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A method for very fast nonrecursive digital filtering is presented in which over three fourths of the coefficients of the filter impulse response are forced to be zero by the judicious choice of filter center frequency, bandwidth, and window. Nearly half of the remaining coefficients can be discarded by taking advantage of the symmetry of the impulse response, A technique is described for separating a signal into octave bands using the same set of coefficients for each filter operation provided that either the data is "decimated" or the impulse response is "stretched" prior to each pass. Timing comparisons show that this method is faster than Radix 2 FFT convolution using filters with up to 300 coefficients. For many applications, real-time filtering can be achieved by using fixed-point arithmetic and an impulse response having as few as seven nonzero values.