Discrete wavelet cycle integration for pulse detection

Current approaches in electromagnetic pulse detection (radar, communications, etc.) use domain transformations so as to concentrate in frequency related information that can be distinguishable from noise. Wavelet transforms are usually described in two main sets: continuous wavelet transforms and discrete wavelet transforms. Although they share mathematical motivation, both transformations have different algorithms and properties. The property we focus on is the time invariance (also called translation invariance). Continuous wavelets are time invariant, but they are also very expensive to calculate. Real time systems find it hard to process all that information with enough accuracy. On the other hand, uniformly sampling the translation parameter as input to the discrete wavelet process destroys this time invariance. In this paper we introduce experimental results that show an alternative way to generate a time invariant representation of a signal using discrete wavelet transforms. This algorithm upgrades the cost-efficiency of pulse detection capability with respect to the basic approach.