**Tasks to do: **

**Low-pass IIR filter design**- 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 = 3 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*), impulse response of designed filter (fcn*impz*) and discuss if designed filters are stable. - 1st checked result:
- Draw magnitude frequency responses in dBs for all 4 filters into one figure and compare achieved results for filters of the same order but various approximations.

- Repeat the design for the following changes of input parameters and compare achieved results.

1. Increase the requirements for the suppression of the signal in stop-band to*Rs=60*.

2. Observe achieved results for orders*N=6, 10, 20*for required suppression of signal in the stop-band*Rs=60*. *HOMEWORK:*

Try to design similar way high-pass filters with the same cutoff frequency.

- Design low-pass filters using same order and different approximation
of magnitude response. Compare frequency repsonses for obtained results.
**Design of bandpass IIR filter**- Design empirically bandpass filter for the band 300 < f < 3400, which should be used for the filtering of acoustic signal into telephone band. Take into acount sampling frequencies 8kHz, 16kHz and 44,1kHz. The suppression of signal in the stop-band should be at least 60 dB, allowed attenuation in the pass-band sould be maximum 0.5 dB. Realize the design according to the following steps.
- 2nd checked result:
- Design filters for sampling frequency
*fs = 8 kHz*and all 4 possible approximations. - Same way as it was done in the previous design of lowpass filters observe achieved magnitude frequency responses in dBs in one figure.
- Within one figure (4x subplot) observe also zero-pole plots of designed filters.
- Within one figure (4x subplot) observe also impulse responses of designed filters.

- Design filters for sampling frequency

**Filtering of speech signal into telephone band**- Try to realize filtering of speech signals saved in the file speech_8_16_44.mat (Binary MATLAB-format file, it contains 3 signals saved in variables sig8, sig16 and sig44. To load them into MATLAB, use the command "load speech_8_16_44.mat") for designed stable filters. Check in the signal spectrograms that required suppression of the signal was achieved in the stop-band.
- 3rd checked result
Filtering of 16kHz speech signal into telephone band:
- Draw achieved frequency response, zero-pole plot, and impulse response of designed filter for sampling frequency
*fs = 16 kHz* - Realize the filtering using designed stable filter fullfiling abive defined requirements.
- Draw spectrogram of original signal
*sig16*and signal filtered into the telephone band.

- Draw achieved frequency response, zero-pole plot, and impulse response of designed filter for sampling frequency
*HOMEWORK - Realize filtering also for signals sampled by**fs = 8*and*44.1 kHz*, i.e. input signals should be sig8 and sig44.