Signal Processing with Continuous Wavelets (Advanced Signal Processing Toolkit)

You can use continuous wavelet tools to perform wavelet transforms on signals that are defined in continuous time. Unlike discrete wavelet tools, which operate on sampled-data signals, continuous wavelet tools operate on signals that are defined for all time over a time region of interest, though the computations are done numerically in discrete time.

The LabVIEW Wavelet Analysis Tools provide two continuous wavelet tools: the continuous wavelet transform (CWT) and the analytic wavelet transform (AWT). The AWT retains both the magnitude and phase information of signals in the time-scale or time-frequency domain, whereas the CWT retains only the magnitude information. The CWT is simpler because the results of the CWT are real values if both the wavelet and the signal are real. The results of the AWT normally are complex values.

From a mathematical point of view, both the CWT and AWT add informational redundancy because the number of the resulting wavelet coefficients in the time-scale or time-frequency domain is larger than the number of time samples in the original signal. Excess redundancy generally is not desirable because more computations and more memory are required to process signals with excess redundancy. However, excess redundancy can be helpful for some applications, such as singularity and cusp extraction, time-frequency analysis of nonstationary signals, and self-similarity analysis of fractal signals.