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Design a second-order Butterworth lowpass filter using the impulse invariance method. Let the digital cutoff frequency be w c =.4(pi) radians. Show H a (s)

Design a second-order Butterworth lowpass filter using the impulse invariance method. Let the digital cutoff frequency be wc=.4(pi) radians. Show Ha(s) for the analog filter. Derive an expression for H(z), using either manual calculation or using the MATLAB impinvar function. Also show the LCCDE for implementing this filter.

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