Question

The property of Fourier Transform which states that the compression in time domain is equivalent to expansion in the frequency domain is ___________

(a) Duality

(b) Scaling

(c) Time scaling

(d) Frequency shifting

The question was posed to me in quiz.

My question is taken from Fourier Series Analysis using Circuits topic in portion Fourier Analysis on Complex Spaces of Signals and Systems

Answer 1

Right answer is (b) Scaling

To elaborate: We know that the definition of Fourier Transform states that Fourier Transform is a function derived from a given function and representing it by a series of sinusoidal functions. The property of Fourier Transform which states that the compression in the time domain is equivalent to expansion in the frequency domain is Scaling can be found by putting the value of pulse function in the definition of Fourier Transform.