1. Use the impulse-invariant method of IIR filter design to design a digital fil

Question

1.     Use the impulse-invariant method of IIR filter design to design a digital filter with the following specifications. List the %u201Ca%u201D and %u201Cb%u201D coefficients for the digital filter and plot the magnitude frequency response with MATLAB fvtool.

a.     Butterworth low-pass response

b.     4th order

c.     Cutoff frequency of 250 Hz

d.     Sampling frequency 2000 Hz.

Hint: Design the equivalent analog filter first and then use the MATLAB command impinvar to carry out the digital design. See the MATLAB %u201Chelp%u201D information for the relevant commands.

Please post all the MatLab code.

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