Digital pulse compression via fast convolution

The mathematical structure of the digital ambiguity function for a matched filtered linear FM (LFM) waveform is derived as a function of time-bandwidth product, sampling rate, and arbitrary delay and frequency shifts. It is found to be well behaved for sampling rates equal to or greater than the swept signal bandwidth, provided that time sidelobes are controlled using standard frequency domain weighting techniques. A digital convolution processor comprised of cascaded pipeline fast Fourier transforms (FFT's) is presented as a viable architecture for real-time filtering of moderately high bandwidth LFM signals, and tradeoffs among radix, pipeline clock rate, and convolutional efficiency are discussed. It is found that a modified floating-point computational scheme performs well in such a context and is especially useful if a large signal dynamic range must be accommodated. A radix-4 4096-point design example is considered and the effects of quantization and finite register length arithmetic upon the digital ambiguity function are demonstrated via simulation. It is found that input data, FFT coefficients, reference filter coefficients, and intermediate results can be represented with mantissas of modest bit length.