Question

Frequency response of a discrete-time LTI system is obtained by

• A. Laplace transform of impulse response
• B. Fourier transform of impulse response
• C. Z-transform with \(z=e^{j\omega}\)
• D. Inverse Z-transform

Hint:

For a discrete-time LTI system, \[ \boxed{ H(e^{j\omega}) = H(z)\Big|_{z=e^{j\omega}} } \] where \(z=e^{j\omega}\) represents the unit circle.

Answer 1

The Correct Option is C

Step 1: Recall the transfer function. The transfer function of a discrete-time LTI system is \[ H(z). \]

Step 2: Obtain the frequency response. The frequency response is obtained by evaluating the transfer function on the unit circle: \[ z=e^{j\omega}. \] Thus, \[ H(e^{j\omega}) = H(z)\Big|_{z=e^{j\omega}}. \] Hence, \[ \boxed{\text{Z-transform with }z=e^{j\omega}} \] is the correct answer. Therefore, \[ \boxed{(C)} \] is the correct answer.