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BE2M31DSP seminar - Inverse filtering

### BE2M31DSP seminar Inverse filtering, impact of channel noise, Wiener filtering

• Simulation of channel distortion (forward filtering)
• Poles of all-pole IIR filter of 2nd order are p_1|2 = 0.98 * e ^ (+/- j* 11*pi/12 ) . Determine coefficients of polynomials in numerator and denominator of transfer function of this filter, which can simulate distortion in transmission channel for the signal with sampling frequency 16 kHz.
• For acoustic speech signal SA001S01.CS0 (sampling frequency is 16000 Hz, to load data into MATLAB use loadbin.m) simulate trasmission via acoustic channel using this filter, observe channel distortion in spectrogram and also by an illustrative listening.
• Result :
• Frequency response of the filter for channel simulation when fs = 16 kHz.
• Time waveforms and spectrograms for signals at input and output of simulated channel for the case of transmitted signal SA001S01.CS0.
• Reference results:
• Power of original signal: P_orig = 0.0010878.
• Power of filtered (distorted) signal: P_distorted = 0.0012058.

• Invere filtering
• Deatermine the coefficients of inverse filter for the compensation of above discussed channel distortion and observe its frequency response.
• Realize this compensation of channel distortion using inverse filtering of the signal at the out of simulated transmission channel and compare obtained result with the original input.
• Observe the channel-distortion compensation in spectrogram and by illustrative listening.
• Result :
• Frequency response of inverse filter for channel-distortion compensation (fs = 16 kHz).
• Waveform and spectrogram of output signal with compensated distortion, i.e. the signal after application of inverse filtering.

• Inverse filtering under the presence of channel noise
• Add a Gaussian white noise of very low level to the signal at the output of simulated channel. Use scaling constant scale=0.002 for Gaussian white noise with normalized variance, i.e. channel noise should be chnoise=scale*randn(slen,1); and determine SNR of the signal at the transmission channel output.
• Repeat the channel-distortion compensation using inverse filtering of the signal at the channel output in the case of present channel noise and determine SNR of compensated signal.
• Observe again the channel-distortion compensation in spectrogram and by illustrative listening.
• Result :
• Waveforms and spectrograms of channel output with additional channel noise, same as of the signal with compensated distortion, i.e. the signal after application of inverse filtering.
• SNRs for both of these two signals.
• Reference results:
• SNR at the input of inverse filter: SNR_distorted = 24.78 dB.
• SNR after inverse filtering: SNR_inv = 16.94 dB.

• Suppression of the impact of channel noise within inverse filtering using WF
• Realize inverse filtering in frequency domain using OLA with general window and confirm that the result is the same like in the case of inverse filtering in the time domain.
• Realize the suppression of noise impact within the inverse filtering using Wiener filter and achieved compensation both of distortion and channel noise influence observe within spectrogram and by illustrative listening.
• Determine again SNR of output signal after the channe-distortion compensation with WF.
• Result :
• Waveform and spectrogram of output signal with compensated distortion using the standard apprach of inverse filtering realized in frequency domain.
• Waveform and spectrogram of output signal with compensated distortion using the standard apprach of inverse filtering realized in frequency domain including also the usage of Wiener filter.
• Determine again SNR of output signal after the channe-distortion compensation with inverse filter with WF.
• Reference results:
• SNR after inverse filtering with WF: SNR_inv,WF = 19.38 dB.