S+Wavelets Examples

Figure1: This screen demonstrates the best wavelet packet analysis of a quadratic chrip signal. The quadratic chirp is in the upper left and wavelet packet quadratic chrip signal components are in the upper right. A best basis selection tree is in the lower left window. The time-frequency plot in the lower right clearly indicates that frequency increases quadratically over time.

Figure2: The acoustic signal of a porpoise chirp and background noise is displayed in the left panel. The de-noised signal, obtained using a wavelet packet transform, is displayed in the right panel. Plotted below the signals are their time-frequency representations. The time-frequency display gives an estimate of the local frequency content of a signal at a given point in time. The porpoise chirp, mostly obscured by background noise in the original signal, stands out clearly in the de-noised time-frequency display.

Figure3: The Donoho and Johnstone "WaveShrink" procedure for signal extraction and time series smoothing. The Doppler signal is in the upper left and a DWT of the signal is in the upper right. The noisy Doppler signal is shown in middle left and the DWT of the noisy signal is shown in the middle right. In the lower left, the WaveShrink estimate of the signal is shown, with the DWT of the WaveShrink estimate in the lower right. WaveShrink eliminates noise by shrinking wavelet coefficients towards zero.