Question

The frequency response of LTI system is given by the Fourier Transform of the \_____ of the system.

• A. Transfer function
• B. Impulse response
• C. Input
• D. Output

Hint:

The impulse response \(h(t)\) or \(h[n]\) completely characterizes an LTI system.
Its Fourier Transform gives the system's frequency response, describing how the system affects different frequency components of an input signal.

Answer 1

The Correct Option is B

For a Linear Time-Invariant (LTI) system, the frequency response \(H(j\omega)\) (for continuous-time systems) or \(H(e^{j\omega})\) (for discrete-time systems) is, by definition, the Fourier Transform of its impulse response \(h(t)\) or \(h[n]\), respectively. \[ H(j\omega) = \mathcal{F}\{h(t)\} \] The transfer function (\(H(s)\) or \(H(z)\)) is the Laplace or Z-transform of the impulse response. The frequency response is obtained by evaluating the transfer function on the \(j\omega\)-axis (\(s=j\omega\)) or unit circle (\(z=e^{j\omega}\)), if they are in the ROC. \[ \boxed{\text{Impulse response}} \]