Fourier transform of Rectangular function is ....................... function.
MH SET - 2021, SET Exam - 2021,
Answer: C
The Fourier transform of a rectangular function is a sinc (printed 'Sin C') function.
For a rectangular pulse of height A and width \(\tau\) centred on t = 0:
\[ \begin{aligned} X(f) &= \int_{-\tau/2}^{\tau/2} A e^{-j2\pi f t}\, dt \\ &= A\tau\, \frac{\sin(\pi f \tau)}{\pi f \tau} = A\tau\, \text{sinc}(f\tau) \end{aligned} \]
A sinusoid or cosine in time transforms to impulses in frequency, not the other way round, and an impulse transforms to a constant. So the sinusoidal, cos and impulse options describe transforms of other signals.
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