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.

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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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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