Test: Fourier Analysis of Signals, Energy & Power Signals - Electronics and Communication Engineering (ECE) MCQ

x₁(t) = sin15πt is a periodic signal having period

x₂(t) = sin√2 πt is a periodic signal having period T₂ equal to 
∴ 

∴ 

A frequency domain representation of a signal shows the frequency content but not necessarily indicate the shape of the waveform or the combined amplitude of all the input components at any specific time. Hence, assertion is a false statement. Reason is a true statement because in frequency domain, a signal is represented by its frequency spectrum and to obtain frequency spectrum of a signal, Fourier series and Fourier transform are used.

For obtaining the Fourier transform of a signal x(t), it must have infinite number of discontinuities in any finite interval T.

Fourier series analysis is a tool used to
1. analyse any periodic signal only.
2. find how many frequency components are present in the signal.
3. find the relative phase difference between various frequency components.
4. represents a periodic waveform in the form of sum of infinite number of sine and cosine terms.
5. find the amplitude of various frequency components of the series.
Hence, statements 2, 3 and 5 are only correct.

The total average power of a signal is the area of curve under s(f).
Hence,

Given, 
∴ Normalized energy of given signal is

The given signal can be represented as
 (Time constant, 
∴ Fourier transform of x(t) is