Digital design of Chebyshev filter
Background. The Type-1 Chebyshev filter is known to provide the lowest deviation in passband for a given filter order. The transfer function for the second order analogue low pass 3-dB passband ripple Chebyshev-1 filter is given by the following expression
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where ωc = 2πfc and fc is a cut off frequency.
A digital implementation of this analogue prototype is required for cut-off frequency fc = 1 kHz. You are to perform the following tasks 2.A-2.D:
2.A. Develop a digital implementation of the given analogue prototype by impulse invariant method.
2.B. Develop a digital implementation of the given analogue prototype by bi-linear transform method.
Draw the schematic diagrams corresponding to both solutions
2.C. Plot the frequency transfer functions H (ejω ) for both solutions 2.A and 2.B for a couple reasonable sample rates of your choice. Comment on the differences.
2.D. Compare the results of the solutions 2.A and 2.B.