Wavelet Translation | Transform from time domain to a subband time-frequency scalogram
|  | Wavelets are small "packets" of signals that can be thought of as high- and lowpass filters. A wavelet transform applies those filters recursively to a signal. This module contains a pyramidal algorithm: The signal is high- and lowpass filtered and decimated (half of the samples are "thrown away"). Then the lowpass filtered signal is again put through the high/lowpass stage and so on until the size of the decimated subband signal is very small (the size of the filter kernel). What you get is a multiresolution subband coded version of the signal, a mixture of a time domain and a frequency domain representation. High frequency information has bad frequency resolution and good time resolution, low frequency information has a fine frequency resolution and a bad time resolution which somehow corresponds to our auditive perception system. Like the fourier transform the transform is invertable. Unlike the fourier transform the signals are always real and not complex and the filter has compact support (i.e. the coefficients are localized in time while the fourier transform uses sinosoidal filters that have an infinite duration).
| Input and output file: Time domain or wavelet domain signal depending on the direction chosen. The output of the forward transform is that of a pyramid: We start with the few coefficients of the last lowpass filter stage followed by the last highpass filter. Next we find the highpass coefficients of the successive scales (going from subbands belonging to lower frequencies to those belonging to high frequencies). Each successive subband is twice as long as its predecessor. Filter: Although an infinite number of filters (wavelets) exist you can only choose between a few that are widely used and were introduced by Ingrid Daubechies. The number after the name corresponds to the filter order (number of coefficients). The difference between the higher order filters is very small while the Daub4 is most different from the others. Try to use different filters for forward and backward transform! Unfortunately the module requests that the input file for a backward transform be of a certain size (the exact size of a forward transform with the same filter). Be careful when you process the forward transformed files because changing the length of the file may cause FScape to reject the file for backward translation. This will be fixed in the next versions. Gain per Scale: Often the coefficents belong to low scales are much higher than those belong to high scales. This can cause problems for integer output files because it will introduce high quantization noise in the high scales. Try to tune this parameter so that the volume of the forward transform output will remain approximately constant over the whole file (alternatively use floating point files). Direction: Forward for time input/ fourier output; backward for fourier input/ time output. Interleaved processing: This is the result of a bug in an early version. By checking this gadget FScape transforms multichannel files not channel by channel but as one big stream of interleaved samples. Beware of monoincompatible phase problems when manipulating the wavelet files! Toolbar: Popup menus for loading and saving settings, presets and options. Refer to a the basic chapter on process windows. Processbar: Buttons for closing the module, starting and stopping processing. Process gauge. Refer to a the basic chapter on process windows. Known bugs: No special treatment of the signal boundaries. Nonzero coefficients beyond the boundaries are thrown away at the moment. For large signals this does not seem to be a problem, however. To be done: Don't refuse input files that have the "wrong" size for backward translation. More filters.
Contents | last modified: 25-Feb-02