The Discrete Wavelet Transform for continuous - time signal processingTechnical

A signal processed by the Discrete Wavelet Transform (DWT) must be periodic for perfect reconstruction to be possible. A signal that is non-periodic but which exists for a nite time can be \periodised" by repeating the signal again at its own end, making it suitable for processing by the DWT. For a continuous-time non-periodic signal, the signal has no end and as such it cannot be periodised and thus is unsuitable for processing by the DWT. We describe two alternative ltering methods for performing the DWT on continuous-time non-periodic signals. Both methods have their respective advantages and disadvantages which are discussed. Startup problems exist for both methods where a speciied number of samples at the beginning of processing are either incorrect or unable to be accurately analysed. The eeects of the startup problems are negligible when compared to the size of the signal being processed.