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 ..