Optimum design of IIR and FIR Filters from Tolerance Scheme

**Tasks to do: **

**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 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")

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

- Observe the shape and the spectrum of Kaiser window for various
values of N and beta (fcn
**Design of narrow-band stopband filter**