### AE2M99CZS Exercise - Digital Filtering - FIR Filters

• 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+1 = 31 (or 51, 81).
• 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 impulse response of the ideal filter on the basis of IDFT (i.e. an estimation of infinite impulse response),
• shortened (zeroed) and weighted impulse response,
• final target frequency response of designed FIR filter with shortened impulse response computed via DFT,
• 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=30 in the first step.
• Observe achieved frequency and impulse response of designed filters (fcn freqz, impz).
• Checked result (1 point): Display:
• frequency responses of designed filters for the order M = 30,
• 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.
• Checked result (1 point):
• Work with the following input speech signals:
- s0001.bin, fs = 8 kHz (use loadbin.m to load binary signals into MATLAB),
- SA106S06.CS0, fs = 16 kHz,
- fc44be305265.ils_a, fs = 44.1 kHz,
• observe frequency responses of designed filters for particular smapling 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.