New approach for detection using wavelet coefficients

Our aim is to detect events in digital signals. To make this detection the signals are considered to be piecewise stationary, with no a priori knowledge of the parameters of the hypotheses on the process state to be detected. The detector is applied on the detail coefficients obtained after the application of the Mallat´s fast decomposition algorithm without reconstruction of the detail signals. The association of wavelet transform and an algorithm of detection such as the cumulative sum applied on adaptive windows produces satisfactory results. The moments of detection obtained on each scale are shifted because the decimation and the convolution between a sequence of an approximation coefficients of a precedent level and the impulsion responses of low pass and high pass filters corresponding to the scaling and wavelet functions respectively. Equations of retiming to obtain the correct moment in original signal show important results.