Tasks to do:

• Low-pass IIR filter design
  • Design low-pass filters using same order and different approximation of magnitude response. Compare frequency repsonses for obtained results.
    Butterword - fc = 800 Hz, fs = 8 kHz, N = 6; (fcn butter)
    Chebysev I (I-st type) - fc = 800 Hz, fs = 8 kHz, N = 6, Rp = 1 dB; (fcn cheby1)
    Chebysev II (II-nd type) - fc = 800 Hz, fs = 8 kHz, N = 6, Rs = 30 dB; (fcn cheby2)
    Elliptic (Cauer) - fc = 800 Hz, fs = 8 kHz, N = 6, Rp = 3 dB, Rs = 30 dB; (fcn ellip)
  • Observe achieved frequency response of the filter, i.e. amplitude and phase response (fcn freqz).
  • Result:
    • Draw magnitude frequency responses in dBs for all 4 filters as well as spectrograms of filtered white noise with Gaussian distribution using filters with all 4 approximations. Generated noise should have the length of 10000 samples, the legnth of short-time frame for spectrogram computatio should be 256 samples. Compare achieved results for filters of the same order but various approximations.
  • Observe location of zeros and poles of filter transfer function (fcn zplane), impulse response of designed filter (fcn impz) and discuss if designed filters are stable.

  • Repeat the design for the following changes of input parameters and compare achieved results.
       Try to design similar way high-pass filters with the same cutoff frequency,
       1. Increase the requirements for the suppression of the signal in stop-band to Rs=60.
       2. Observe achieved results for orders N=6, 10, 20 for required suppression of signal in the stop-band Rs=60.

• Design of bandpass IIR filter
  • Design empirically bandpass filter for the band 300 < f < 3400, which should be used for the filtering of acoustic signal into telephone band. Take into acount sampling frequencies 8kHz, 16kHz and 44,1kHz. The suppression of signal in the stop-band should be at least 60 dB, allowed attenuation in the pass-band sould be maximum 0.5 dB. Realize the design according to the following steps.
  • Result:
    • Design filters for sampling frequency fs = 8 kHz and all 4 possible approximations.
    • Same way as it was done in the previous design of lowpass filters observe achieved magnitude frequency responses in dBs in one figure.
    • Within one figure (4x subplot) observe also zero-pole plots of designed filters.
    • Within one figure (4x subplot) observe also impulse responses of designed filters.

• Filtering of speech signal into telephone band
  • Try to realize filtering of speech signals saved in the file speech_8_16_44.mat (Binary MATLAB-format file, it contains 3 signals saved in variables sig8, sig16 and sig44. To load them into MATLAB, use the command "load speech_8_16_44.mat") for designed stable filters. Check in the signal spectrograms that required suppression of the signal was achieved in the stop-band.

  • Result: Filtering of 16kHz speech signal into telephone band:
    • Draw achieved frequency response, zero-pole plot, and impulse response of designed filter for sampling frequency fs = 16 kHz
    • Realize the filtering using designed stable filter fullfiling abive defined requirements.
    • Draw spectrogram of original signal sig16 and signal filtered into the telephone band.

  • HOMEWORK - Realize filtering also for signals sampled by fs = 8 and 44.1 kHz, i.e. input signals should be sig8 and sig44.