### XE31CZS Exercise - Design of IIR Filters

• IIR filters design - low-pass
• Design low-pass filters using same order and different approximation of magnitude response. Compare frequency repsonses for obtained results.
Butterword - fc = 800 Hz, fs = 8 kHz, N = 6
Chebysev I (I-st type) - fc = 800 Hz, fs = 8 kHz, N = 6, Rp = 1 dB
Chebysev II (II-nd type) - fc = 800 Hz, fs = 8 kHz, N = 6, Rs = 30 dB
Elliptic (Cauer) - fc = 800 Hz, fs = 8 kHz, N = 6, Rp = 1 dB, Rs = 30 dB
• 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) - Discuss if designed filters are stable.
• Compare these equivalent results for different approximation.
• Try to design similar way high-pass, band-pass, and band-stop filters according to your own specification.

• Design of IIR filter from given tolerance scheme
• Design high-pass IIR filter fulfilling following requirements:
- fs = 8000 Hz
- pass-band border: fp = 300 Hz
- stop-band border: fs = 200 Hz
- pass-band ripple: Rp = 0.1 dB
- stop-band ripple: 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) and compare achieved orders.
• Compare frequency responses of achived filters and check their stability!

• Design of equiripple FIR filter
• Design the Park-MCClellan equiripple high-pass FIR filter (Remez algorithm) fulfilling same requirements as in the task above.
• Use functions firpmord and firpm (in older MATLAB version remezord and remez).
• Compare achieved order and frequency responses with above achieved results for IIR filters.