**Tasks to do: **

- 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 two complementary half-band FIR filters of the order 30 using window method
(fcn
- 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.

- Use above designed filters for filtering following available
signals: