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Let hLPF(n) be the impulse response of a discrete-time low-pass filter with frequency response HLPF (ej). Show that a discrete-time filter whose impulse response h(n) is given by h(n) = (1)" hLPF (n) is a high-pass filter with the frequency response H(ejw) = HLPF(ej(w−π)). Graph both the responses.

Let hLPF(n) be the impulse response of a discrete-time low-pass filter with frequency response HLPF (ej). Show that a discrete-time filter whose impulse response h(n) is given by h(n) = (1)" hLPF (n) is a high-pass filter with the frequency response H(ejw) = HLPF(ej(w−π)). Graph both the responses.

Operations Research : Applications and Algorithms
Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter9: Integer Programming
Section9.6: Solving Combinatorial Optimization Problems By The Branch-and-bound Method
Problem 3P
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Let hLPF(n) be the impulse response of a discrete-time low-pass filter with frequency response HLPF (ej). Show that a discrete-time filter whose impulse response h(n) is given by h(n) = (1)" hLPF (n) is a high-pass filter with the frequency response H(ejw) = HLPF(ej(w−π)). Graph both the responses.
Transcribed Image Text:Let hLPF(n) be the impulse response of a discrete-time low-pass filter with frequency response HLPF (ej). Show that a discrete-time filter whose impulse response h(n) is given by h(n) = (1)" hLPF (n) is a high-pass filter with the frequency response H(ejw) = HLPF(ej(w−π)). Graph both the responses.
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