AE2M99CZS Exercise - Digital Filtering - FIR Filters
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. shorten the length of impulse to M = 31 (or 51,
Display the particular results of a FIR filter design, i.e.:
ideal frequency response of the above specified filter with the length of N=1000 samples,
the estimation of frequency response of the ideal filter on the basis of
DFT (i.e. an estimation of infinite impulse response),
shortened and weighted impulse response,
final target frequency response of designed FIR filter with shortened impulse response,
frequency and impulse responses of filter designed usin MATLAB function fir1,
observe the influence on used weghting window (rectangular vs. Hamming).
Design of FIR filters using MATLAB implementation of window method (fcn fir1) - Low-Pass and High-Pass
Design two FIR filters for the splitting of a signal into two bands of the same bandwidths. Requirements for the frequency response of these filters are
a) |H| = 1 for 0 < f < fs/4 (low-pass filter),
b) |H| = 1 for fs/4 < f < fs/2 (high-pass filter).
Use the order M=31 in the first step.
Observe achieved frequency and impulse response of designed filters
(fcn freqz, impz).
Checked result (1 point):
frequency responses of designed filters for the order of 31
(M = 30 in MATLAB for fir1),
impulse responses of designed filters,
repeat both points for other orders: try M = 10, 50,
100, 200, 500.
Create band-limited (colour) noise by the filtering of Gaussian white noise using above designed filters.
From above designed filters used those with the order of M = 50.
Gaussian white noise should be 20000 samples long.
Checked result (1 point):
Display frequency responses of used filters,
create colour noise by the filtering of white noise,
observe the first 1000 samples of the waveforms of the input white or the colour outpu noise respectively,
display the smoothed estimation of PSD of output colour noise (use the length of short-time frame N = 512 samples).
Design of bandpass 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 minimally 20 dB. Observe the orders required for different sampling frequencies, i.e. fs = 8, 16,
or 44.1 kHz respectively.