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)??
$$ \mathbf {e^{-at^2}\Leftrightarrow \sqrt{\frac{\pi}{a}}\,e^{-\frac{\pi^2 \omega^2}{a}}} $$
Can You Think of Any Other Signals other Than Zero(Which is Trivial)??
According to Symmetry Property of Fourier Transform
ReplyDeleteif $$ x(t) \Leftrightarrow X(f) $$
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 ..