# ~~~ Filtering ~~~

Started by 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 ===== Mithun Aiyswaryan Sridharan