The type-1 chebyshev filter nbspis known to provide the

Question

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

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.

Answer 1

The assignment is all about the Digital design of Chebyshev filter. Background: The Type-1 Chebyshev filter is recognized to give the lowest deviation in pass band for a given filter order. The transfer function for the IInd order analogue low pass 3-dB pass band ripple Chebyshev-1 filter is provided by the given expression. Q1. Build up a digital implementation of the particular analogue prototype by impulse invariant process. Q2. Build up a digital implementation of the given analogue prototype via bi-linear transform process. Sketch the schematic diagrams corresponding to both solutions. Q3. Plot the frequency transfer functions H (ej?) for both the solutions 2.A and 2.B for a couple reasonable sample rates of your choice. Remark on the differences. Compare the outcomes of the solutions from the above.