n x l s m n x v m l th source at the m th microphone was computed using the

N x l s m n x v m l th source at the m th microphone

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n x l s m ] [ ) ( n x v m l -th source at the m -th microphone was computed using the following formula: ( ) ( ) = = = N n v m N n s m s m n x n x SNR l l 1 2 ) ( 1 2 ) ( 10 ) ( ] [ ] [ log 10 . (3.1) where N is the length (number of samples) of both recordings. A zero-phase, FIR high-pass filter was applied to each microphone signal prior to this computation, which removed the DC component and its skewing effects on the SNR. Equation 3.1 can be expressed in terms of the source signal, , and the noise signal, , using the discrete-time form of Equation 2.6. With this room impulse response model, the ] [ n s l ] [ n v m m -th microphone signal from the N -point recording of source l can be expressed as: N n n v n d h n s n x m s m l s m l l K r 1 for ] [ ] , [ ~ * ] [ ] [ ) ( ) ( = + = 28
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The impulse response ] , [ ~ ) ( n d h l s m r represents the acoustic system from source l , located at ) ( l s d r , to the m -th microphone in the array. In the conference-room data set, there are 15 microphones in the array and three unique source locations. Hence, 15 1 K = m and 3 1 K = l . During the recording of the background noise, there was no source signal, resulting in 0 ] [ = n s and . During the recording of the Gaussian source, the noise was negligible. Using this model, the SNR, as computed by Equation 3.1, can be expressed as follows: ] [ ] [ n v n x m m = ] [ n v m ( ) ( ) = = = N n m N n s m l s m n v n d h n s SNR l l 1 2 1 2 ) ( 10 ) ( ] [ ] , [ ~ * ] [ log 10 r (3.2) The “signal” power in Equation 3.2 (numerator) is the sum of all the power generated by the source, including the reverberation that is implicit in the convolution with the room impulse response. While it Figure 3.7 Estimated SNRs of all 15 microphone channels for each Gaussian source. 29
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may be more accurate to use only the direct-path component of the source to compute the “signal” power, Equation 3.2 is effective in expressing the power of the source in relation to the power of the background noise. Furthermore, there is no simple way to measure the direct-path sound exclusively. The estimated SNRs of all 15 microphone-channels and for each source location are plotted in Figure 3.7. Notice that all SNRs are generally very high (above 31 dB). As expected, source 3 has the highest SNRs, since its location was the closest to the microphone array. As the bar graph shows, there is some variation among channels. It is likely that this effect is due to variations in the system’s hardware, as well as differences in the reverberation patterns for each microphone and source. Nonetheless, all microphones signals in the conference room dataset have negligible contributions from the background noise. Any effects that significantly distort the microphone signals must come from the acoustic path from source to receiver, which makes this dataset ideal for studying the sole effects of room reverberation on location estimation.
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