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Question 3 a) Give an example of a second order (three coefficient) FIR filter that has a linear phase response. Show that the obtained FIR filter has a linear phase. [15%] b) Plot the positions of the zeros for the obtained FIR filter in (a). [15%] c) Compute the coefficients of a fourth order (five coefficient) FIR highpass filter which operates at a sampling frequency of 10 kHz and has a cut-off frequency of 2.5 kHz. Use a Hamming window to modify the impulse response of the filter and explain the effect that this has on the amplitude response. [70%]

          Question 3
a) Give an example of a second order (three coefficient) FIR filter that has a linear phase response. Show that the obtained FIR filter has a linear phase. [15%]
b) Plot the positions of the zeros for the obtained FIR filter in (a). [15%]
c) Compute the coefficients of a fourth order (five coefficient) FIR highpass filter which operates at a sampling frequency of 10 kHz and has a cut-off frequency of 2.5 kHz. Use a Hamming window to modify the impulse response of the filter and explain the effect that this has on the amplitude response. [70%]

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Question 3
a) Give an example of a second order (three coefficient) FIR filter that has a linear phase response. Show that the obtained FIR filter has a linear phase. [15%]
b) Plot the positions of the zeros for the obtained FIR filter in (a). [15%]
c) Compute the coefficients of a fourth order (five coefficient) FIR highpass filter which operates at a sampling frequency of 10 kHz and has a cut-off frequency of 2.5 kHz. Use a Hamming window to modify the impulse response of the filter and explain the effect that this has on the amplitude response. [70%]

Added by Crystal M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

06/02/2023

Step 1

e., $h_0 = h_2$. Let's consider an example with $h_0 = h_2 = 1$ and $h_1 = 2$. So, the FIR filter becomes: $$ H(z) = 1 + 2z^{-1} + z^{-2} $$ To show that this filter has a linear phase response, we can compute the phase response as follows: $$ \angle H(z) = Show more…

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Question 3 a) Give an example of a second order (three coefficient) FIR filter that has a linear phase response. Show that the obtained FIR filter has a linear phase. [15%] b) Plot the positions of the zeros for the obtained FIR filter in (a). [15%] c) Compute the coefficients of a fourth order (five coefficient) FIR highpass filter which operates at a sampling frequency of 10 kHz and has a cut-off frequency of 2.5 kHz. Use a Hamming window to modify the impulse response of the filter and explain the effect that this has on the amplitude response. [70%]

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