Tasks to do:

• Design of IIR filter from given tolerance scheme
  • Design bandpass IIR filter fulfilling requirements of the following tolerance scheme:
    - sampling frequency: fs = 16000 Hz
    - pass-band boundary: 400 Hz, 3300 Hz
    - stop-band boundary: 200 Hz, 3500 Hz
    - maximum ripple in passband: Rp = 1 dB
    - minimum ripple in stopband: Rs = 40 dB
  • Find the lowest order fulfilling given requirements for all possible approximations of IIR filter magnitude response (use functions buttord, cheb1ord, cheb2ord, ellipord).
  • Compare achieved orders, frequency responses of achieved filters and check their stability!
  • Realize the filtering of signals saved in the file speech_8_16_44.mat (binary MATLAB format, it contains 3 signals saved in variables sig8, sig16 and sig44 for fs=8, 16 or 44.1 kHz respectively. To load signals into MATLAB use the command "load speech_8_16_44.mat")
  • Checked result:
    • observe frequency responses of designed filters for all sampling frequencies fs = 8, 16, and 44.1 kHz,
    • compare achieved orders of designed filters and check their stability,
    • for signal sig16 sampled by sampling frequency of 16 kHz realize the filtering and observe spectrograms of original and filtered signals.

• Design of FIR filters from tolerance scheme
  • Observe the shape as well as the spectrum of Kaiser window for various values of N and beta (fcn kaiser)
  • Checked result:
    • display Kaiser window of the same length of M=101 samples for values beta = 0, 2, 8, 15 and observe also their power spectra in dB for NFFT = 1024,
    • analogous way, display Kaiser window with the same beta = 8 with lengths M=31, 51, 101, 201 samples as well astheir power spectra in dB (again for NFFT = 1024).

  • Designs bandpass filter using Kaiser method (fcn kaiserord, fir1) fulfilling the requirements mentioned above.
    (ATTENTION! The parameters of tolerance scheme must be specified slightly differently in domparison to IIR filter design).
  • Compare achieved order and frequency responses with above achieved results for IIR filters (for both sampling frequencies).
  • Repeat the design using the Park-McClellan equiripple FIR filter (Remez algorithm, MATLAB functions firpmord and firpm) and observe difference in ripples in passband and stopband same s achieved orders of designed filters.
  • Checked result:
    • observe frequency responses of designed filters for all sampling frequencies fs=8, 16, and 44.1 kHz,
    • compare orders of designed filters (compare it also to IIR filters).

• Comparison of signal filtered using IIR and FIR filters
  • For above mentioned signal sig16 sampled by the frequency 16 kHz observe waveforms of input and output signals using FIR filters (designed by Kaiser method as well as by Parks-McClellan approximation) and an IIR filter (anyone with stable solution for given sampling frequency)
  • Checked result:
    • display always within 3 particular figures the input signal sig16 and the result of each of previously mentioned 3 filters and observe the delay of output signals as well as the possible change of signal shape.
    • observe also frequency resposes of used FIR and IIR fileters and compare especially their pahse responses.

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  HOMEWORK

• Design of narrow-band stopband filter
  • Design stopband filter to remove 50 Hz disturbance in ECG signal. Take into account the stop band with boundaries 48 < f < 52 and sampling frequency 200 Hz.
    - ECG: ekg1.asc, fs = 200 Hz, ASCII format, use load to download the signal into MATLAB.
    - ECG with 50Hz disturbance: ekg50.asc, fs = 200 Hz.