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What is the relationship between the impulse response h[n] of a system and its frequency response H(ejωe^ {jω}ejω​) ?
Question

What is the relationship between the impulse response h[n] of a system and its frequency response H(ejωe^ {jω}​) ?

A.

The frequency response is the DTFT of the impulse response

B.

The impulse response is the inverse DTFT of the frequency response

C.

The impulse response is equal to the frequency response at ω=0

D.

The impulse response is the Fourier series of the frequency response

Correct option is A

For a discrete-time LTI system: The impulse response is h[n] The frequency response is obtained by taking the Discrete-Time Fourier Transform (DTFT) of h[n]H(ejω)=n=h[n]ejωnThus, the frequency response describes how each frequency component of the input is affected by the system.\text{For a discrete-time LTI system:} \\[8pt]\bullet \ \text{The impulse response is } h[n] \\[4pt]\bullet \ \text{The frequency response is obtained by taking the Discrete-Time Fourier Transform (DTFT) of } h[n] \\[10pt]H(e^{j\omega}) = \sum_{n=-\infty}^{\infty} h[n] e^{-j\omega n} \\[10pt]\text{Thus, the frequency response describes how each frequency component of the input is affected by the system.}​​

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