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~~~ Filtering ~~~

Started by Mithun Aiyswaryan Sridharan April 28, 2003
dear krishnamachary,

filtering in the "frequency domain" does not mean
convolution in this domain. filtering means u are
taking a product of the Fourier transforms of the
signal x(n) and the system impulse response h(n). the
fourier transforms are X(n) and H(n) and the response
is Y(n). the mapping is x(n)-> FT->X(n) thro FFT which
is computationally faster as to ordinary FT. filtering
is the operation X(n)H(n), the inverse of which gives
teh filtered signal y(n). Y(n)->inverse FT->y(n). the
product in the frequency domain is the convolution of
the time domain signals (ie) y(n)=x(n) conv h(n). this
multiplication and convolution make the fourier
transform pair.

and as to the Fourier co efficients, the FCs are for a
"periodic" signal and NOT for aperiodic sequences. for
aperiodic sequences, u set the periodicity to infinity
and approximate to yield fourier transform. the FT of
a discrete time sequence is a continuous signal in the
Frequency domain. the Fourier coefficients are the
samples of the freqency domain signal. just for the
basic ideas,refer to Proakis. bye

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Mithun Aiyswaryan Sridharan