### DSP - Task 1 - Filter Design and Digital Filtering in MATLAB

OVERVIEW:

1. Design different types of FIR and IIR filters for different frequency responses and 2 different sampling frequencies.
2. Filtering of the signal and checking of correct band suppression of output signal (see spectra of input and filtered signals).
3. Discussion on filter design and filtering results.

POINTS TO DISCUSSION:

Comparison of results for different filter design (order, stability, phase characteristics, delay of output, etc. - FIR x IIR - different IIR filters aproximations)

SIGNALS TO PROCESSING:

HELP: (more details in [4] and [5])

• The filtration in MATLAB is implemented by function FILTER.

• Design of FIR filters (MATLAB functions)
• FIR1 (FIR2) - design using window method
• REMEZ (REMEZORD) - Parks-McClellan algorithm

• Design of IIR filters (MATLAB functions)
• BUTTER (BUTTORD) - Butterworth approximation
• CHEBY1 (CHEB1ORD) - Chebyshev approximation with ripple in pass-band
• CHEBY2 (CHEB2ORD) - Chebyshev approximation with ripple in stop-band
• ELLIP (ELLIPORD) - Elliptic filters (ripple in stop and pass bands)

• Results visualization (MATLAB functions)
• FREQZ - Frequency response of digital filter
• ZPLANE - Zero-poles plot of digital filter transfer function
• ROOTS - Evaluation of polynomial roots (looking for zeros and poles)

GUIDELINES IN DETAILS:

1. Comparison of the design with same order and different filter types
• Design of half band filter with pass band 0 - fs/4.
• Use same order - 10.
• Provide design of FIR and IIR filters.
• See frequency responses and zero-poles plots of obtained results.

2. Design of high-pass, band-pass, and stop-band filters

Repeat the design of above described filter for high-pass filter 0 - fs/4, band pass filter fs/8 - 3*fs/8, and stop-band filter fs/8 - 3*fs/8.

3. Comparison of the design with same tolerance field
• Design of half band filter with following requirements:
- Sampling frequnecy : fs = 8000 Hz
- Pass band cut-off frequnecy : f1 = 3800 Hz
- Stop band cut-off frequnecy : f2 = 4200 Hz
- Maximal ripple in the pass band : Rp = 1 dB
- Minimal ripple in the stop band : Rs = 40 dB
• Provide design of FIR and IIR filters.
• See frequency responses and zero-poles plots of obtained results.

4. Design of band-pass filter into telephone band
• Filter requirements
- sampling frequnecy: 16000 Hz
- pass-band edges: 300 and 3400 Hz
- stop-band edges: 50 and 4000 Hz
- maximal attenuation in pass-band: 0.5 dB
- minimal attenuation in stop-band: 30 dB
• Find a filter fulfiling above given requirements.
• Provide filtering of signal
• reh16.bin and listen results.

5. Filter for removing low frequency noise in speech
• Filter requirements:
- stop-band cut-off frequency: 300 Hz
- pass-band cut-off frequency: 400 Hz
- minimal attenuation in stop-band: 40 dB
- minimal attenuation in stop-band: 1 dB
- sampling frequnecy: 16000 Hz, 8000 Hz
• Find a filter fulfiling above given requirements.
• Provide filtering of signals
• reh16.bin and
• s0001.bin.
• Compare the results of design for different sampling frequencies.