The Fourier transform of f(x) is \hat{f}(k)={\int }_{- \infty }^{+\infty } dx{e}^{ikx}f(x). If f(x)=\alpha \delta (x)+\beta {\delta }^{\prime }(x)+\gamma {\delta }^{\prime \prime }(x), where \delta (x) is the Dirac delta-function (and prime denotes derivative), what is \hat{f}(k)?

Fourier Transform — CSIR Net PYQ (Question 1)

A Fourier Transform previous-year question (PYQ) from Mathematical Physics (CSIR Net). Read the question, check the correct answer, then practise the full topic.

Question 1 of 6 · 3.5 marks

The Fourier transform of

f (x)

\hat{f} (k) = \int_{- \infty}^{+ \infty} d x e^{ik x} f (x)

.
If

f (x) = α δ (x) + β δ^{'} (x) + γ δ^{''} (x)

, where

δ (x)

is the Dirac delta-function (and prime denotes derivative), what is

\hat{f} (k)

1 $α + i β k + iγ k^{2}$
2 $α + β k - γ k^{2}$
3 $α - i β k - γ k^{2}$
4 $i α + β k - iγ k^{2}$

Correct answer: Option 3

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This Fourier Transform PYQ is part of the Mathematical Physics section of CSIR Net. Browse more Fourier Transform questions or join the PhysicsByAaryan live batch for full conceptual coverage.