Fourier transform same as signal.

[bhupala]

Hi friends,

I was looking for signals which will have themselves as the Fourier transform. Few of them are given below.

$$\frac{1}{\sqrt{2\pi}}e^{-\frac{t^2}{2}}\longrightarrow e^{-\frac{\omega^2}{2}}$$

$$\sum_{k=-\infty}^{\infty}\delta(t-kT)\longrightarrow \frac{2\pi}{T}\sum_{n=-\infty}^{\infty}\delta(\omega-\frac{2\pi n}{T})$$

can you suggest any other signals which satisfy the property?

regards,
bhupala.

 

[skeptic2]

A pulse in the shape of a gaussian curve?

 

[bhupala]

That is what I have given as the first example.

 

[Redbelly98]

Hi friends,

I was looking for signals which will have themselves as the Fourier transform.
.
.
.
... can you suggest any other signals which satisfy the property?

regards,
bhupala.

Interesting question. What is your application?