## Wednesday, 13 July 2011

### Give me Some Signals which are Fourier Transforms of itself

One Famous Signal is Gaussian Pulse:

$$\mathbf {e^{-at^2}\Leftrightarrow \sqrt{\frac{\pi}{a}}\,e^{-\frac{\pi^2 \omega^2}{a}}}$$

Can You Think of Any Other Signals other Than Zero(Which is Trivial)??

#### 1 comment:

1. According to Symmetry Property of Fourier Transform

if $$x(t) \Leftrightarrow X(f)$$

Then $$X(t) \Leftrightarrow x(-f)$$

so By Linearity:

$$x(t)+X(t) \Leftrightarrow x(-f)+X(f)$$ and if $x(t)$ is even function Then

$$x(t)+X(t) \Leftrightarrow x(f)+X(f)$$

so FT of Sum of any even Signal and its Fourier Transform is itself. if you find any exceptions plzz comment ..