You will design a computationally efficient digital IIR band pass filter to meet the following specifications. specbox.m routine is provided to verify that specs are satisfied.
Passband ripple: ±0.005
Lower and upper passband cutoff frequencies: 0.125 and 0.335
Stopband ripple: -42 dB
Lower stopband and upper stopband cutoff frequencies: 0.085 and 0.36
1. Design a normalized lowpass analog filter by using one of Matlab's routines: buttap, cheb1ap, cheb2ap, ellipap to get your analog poles, zeros, and gain. You may also use the corresponding order estimate routines.
2. Perform bilinear and spectral transforms: implement and show your own Matlab module for pole to pole transformation etc for both bilinear transform and spectral transform. Note: you are not allowed to use Matlab routines for bilinear or spectral transforms!
3. Evaluate the magnitude of frequency response for your filter (you may use freqz routine). Using the specbox routine, verify whether the specifications are satisfied. Show all steps of the design process: in particular, include observations and actions taken during multiple design cycles. No one should expect a completely satisfactory design to result from the first design cycle: therefore, you may need to repeat steps 1, 2, and 3 a number of times.
4. Download the file "P2.wav" into Matlab workspace. Use this sound to test your filter: you may use Matlab function filter for this purpose. What do you conclude from listening to the filtered sound? Use "frequency terms".
5. Convert your filter into a cascade of SOS (you may use zp2sos) and repeat filtering the sound by the Matlab module you have developed for the Fundamental form of SFG implementation in P1. What are your observations? Are two filtered signals sound differently? What additional tests would you propose to verify correct functioning of your filter?
6. (Graduate students only) For the cascade of SOS designed in 5, estimate the unit pulse response of the overall system by designing appropriate input/output tests. Report and discuss the result, comment on your method and its advantages/disadvantages.