1. An apparatus for computing the discrete Fourier transform of a waveform comprising: input register means for receiving a series of digital data samples representative of said waveform; subtract and hold means connected to said input register means for subtracting the oldest data sample stored in said input register from the newest data sample stored in said input register means; an adder network connected to the output of said subtract and hold means; a multiplier network having a first input connected to the output of said adder network and having a second input; constants storage means connected to said second multiplier network input for outputting to said multiplier network a series of predetermined digital constants; output register means having an input connected to said multiplier network and an output connected to said adder network second input; timing means for gating said input and output register means, said subtract and hold means, said adder network, said multiplier network and said constants storage means at predetermined intervals.