Tasks to do:

• Manual design of FIR filter using "Window Method" - low-pass filter
  • Describe and explain principles of FIR filter design using "Window Method".
  • Realize step by step a design of low-pass (LP) filter with cutoff frequency f_c = f_s / 4. Use FIR filter order of M = 30 (or 50, 80), i.e. the length of impulse should be M+1 = 31 (or 51, 81).
  • Result : Display the particular results of a FIR filter design, i.e.:
    • the part of infinite impulse response of an ideal filter computed on the basis of Fourier series (use n = -200 : 200),
    • shortened finite impulse response of the filter with the order M = 30,
    • achieved frequency response of designed FIR filter of the order M (the length of displayed twoside frequency response should be 1000 samples and display both magnitude response in linear scaling as well as magnitude response in dBs),
    • to compare with achieved frequency repsonse of designed filter, add to the same figure the ideal frequency response with the length of N=1000 samples,
    • repeat and observe an influence on used weghting window (rectangular vs. Hamming).

• Design of FIR filters using MATLAB implementation of window method (fcn fir1)
  • Design highpass and lowpass FIR filter with the cutoff frequency fc = fs/4,
  • Use the order M=30 and Hamming window in the first step.
  • Observe achieved frequency and impulse response of designed filter (fcn freqz, impz).
  • Result :
    • Observe achieved frequency and impulse response (fcn freqz, impz) of both designed filters (lowpass as well as highpass) for the order 30.

  • Repeat the above mentioned FIR-filter design for various orders and observe resulting change in magnitude frequency response in dBs (use orders M = 10, 30, 50, 200 and default Hamming window).
  • Repeat the design and observe magnitude frequency response in dBs for filters of the order M = 30 and used rother weigthing window (use Blackman, rectangular, Hamming window).

  • Compare magnitude frequency response in dBs for designed FIR filter of the order M = 50 and used Hamming window with magnitude responses of high-pass IIR filters with same cuttoff frequency and the order M = 10 (for inverse Chebyshev aproximation - ripple in stop-band should be R_s = 50 dB ).

• Design of bandpass FIR filter
  • Design empirically bandpass filter for the band 300 < f < 3400, which can be used for the filtering of an acoustic signal (speech) into the telephone band. Design the filters for sampling frequencies 8kHz, 16kHz and 44,1kHz. Find the order for which the suppression of the signal in stop band will be minimum 40 dB. Observe the orders required for different sampling frequencies, i.e. fs = 8, 16, or 44.1 kHz respectively.
  • Result :
    • Work with the speech signals available in 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"),
    • observe frequency responses of designed filters for particular sampling frequencies,
    • spectrograms of original and filtered signals.

  • In suitably selected zoomed part observe also a time-shift between original and filtered signals .

  • Try to listen input and output speech signals.