Which one of the following is the correct relation ? (a > 0)

Question

Question

This question was previously asked in

NIELIT Scientific Assistant ECE 5 Dec 2021 Official Paper

Answer 1

The correct answer is option 4

Concept:

The time scaling property of Fourier transform states that:

If

Then:

‘a’ any real constant.

Proof:

For a > 0:

Let at = τ. Thus adt = dτ

The above expression can now be written as:

For a < 0:

Let -at = ui – adt = du

Note:

The scaling property states that time compression of signal results in its spectral expansion and vice-versa.