Tasks to do:

• For discrete-time systems described by following difference equations draw block scheme, compute difference equation, transfer function, zeros and poles of transfer function, impulse response, and estimate frequency response.

  1. y[n] = x[n] - 0.97 x[n-1]

  2. 

  3. y[n] = x[n] + 2 y[n-1]

• For above described system observe in MATLAB:
  • zeros and poles of transfer function (fnc zplane, roots)
  • frequency response of the system (fnc freqz)
  • impulse response of given system (fnc impz)

• Realization of filtering in MATLAB
  • Realize filtering of the following signals in MATLAB for particular above mentioned systems using function filter and observe PSDs or spectrograms for filtered signals (for speech signals, try also illustrative listening using fcn sound).
  • Used signals:
    - white noise of length 10000
    - speech signals (fs = 16 kHz) : sm2.bin, sf2.bin - Czech utterance "1 0 6 4 7" - male/female),
    (Binary signals can be loaded into MATLAB using function loadbin.m)

  • Result:
    Realize the filtering of speech signal sm2.bin using the system No. 1 and display:
    • time waveforms of input and output signals,
    • spectrograms of input and output signals using short-time frame length of 32 ms,
    • frequency response of used system.

  • Result:
    Realize the filtering of Gaussian white noise with the length of 10000 samples using the system No. 2 and display :
    • time waveforms of input and output signals,
    • short-time power spectrum of input and output signals computed from the frame with the length of 256 samples,
    • smoothed estimation of PSD for input and output signals, the length of short-time frame should be again 256 samples,
    • frequency response of used system.

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• Check also interactive tool fvtool