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

The frequency response of a Linear Time-Invariant (LTI) system can be derived by applying the Fourier Transform to its impulse response. To understand why, consider the following explanation:

Impulse Response in LTI Systems:

An LTI system is completely characterized by its impulse response \( h(t) \). The impulse response defines how the system reacts to an input that is an impulse function (a pulse of infinitesimally short duration and unit area).

Fourier Transform:

The Fourier Transform is a mathematical tool that converts a time-domain signal into its frequency-domain representation. It is defined as:

\[ H(f) = \int_{-\infty}^{\infty} h(t)e^{-j2\pi ft}dt \]

Here, \( H(f) \) is the frequency response of the system, and it provides information regarding how different frequency components are altered by the system.

Conclusion:

Thus, given the options, the frequency response of an LTI system is indeed obtained by taking the Fourier Transform of its impulse response.