### XE31CZS Exercise - Basics of Digital Filtering and Design of FIR Filters

• Theoretical exercise
• Repeat the basic properties of Z-transform and its relation to DTFT.
• Repeat the evaluation of transfer function fom difference equation of digital filter.

• FIR filters design - low-pass and high-pass filters
• Design two complementary half-band FIR filters of the order 30 using window method (fcn fir1) for spliting the signal into two same bands, i.e. requirements for 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).
• Observe achieved frequency response of the filter, i.e. amplitude and phase response (fcn freqz).
• Observe location of zeros and poles of filter transfer function (fcn zplane).
• Observe impulse response of designed filters.
• Observe same results also for filter of other orders, i.e. N= 10, 100, 200, 500.
• Repeat the design of low-pass FIR filter using window method for general cut-off frequency, i.e.
|H| = 1 for 0 < f < fc (low-pass filter), fc = fs/4, fs/10, fs/50 ,
and observe fulfilling of frequency response requirements for different orders.

• Design of FIR band-pass nad band-stop filters
• Design experimentally band-pass filter for the frequency band 300 < f < 3400 for sampling frequency 8 kHz with minimal suppression in stop-band 20dB.
• Design experimentally band-stop filter for the frequency band 48 < f < 52 for sampling frequency 200 Hz with minimal suppression in stop-band 20dB.

• Filtering of signals in discrete-time domain
• Use above designed filters for filtering following available signals:
- speech signal: s0001.bin, fs = 8 kHz, use loadbin.m to read signal into MATLAB.
- ekg: ekg.asc, fs = 200 Hz, use function load to read signal into MATLAB.
- ekg with additive harmonic disturbance at 50Hz: ekg506.asc, fs = 200 Hz, use function load to read signal into MATLAB.
• Observe or listen signals and compare input and output signal.