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\(N\)-point DFT using FFT algorithms (radix-2) requires the following complex multiplications

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DFT complexity: \[ O(N^2) \] FFT complexity: \[ O(N\log_2 N) \] This reduction is the main reason FFT is widely used in DSP applications.

Updated On: Jun 25, 2026

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A periodic signal \(x(t)\) of period \(T_0\) is given by \( x(t) = \begin{cases} 1, & |t|<T_1 \\ 0, & T_1<|t|<\frac{T_0}{2} \end{cases} \). The dc component of \(x(t)\) is
- CUET (PG) - 2025
- Electronics Engineering
- Signals and Systems
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Signals and their Fourier Transforms are given in the table below. Match LIST-I with LIST-II and choose the correct answer.

LIST-I	LIST-II
A. \( e^{-at}u(t), a>0 \)	I. \( \pi[\delta(\omega - \omega_0) + \delta(\omega + \omega_0)] \)
B. \( \cos \omega_0 t \)	II. \( \frac{1}{j\omega + a} \)
C. \( \sin \omega_0 t \)	III. \( \frac{1}{(j\omega + a)^2} \)
D. \( te^{-at}u(t), a>0 \)	IV. \( -j\pi[\delta(\omega - \omega_0) - \delta(\omega + \omega_0)] \)