# Optimum Detection of Spread Spectrum Signals

Signal detection and processing are now mostly frequency domain operations due to the easy availability of FFT chips. The paper derives the optimal frequency domain detector which (i) computes the spectral components of the input, (ii) weights each component with the corresponding true spectral component of true signal and (iii) compares the weighted sum against a threshold. When the true signal spectrum is not available, a sub-optimum detector takes simply the peak of the input spectrum as the test statistic. However, the segment length used in the Bartlett spectral estimator for computing the input spectrum has an e ect on the detection performance. The best segment length is inversely proportional to the signal bandwidth. Veri cation of the theoretical development is by simulation of the detection of a frequency hop, digital FM signal.