Srinu said:
Hi all, this topic is of electronics-communication interest. Here my
query is, what is the usage of Fourier transform ? Why it is so widely
used in image processing and communication equipments ? Please suggest.
I don't know much about image processing. But it can be very hard to
work out, e.g., the effect of a filter on an arbitrary input signal.
And you can't work it out if you don't know what the signal is. But
that signal can be decomposed into the sines and cosines in the Fourier
transform, and transforming a differential equation can turn it into an
algebraic equation that is much easier to solve. And you can plot
curves of output versus input strength versus frequency, and phase
advance versus frequency, which completely characterizes its behavior.
As long as the circuit is linear, and you know its effect on pure
sinusoidal waves, you're just a Fourier transform away from determining
its effect on all signals.
There's also a great deal of intuition built on that. For instance, a
low-pass filter will block higher frequencies. Its effect on an
arbitrary signal is to smooth out rapid changes. I'm not sure of a good
way to characterize or even to name a low-pass filter if you didn't have
the concept of frequency that comes in with sinusoidal signals.
