Optimum design of IIR and FIR Filters from Tolerance Scheme

**Tasks to do: **

**Design of IIR filter from given tolerance scheme**- Design bandpass IIR filter fulfilling requirements of the
following tolerance scheme:

- sampling frequency: fs = 16000 Hz

- pass-band boundary: 400 Hz, 3300 Hz

- stop-band boundary: 200 Hz, 3500 Hz

- maximum ripple in passband: Rp = 1 dB

- minimum ripple in stopband: Rs = 40 dB - Find the lowest order fulfilling given requirements for all
possible approximations of IIR filter magnitude response (use
functions
*buttord*,*cheb1ord*,*cheb2ord*,*ellipord*). - Compare achieved orders, frequency responses of achieved filters and check their stability!
- Realize the filtering of signals saved in the file speech_8_16_44.mat (binary MATLAB format, it contains 3 signals saved in variables sig8, sig16 and sig44 for fs=8, 16 or 44.1 kHz respectively. To load signals into MATLAB use the command "load speech_8_16_44.mat")
- Checked result (1 point):
- observe frequency responses (with checked stability) of designed filters for all sampling frequencies fs = 8, 16, and 44.1 kHz,
- for signal
*sig16*sampled by sampling frequency of 16 kHz realize the filtering and observe spectrograms of original and filtered signals.

**Design of FIR filters from tolerance scheme**- Observe the shape and the spectrum of Kaiser window for various
values of N and beta (fcn
*kaiser*). - Designs bandpass filter using Kaiser method
(fcn
*kaiserord*,*fir1*) fulfilling the requirements mentioned above.

(ATTENTION! The parameters of tolerance scheme must be specified slightly differently in domparison to IIR filter design). - Compare achieved order and frequency responses with above achieved results for IIR filters (for both sampling frequencies).
- Repeat the design using the Park-McClellan equiripple FIR filter (Remez
algorithm, MATLAB functions
*firpmord*and*firpm*) and observe difference in ripples in passband and stopband same s achieved orders of designed filters. - Checked result (1 point):
- observe frequency responses of designed filters for all sampling frequencies fs=8, 16, and 44.1 kHz,
- compare orders of designed filters (compare it also to IIR filters).

- Observe the shape and the spectrum of Kaiser window for various
values of N and beta (fcn
**Design of narrow-band stopband filter**- Design stopband filter to remove 50 Hz disturbance in ECG
signal. Take into account the stop band with boundaries
48 < f < 52 and sampling frequency 200 Hz.

- ECG: ekg1.asc,*fs = 200 Hz*, ASCII format, use*load*to download the signal into MATLAB.

- ECG with 50Hz disturbance: ekg50.asc,*fs = 200 Hz*.

- Design stopband filter to remove 50 Hz disturbance in ECG
signal. Take into account the stop band with boundaries
48 < f < 52 and sampling frequency 200 Hz.
*HOMEWORK -***The demonstration of non-linear phase response impact**- Generate 10 periods of rectangular signal with maximum and minimum values +/- 1 which have the period of 200 samples.
- Design FIR lowpass filter with the order 100 which have normalized cutoff frequency 0,2 and aply it to generate rectangular signal.
- Design IIR lowpass filter with Chebyshev approximation (Type I) with the following parameters: order 6, ripple in passband 0.05 dB, and same normalized cutoff frequency 0,2.
- Compare frequency responses of designed FIR and IIR filters.
*Realize the filtering of previously filtered rectangular signal by*

a) the same FIR filter (one more time),

b) designed IIR filter,

and compare achieved results (observe possible changes of the shape of output signal).

- Design bandpass IIR filter fulfilling requirements of the
following tolerance scheme: