approximated by < µ < 2 pe{ x(n) 2 } where p is the filter length and E{ x(n) 2 } is estimated with Ê{ x(n) 2 } = 1 p n m=n p+1 (2.3) x(m) 2 (2.4) 11

15 L= L= L= L= Filter taps Frequency [Hz] Figure 2.5: The left column shows impulse responses for the mask channel equalizing filter. The filters were calculated using the correlation method. The filter lengths are L=5, L=11, L=256 and L=512. The right column shows the corresponding transfer functions. The transfer functions were calculated using the MatLab function freqz. In reality, this step size approximation can seldom or never be used. Instead, as a rule of thumb, a step size at least an order of magnitude smaller than the maximum value allowed, should be used [2]. Nevertheless there are applications that may allow larger step sizes. Delay The choice of delay has a substantial effect on the quality of the channel equalizer. The Mean Square Error (MSE) measures the quality in this case. As a rule of thumb, the delay can be chosen equal to half the adaptive filter length [3]. In fig. 2.6 the MSE is plotted as a function of the delay. It is clear that a delay of about 1 samples gives the least MSE if the filter length is 2. Note that the introduction of a delay is crucial for the quality of a channel equalizer but that the length of the delay is not critical. According to the figure, the delay could have been as short as 5 samples and as long as 15 samples with maintained low level of the MSE. However, to leave out the delay results in an unacceptably high MSE. The physical delay that the limited speed of sound propagation c introduces 12

16 5 x Mean Square Error Delay [Samples] Figure 2.6: MSE plotted as a function of the delay. The length of the adaptive filter is L=2. to the system, is best illustrated with a plot of the impulse response of the mask, i.e. the crosscorrelation between the loudspeaker and the microphone. This plot is shown in fig. 2.7 and is based on an estimate made by the Hewlett-Packard 3657A signal analyzer. Note that the amplitude of the impulse response is not correctly scaled. The crosscorrelation is approximately zero during the time,2 ms. This delay is due to the propagation time for the first sound wave that reaches the microphone. If we approximate c 33 m/s as the speed of sound and ms delay, the distance L between the loudspeaker and the microphone can be calculated by L = c (2.5) which yields a distance between the loudspeaker and the microphone of about 6.5 cm. This distance corresponds well to the real distance. Filter length The filter length is of course a key parameter in all sorts of filter design. Theoretically, the length can be chosen arbitrarily but in a realization of a filter in, for example, a digital signal processor (DSP), the length of the filter is limited by memory size as well as by mathematical complexity. Hence, we have a classical trade-off situation between efficiency and quality. To motivate the 13

17 x x Time [Seconds] x 1 4 Figure 2.7: The plots shows the impulse response of the mask, i.e. the crosscorrelation between the loudspeaker and the microphone. The lower plot is a zoomed version of the upper plot. choice of filter length, fig. 2.8 shows the MSE plotted as a function of the filter length. The result from all LMS-based adaptive algorithms used in this thesis are plotted. Note that when the filter lengths increases beyond a certain point the MSE actually increases. The reason for this is that as the number of filter coefficients is increased, the error due to stochastic jumps of these coefficients on the error surface also increases. This error is called the Excess MSE. Results The LMS algorithm was used to perform both a channel identification and a channel equalization. The corresponding plots is shown in fig The NLMS Algorithm Normalized LMS (NLMS) uses a time varying step size as follows µ(n) = β x T (n)x(n) + ɛ = β x(n) 2 + ɛ (2.6) In this thesis, only real signals are used, hence the transpose in the denominator of (2.6). If x(n) was a complex signal, the transpose would be a hermitian trans- 14

18 5 x LMS,.25 of max step size LMS,.5 of max step size LMS,.1 of max step size NLMS, beta=.5 NLMS, beta=.1 NLMS, beta=.2 LLMS,.25 of max step size LLMS,.5 of max step size LLMS,.1 of max step size RLS, lambda=1 Mean Square Error Filter Length Figure 2.8: The MSE plotted as a function of filter length for LMS, NLMS, LLMS and RLS. The delay is half the length of the filter plus eight samples due to the physical delay introduced by the system. Three different step sizes was used for each algorithm (except for the RLS algorithm). The input signal was 5 samples of flat bandlimited noise with the variance σ 2 = 1 except for the RLS algorithm where 1 samples of noise were used. pose. Also note that to avoid division by zero, a small constant ɛ is introduced in the denominator. If equation 2.6 is inserted into equation 2.2, we obtain w(n + 1) = w(n) + β x(n) e(n) (2.7) x(n) 2 With a correct statistical assumption it can be shown that the NLMS algorithm will converge if < β < 2 [2]. Therefore, the NLMS algorithm requires no knowledge about the statistics of the input signal in order to calculate the step size. Another advantage of the NLMS algorithm, is its insensitivity to the amplification of the gradient noise that a high-amplitude input signal introduces. This insensitivity comes from the normalization in (2.7). The delay requirement is the same as when using the LMS algorithm. 15

19 L=5 L=11 L=256 L= Filter taps Frequency [Hz] Figure 2.9: The left column shows impulse responses for the mask. The filters were calculated using the LMS algorithm. The filter lengths are L=5, L=11, L=256 and L=512. The right column shows the corresponding transfer functions. The transfer functions were calculated using the MatLab function freqz The LLMS Algorithm If the eigenvalues of an autocorrelation matrix is zero, the LMS algorithm does not converge as expected. The LLMS algorithm (Leaky LMS) solves this problem by adding a leakage coefficient γ to the filter coefficients according to w(n + 1) = (1 µγ)w(n) + µe(n)x(n) (2.8) This leakage coefficient forces the filter coefficients to zero if either the input signal or the error signal becomes zero. The obvious drawback of this method, is that a bias is introduced to the solution. This bias becomes evident in fig In this case, the LLMS algorithm has approximately twice as large MSE compared to the other algorithms in the plot. The delay requirement is the same as when using the LMS and NLMS algorithms The RLS Algorithm If an increased computational complexity is acceptable, the time for convergence can be reduced considerably by using the RLS algorithm. For a more thorough 16

20 L= L=11 2 L=512 L= Filter taps Frequency [Hz] Figure 2.1: The left column shows impulse responses for the equalizing filter. The filters were calculated using the LMS algorithm. The filter lengths are L=5, L=11, L=256 and L=512. The right column shows the corresponding transfer functions. The transfer functions were calculated using the MatLab function freqz. description of this algorithm, see [2]. One important property of the RLS algorithm, is that the step size depends on the size of the error: If the estimate ˆd(n) is close to the desired signal d(n), small corrections of the filter coefficients will be made. Hence, the step size will be large at the beginning of the convergence and then, as ˆd(n) approaches d(n), become smaller and smaller. A plot of the MSE as a function of the filter length is shown in fig Due to the complexity of the algorithm, the plot has been calculated from 1 samples of flat bandlimited noise (σ 2 = 1). 17

21 2.5 Minimum-Phase Approach If we were to design a channel equalizer for hifi audio purposes, a linear phase filter would be the only acceptable choice since all frequencies are delayed equally when passed through such a filter. In the case of the mask, this constraint is substantially relaxed. This channel equalizer is supposed to operate in a telephone network (PSTN) using the frequency band 3-34 Hz. Since the channel equalizer is designed to operate in such a large system, it is desirable to reduce the delay caused by the filtering and in this way minimize the total delay introduced by the whole system, i.e. the PSTN. One powerful method of minimizing the delay of a system, is to design it as a minimum-phase filter. A minimum-phase filter has all of its zeros inside of or possibly on the unit circle. This type of filters can be obtained from a linear-phase filter by reflecting all of the zeros that are outside the unit circle to the inside of the unit circle. The resulting filter will have minimum-phase and, except for a scaling factor, the same magnitude as the linear-phase filter [6] Filter taps Figure 2.11: The upper plot shows the impulse response for a minimum-phase filter and the lower plot shows the impulse response for a linear-phase filter. Note how the centre of gravity of the linear-phase filter has been shifted to form the minimum-phase filter. The plots in fig shows the impulse response for a mask channel equalizing minimum-phase filter and the corresponding linear-phase filter. The filter length of the linear-phase filter is 128 and thus the delay when using this filter, 18

22 will be 64 samples due to its symmetry. In figure 2.12 the corresponding amplitude functions are plotted. It is clear that the minimum-phase filter indeed 2 1 Amplitude [] Desired Frequency Response Minimum Phase Frequency Response Amplitude [] Desired Frequency Response Linear Phase Frequency Response Frequency [Hz] Figure 2.12: Amplitude for the minimum-phase filter (upper plot) and linearphase filter (lower plot). Note that the overall performance is approximately the same for both filters results in approximately the same amplitude as the linear-phase filter. Another interesting question, is how the phase behaves over the frequency band. This is illustrated in fig The group delay τ g is defined to be τ g = dθ(ω) dω (2.9) where θ(ω) is the phase. For a linear-phase system the group delay is, by definition, constant. The group delay for the different filters is shown in fig It is clear that the usage of a linear-phase filter of length L will introduce a constant delay of L/2 samples. If a minimum-phase filter is used, the delay will be reduced substantially but on the other hand it will not be constant over the frequency band. 19

23 5 Radians Radians Frequency [Hz] Figure 2.13: The phase for the minimum-phase filter (upper plot) and linearphase filter (lower plot). 1 5 Samples 5 Minimum Phase Linear Phase Frequency [Hz] Figure 2.14: The group delay for the minimum-phase filter and the linear-phase filter. 2

24 2.6 Results of Mask Channel Equalization When talking about speech quality and speech intelligibility it is hard to decide what is high quality speech and low quality speech. One needs some sort of measure to be able to draw conclusions on whether one speech sample is better than another. There are nevertheless a great deal of subjective feelings about speech quality and intelligibility. In the case of the mask channel equalization, both correlation methods and adaptive methods proved to be a powerful tool in channel equalization. Both methods managed to substantially improve the speech quality and intelligibility using reasonable filter lengths. A subjective listening test showed that at a sampling frequency of F s = 12 khz, a filter length of about L = 1 taps significantly improved the speech quality. There was also little or no difference at all between the results of the different adaptive algorithms and this is the reason why only the LMS algorithm is used as adaptive method in chapter 3 where an equalization of the mouth-ear channel is performed. When a minimum-phase filter was used to equalize the mask channel, a subjective listening test could not differ a speech sample filtered by such a filter from a speech sample filtered by a corresponding linear-phase filter. This suggests that minimum-phase filters can be used without loss off speech quality in speech communication system. 21

25 Chapter 3 Equalization of Mouth-Ear Channel In chapter 2 we saw that it is possible to equalize the channel that a mask represents using both correlation methods and adaptive methods. We now move on to next issue: Placing the microphone inside a persons auditory meatus and identify and equalize the channel between the mouth and the ear. The first problem that arises, is how to generate a noise signal. When using the test dummy head, a signal analyzer could be used to generate the reference input signals (see section 2.1). Now, when placing the microphone inside a human auditory meatus, the skull itself represents the channel to be equalized. Thus, the test subject himself must generate a broadband noise-like signal to excite the channel/skull. This may seem like an impossible task but in fact it is quite possible to generate a broadband noise-like sound. The power spectral density for such a noise-like sound, made by a human speech organ, is shown in fig Amplitude [] Frequency [Hz] Figure 3.1: Power spectrum of broadband noise-like sound generated by human speech organ. 22

26 3.1 Gathering of Measurement Data The equipment used was a DAT-recorder 1, a custom made microphone amplifier, two microphones 2 and a pair of ear-muffs 3. One of the microphones was placed in front of the test subjects mouth and the other was placed inside the test subjects auditory meatus. The ear-muffs was then placed on the test subjects head. This is advantageous since the signal path outside the skull is damped considerably. Also, a pair of ear-muffs damps disturbing or even harmful environmental noise. The test subject was placed in a semi-damped room and pronounced a number of sentences chosen a priori. He also tried to make noise-like sounds. The two-channel data was recorded at 44.1 khz and then the sampling frequency was reduced to khz in the same manner as the data from the mask measurements (see section 2.1.) For a block scheme of the complete measurement setup, see fig. 3.2 and 3.3. Figure 3.2: Block scheme of the complete measurement setup. Figure 3.3: Microphone placement in auditory meatus. 1 Sony TCD-D8 2 Sennheiser 3 Hellberg 23

27 3.2 Coherence Function of Mouth-Ear Channel Using the noise signal generated by the human speech organ, the coherence was calculated as in (2.1). The result is shown in fig As described in Frequency [Hz] Figure 3.4: Coherence function of mouth-ear channel (FFT-length 248). section 2.2, the ideal coherence function is equal to one which means that a perfectly linear and noise-free system is being measured. As fig. 3.4 illustrates, this is not the case with the mouth-ear channel. It has been showed that sound propagation through the skull is perfectly linear in the frequency band at interest [7]. Furthermore, the signal recorded in the auditory meatus is severely damped (see section 3.3) and this indicates that the problem is a poor signal-to-noise ratio (SNR) rather than a non-linear problem. An additional problem is that the excitation signal is not used as reference signal when identifying the system. However, one should not concentrate on the coherence function to the exclusion of other information about the signals. It will be clear in later sections, that a satisfactory channel equalization can be performed even though the coherence function at some frequencies (or frequency bands) falls far below unity. 24

28 3.3 Channel Equalization Using tfe The MatLab function tfe uses correlations to calculate a transfer function, as described in (1.14), section 1.1. The transfer functions and impulse responses for a number of different filter lengths are shown in fig The procedure of calculating the impulse response from the transfer function given by tfe, was the same as in section 2.3. It is evident that the skull performs a relatively simple low-pass filtering with a cut-off frequency of about 5 Hz and a stopband damping of about 3-4. The strange behaviour of the impulse response can probably be explained by the aggravating circumstances mentioned in section 3.2. L=5 L= L= L= Filter taps Frequency [Hz] Figure 3.5: The left column shows impulse responses for the mouth-ear channel. The filters were calculated using the correlation method. The filter lengths are L=5, L=11, L=256 and L=512. The right column shows the corresponding transfer functions. The transfer functions were calculated using the MatLab function freqz. 3.4 Adaptive Channel Equalization Due to the small differences between the results of the different adaptive algorithms used in chapter 2.4, only the standard LMS algorithm will be used as an example of adaptive channel equalization of the mouth-ear channel. 25

29 2 4 L= L= L= L= Filter taps Frequency [Hz] Figure 3.6: The left column shows impulse responses for the mouth-ear channel equalizing filter. The filters were calculated using the correlation method. The filter lengths are L=5, L=11, L=256 and L=512. The right column shows the corresponding transfer functions. The transfer functions were calculated using the MatLab function freqz The LMS Algorithm As in the case with the mask, a number of parameters must be calculated to obtain an effective equalizing filter. Step size and Filter Length To find a proper step size, the MSE was plotted as a function of the filter length L. Different fractions of the maximum step size was used and the result is shown in fig According to this figure, a step size of about one fifth of the maximum allowed step size, seems to be a reasonable choice. For a start, the delay was chosen as half the filter lengths. Later, a more thorough investigation of an optimal delay is performed. Delay As in the case of the mask channel equalization, a proper delay must be chosen. However, a problem arises when the human speech organ is considered. The test dummy head used in the mask channel equalization had a loudspeaker placed in 26

30 1 x of maximum my.5 of maximum my.1 of maximum my.2 of maximum my.4 of maximum my 8 Mean Square Error Filter Lenght Figure 3.7: The MSE plotted as a function of filter length for the LMS algorithm. The delay was half the filter length. Five different step sizes was used and the input signal was noise generated by a human speech organ. its mouth. Hence, the source of the speech or noise was generated at a certain isolated point. When a person is talking, this is not the case. Instead, the vocal chords acts together with the throat, mouth and nostril cavities to form sounds. This means that the speech or noise no longer is generated at one isolated point. Rather, the sound is a result of many systems cooperating. Since we are forced to use a human skull instead of a test dummy head to collect data, it is difficult to predict a certain optimal delay for a mouth-ear channel equalizer. According to [3], a delay of half the filter length is a rule of thumb. This rule can of course be used without further investigations but a simple plot of the MSE as a function of the delay can offer interesting information about the optimal delay. Fig. 3.8 shows the MSE plotted as a function of delay for eight mouth-ear channel equalizing filters. The filter lengths are L = 1, L = 3, L = 5, L = 7, L = 9, L = 11, L = 256 and L = 512 and the delay was 2L. Using this information, the LMS algorithm was used to identify and equalize the mouth-ear channel. The results of these operations are shown in fig

31 L=1 L=5 L=9 L= x x x x Delay [Samples] L=3 L=7 L=11 L= x x x x Delay [Samples] Figure 3.8: The MSE plotted as a function of delay for eight mouth-ear channel equalizing filters, each of different length L and with a delay of 2L. The filters were calculated using the LMS algorithm. 3.5 Results of mouth-ear channel equalization The mouth-ear channel represents a far more complex system and measurement environment, than the mask channel does. The speech signal inside the auditory meatus is severely damped and this means that great demands are made upon the microphones and amplifiers. Furthermore, the signal that is used as the reference signal, i.e. the speech signal at the mouth, is not the excitation signal of the system/skull. Most likely, these factors concurs to a poor coherence function and a poor estimate of the channel. Nevertheless, it is possible to significantly enhance the speech intelligibility by using some of the methods described in this chapter. The performance of the correlation method was particularly good while some problems were encountered when trying to make the adaptive algorithms converge properly. 28

32 L=11 L=256 L=512 L= Filter taps Frequency [Hz] Figure 3.9: The left column shows impulse responses for the mouth-ear channel. The filters were calculated using the LMS algorithm. The filter lengths are L=5, L=11, L=256 and L=512. The right column shows the corresponding transfer functions. The transfer functions were calculated using the MatLab function freqz. 29

33 L=512 L=5 L=11 L= Filter taps Frequency [Hz] Figure 3.1: The left column shows impulse responses for the mouth-ear channel equalizing filter. The filters were calculated using the LMS algorithm. The filter lengths are L=5, L=11, L=256 and L=512. The right column shows the corresponding transfer functions. The transfer functions were calculated using the MatLab function freqz. 3

34 Chapter 4 Identification of True Mouth-Ear Channel Most types of measurements in some way affects the item being measured. In the case of the mouth-ear channel identification and equalization, the cables, analog-to-digital converters (ADC) and the microphones forms a system that distorts the signal in some way. However, it is possible to equalize this system as well and in this way find an approximation of the true channel. 4.1 Basic Approach In fig. 4.1 a principal block scheme illustrates how the measurements are performed. S E is the signal recorded in the auditory meatus, i.e. the Ear, and S M is the signal recorded at the Mouth. H T is the true ear-mouth channel and H is the true ear-mouth channel distorted by the measurement equipment. The microphones, cables and ADCs can be viewed upon as a system. Suppose we perform a measurement and uses equipment/system G M to record data at the mouth and equipment/system G E to record data in the auditory meatus. We then have the situation shown in fig H 1 is the first estimate of the channel. This setup means that S M = S E H T (4.1) The output from H 1 will be S E G E H 1 and the output from G M will be S M G M. This means that H 1 = S M G M S E G E (4.2) Then, the microphones are switched so that the equipment that was used to record data in the auditory meatus in the first measurement now is placed in front of the mouth and vice versa. Fig. 4.3 shows this new setup. Note that G E and G M are switched. This means that H 2 = S MG E S E G M (4.3) If (4.1) is substituted into (4.2) and (4.3) and H 1 and H 2 are multiplied we obtain H T = H 1 H 2 (4.4) 31

35 S E S M H T ADC etc. ADC etc. H Figure 4.1: Block scheme of how the measurements are performed. i.e. the true channel. The result of applying the operations described in this section to the mouthear channel equalizing problem is shown in fig A MatLab function for estimating H T is listed in appendix A.7. 32

36 S E S =S H M E T H T G E G M H 1 S G H =S G E E 1 M M Figure 4.2: Block scheme where the measurement equipment is viewed upon as a system, one in front of the mouth, G M, and one in the auditory meatus, G E. S E S =S H M E T H T G M G E H 2 S G H =S G E M 2 M E Figure 4.3: Block scheme of the second measurement where G M and G E are switched, resulting in another identified channel, H 2. 33

37 4 3 Amplitude [] Transfer Function Left channel at mouth 2 Transfer Function Right channel at mouth Estimate of "true" channel Frequency [Hz] Filter taps Figure 4.4: Estimated transfer functions (upper plot) and impulse response for the true channel (lower plot). 34

38 Chapter 5 Conclusions The goal of this Master thesis has been to investigate the possibility of placing a microphone for communication purposes inside a preservative mask as well as the possibility of placing the microphone inside a persons auditory meatus and digitally equalize the speech path in question. A number of methods has been evaluated, both adaptive and non-adaptive. The work shows that the correlation method is a powerful and straightforward way of identifying a system. Subjective listening tests indicates that this method was able to identify and equalize the mask channel with a satisfactory result and with reasonable filter lengths. The mouth-ear channel presented more difficulties because of its non-ideal circumstances. The mask was attached to a test dummy head equipped with a loudspeaker in its mouth and bandlimited noise was used as reference signal. When the mouth-ear channel was to be identified, a real human skull had to be used and the test subject had to excite the skull himself. Partly because of this, a proper transfer function for this channel was difficult to find. The work also shows that the speech signal detected inside the auditory meatus is substantially damped and this raises the requirements on the measurement equipment because of the low SNR. Another factor that affects the final result is that the excitation signal of the skull is not used as reference/desired signal. Instead, the speech at the test subjects mouth is used as the desired signal when identifying an equalizing filter. This makes the identification process far more complex than in the case with the test dummy head and the protective mask. Nevertheless, subjective listening tests revealed that a substantial improvement in speech intelligibility was achieved when using the correlation method. The adaptive methods performed less well, mainly because of convergence problems. 5.1 Further Work Further improvements may be achieved by using one ore more of the suggestions below: To identify a channel between the mouth and the auditory meatus, lownoise microphones and amplifiers probably have to be used. This would most likely raise the SNR and improve the final results. 35

39 It has been shown that the sound pressure level varies depending on where inside the auditory meatus the microphone is placed [8]. It is possible that a small change in the position of the microphone may increase the SNR to some extent. The excitation signal used when identifying the mouth-ear channel probably causes problems. This signal is far from ideal and furthermore it does not stem from the vocal chords. Another way of exciting the skull would be to simply talk for a few minutes and in this way excite all the frequencies needed for an identification of the channel. 36

40 Appendix A MatLab functions A.1 LMS Algorithm function [yout,eout,f]=lms(x,d,mu,nord) % [yout,eout,f]=lms(x,d,mu,nord) % % x - Input Signal % d - Desired Signal % mu - Step size % nord - Filter length % yout - Filter output % eout - Error during convergence % f - Filter taps % % (c)nils Westerlund, 2 L=length(x); f=zeros(nord,1); yout=zeros(1,l); eout=zeros(1,l); for K=nord:L, xn=x(k:-1:k-nord+1); y=xn *f; yout(k)=y; e=d(k)-y; eout(k)=e; f=f+mu*e*xn; end 37

41 A.2 NLMS Algorithm function [yout,eout,f]=nlms(x,d,mu,nord) % [yout,eout,f]=nlms(x,d,mu,nord) % % x - Input Signal % d - Desired Signal % mu - Step size % nord - Filter length % yout - Filter output % eout - Error during convergence % f - Filter taps % % (c)nils Westerlund, 2 L=length(x); f=zeros(nord,1); yout=zeros(1,l); eout=zeros(1,l); for K=nord:L, xn=x(k:-1:k-nord+1); y=xn *f; yout(k)=y; e=d(k)-y; eout(k)=e; nrm=xn *xn+eps; f=f+mu*e*(xn/nrm); end 38

42 A.3 LLMS Algorithm function [yout,eout,f]=llms(x,d,mu,gamma,nord) % [yout,eout,f]=llms(x,d,mu,gamma,nord) % % x - Input Signal % d - Desired Signal % mu - Step size % gamma - Leakage factor % nord - Filter length % yout - Filter output % eout - Error during convergence % f - Filter taps % % (c)nils Westerlund, 2 L=length(x); f=zeros(nord,1); yout=zeros(1,l); eout=zeros(1,l); for K=nord:L, xn=x(k:-1:k-nord+1); y=xn *f; yout(k)=y; e=d(k)-y; eout(k)=e; f=(1-mu*gamma)*f+mu*e*xn; end 39

43 A.4 RLS Algorithm function [W]=rls(x,d,nord,lambda) % [W]=rls(x,d,nord,lambda) % % x - Input Signal % d - Desired Signal % nord - Filter length % lambda - Forgetting factor % W - Filter taps % % (c)nils Westerlund, 2 x=x(:) ; d=d(:) ; delta=.1; P=inv(delta)*eye(nord); xflip=fliplr(x); xflip=[zeros(1,nord-1) xflip zeros(1,nord-1)]; W=zeros(length(xflip)-2*nord+2,nord); z=zeros(5,1); g=zeros(5,1); alpha=; for k=1:length(xflip)-2*nord+1, z=p*xflip(end-k-nord+1:end-k) ; g=z/(lambda+xflip(end-k-nord+1:end-k)*z); alpha=d(k+1)-xflip(end-k-nord+1:end-k)*w(k,:). ; W(k+1,:)=W(k,:)+alpha*g. ; P=(P-g*z. )/lambda; end W=W(end,:); 4

44 A.5 Minimum-Phase Filter Design function [x2,h]=minfas(admag,ndft) % [x2,h]=minfas(admag,ndft) % % Admag - Desired frequency response % Ndft - Length of DFT % x2 - Minimum-phase Impulse response % h - Linear-phase Impulse response % Admag=Admag(:); Admag=Admag ; fs=12; f=1*(1.2589).^(3:length(admag)+2); Admagi=Admag; Admagi=[Admagi ]; Ad=1.^(Admagi/2); Ad=Ad(:); Mag(1:Ndft/2+1)=Ad; Mag(Ndft/2+2:Ndft)=flipud(Ad(2:Ndft/2)); xehat=real(ifft(log(mag))); xhat(1)=xehat(1); xhat=2*xehat; N=Ndft/2; x2=real(ifft(exp(fft(xhat(1:n),ndft)))); x2=x2(1:n); % % Linear phase - FFT method % L=Ndft/2; M=(L)/2; Adh=Ad(1:length(Ad)-1).*exp(-j*2*pi*M*((:length(Ad)-2)) /Ndft); Magh(1:Ndft/2)=Adh; Magh(Ndft/2+1)=Ad(Ndft/2+1); Magh(Ndft/2+2:Ndft)=flipud(conj(Adh(2:Ndft/2))); h=real(ifft(magh)); h=h(1:l+1); 41

45 A.6 Coherence Function and Estimate of Transfer Function function [Txy_H1,Txy_H2,Cxy]=sysest(x,y,nfft,winflag) % [Txy_H1,Txy_H2,Cxy]=sysest(x,y,nfft,winflag) % % x - Input Signal % y - Output Signal % nfft - FFT Length % winflag - 1-> windowing -> no windowing % Txy_H1 - H1-estimate of transfer function % Txy_H2 - H2-estimate of transfer function % Cxy - Coherence Function % % (c)nils Westerlund, 2 x=x(:); y=y(:); win=hanning(nfft); k=fix(length(x)/nfft); u=inv(nfft)*sum(abs(win).^2); Pxx=zeros(nfft,1); Pxy=zeros(nfft,1); Pyy=zeros(nfft,1); if(winflag) disp( Windowing... ) else disp( No windowing... ) end for i=:k-1 if(winflag) xw=win.*x(i*nfft+1:(i+1)*nfft); yw=win.*y(i*nfft+1:(i+1)*nfft); else xw=x(i*nfft+1:(i+1)*nfft); yw=y(i*nfft+1:(i+1)*nfft); end X=fft(xw,nfft); X2=abs(X).^2; Y=fft(yw,nfft); Y2=abs(Y).^2; XY=Y.*conj(X); Pxx=Pxx+X2; Pyy=Pyy+Y2; Pxy=(Pxy+XY); end Txy_H1=Pxy./Pxx; 42

46 Txy_H2=Pyy./conj(Pxy); Txy_H1=Txy_H1(1:nfft/2); Txy_H2=Txy_H2(1:nfft/2); Cxy=(abs(Pxy).^2)./(Pxx.*Pyy); Cxy=Cxy(1:nfft/2); A.7 Estimate of True Channel function [Htrue,htrue,lchm_Hinv,rchm_Hinv]=... truechan(lchm_innoise,lchm_outnoise,rchm_innoise,rchm_outnoise) % [Htrue,htrue,lchm_Hinv,rchm_Hinv]=... % truechan(lchm_innoise,lchm_outnoise,rchm_innoise,rchm_outnoise) % lchm_innoise - Left channel at mouth, input noise % lchm_outnoise - Left channel at mouth, output noise % rchm_innoise - Right channel at mouth, input noise % lchm_outnoise - Right channel at mouth, output noise % Htrue - "True" channel transfer function % htrue - Impulse response for "true" channel % lchm_hinv - Est. of equ. transfer func., left ch. at mouth % rchm_hinv - Est. of equ. transfer func., right ch. at mouth % % (c)nils Westerlund, 2 [lchm_hinv,f]=tfe(lchm_outnoise,lchm_innoise,512); [rchm_hinv,f]=tfe(rchm_outnoise,rchm_innoise,512); nfft=2*length(lchm_hinv); Htrue=sqrt(lchm_Hinv.*rchm_Hinv); Htrue=[Htrue;flipud(conj(Htrue(2:end-1)))]; htrue=real(ifft(htrue)); htrue=[htrue(nfft/2+1:end);htrue(1:nfft/2)]; Htrue=Htrue(1:nfft/2); 43