Redundant processing sensitivity

The computational speed of special-purpose Fourier transformers has made redundant processing of data with very narrow resolution bandwidths feasible. One prominent application of this type of equipment is its use as an optimum receiver for detection of narrow-band signals with random phase and unknown frequency. As shown in this paper, the redundantly processed data can be usefully employed to improve the minimum detectable signal over that attainable with independent data. The relationships for processing gain with both time redundancy and frequency redundancy are developed. The values for the processing gains are presented as a function of the amount of redundancy in the data.