# Introduction to DSP - filtering: FIR Filter design by window method I

 So the filter coefficients for an FIR filter can be calculated simply by taking the inverse Fourier transform of the desired frequency response. BUT... The inverse Fourier transformhas to take samples of the continuous desired frequency response. to define a sharp filter needs closely spaced frequency samples - so a lot of them so the inverse Fourier transform will give us a lot of filter coefficients but we don't want a lot of filter coefficients We can do a better job by noting that: the filter coefficients for an FIR filterare also the impulse response of the filter the impulse response of an FIR filter dies away to zero so many of the filter coefficients for an FIR filter are small and perhaps we can throw away these small values as being less important Here is a better recipe for calculating FIR filter coefficients based on throwing away the small ones: pretend we don't mind lots of filter coefficients specify the desired frequency response using lots of samples calculate the inverse Fourier transform this gives us a lot of filter coefficients so truncate the filter coefficients to give us less then calculate the Fourier transform of the truncated set of coefficients to see if it still matches our requirement BUT...