In this thesis, we present a development of the discrete evolutionary transform (DET) and its application to the excision of multi-component jamming signals in spread spectrum communications. The discrete evolutionary transform provides a time-frequency kernel from which the evolutionary spectrum and the representation of a non-stationary signal are obtainable. We consider the Malvar wavelet expansion to define the window used in the DET. Two types of transform are shown: the sinusoidal and the chirp DETs.; Instantaneous frequency, an important characteristic of signals found in practical applications, is estimated by using the DET and the Hough transform. The Hough transform of the evolutionary spectrum provides a piecewise linear estimate and information about the number of components contained in the signal. The estimation is done locally without parameters. The estimates are then improved by a recursive correction procedure. Involving the estimated instantaneous frequency in the chirp DET yields an improved time-varying spectral representation of the signal.; To protect transmitted data bits against unintentional or intentional interferences, military and civilian communications rely on spread spectrum communications techniques. Although, robust to noise and narrow-band jammers, the protection provided by direct sequence spread spectrum (DSSS) might be insufficient against wide-band jammers. We propose a jammer excision procedure to enhance the interference resistance of the DSSS system by subtracting a synthesized jammer from the received signal. The synthesis of a multi-component jammer is done by either lowpass filtering, singular value decomposition or averaging. The DSSS simulation results show that the proposed excision method is capable of removing the jamming signal thereby decreasing the bit error rate. The recently proposed projection method, based on instantaneous frequency of jammers, is used to compared with our procedure.; Statistical analysis of the excision performance is presented in terms of signal to interference and noise ratio (SINR) and probability of bit error. The SINR can be used to indicate how much jamming signal leaks from the exciser. To compute the SINR, two cases are considered: perfect phase, and estimated phase with errors assumed to be Gaussian distributed. The SINR resulting from our exciser is close to the best SINR (no jamming) for the case of perfect phase and it is greater than the worst SINR (no excision) for the case of estimated phase. The comparisons between SINRs obtained from simulations and the theoretical SINRs, derived from using the proposed excision and the projection excision, are given. The probabilities of bit error have the same trend as the bit error rates.
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