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...
Convolution for a CT signal is defined as
y(t) = \int_{-\infty}^{\infty}x(\tau)h(t-\tau)d\tau
and for DT it is defined as
y[n] = \sum_{k=-\infty}^{\infty}x[k]h[n-k]
Thus for DT signal we do not have integral but summation.
Just to distinguish for DT case we call it convolution...
Mr EvLer,
There is no big deal in taking j instead of i for imaginary numbers. For engineers, 'i' represents current. To avoid confusion engineers take 'j' for imaginary part.
The Parseval's relation gives you the concept of law of conservation of energy. Both RHS and LHS are just real numbers. You can use frequency domain stuff to calculate Z(\omega) but not by using Paarseval's relation.