.Wavelet.Transform.cwt

Information

One-dimensional CWT transforms a vector to a two dimensional image. The first dimension (horizontal axis) is the same as the original data. The second dimension (vertical axis) is the scale, similar to frequency. The scales are defined by the input parameter, scales. Larger scale values correspond to lower frequencies.

Refer to the section of wavelet Families for the detailed information about the available wavelets.

The default input values provide a quick example with a simple saw-tooth signal.

Interface

function cwt
  import Modelica.Math.Vectors.*;
  import Wavelet.General.*;
  input Real[:] u = {1.0000, 1.0000, 0.9999, 0.9996, 0.9987, 0.9968, 0.9933, 0.9877, 0.9790, 0.9665, 0.9491, 0.9257, 0.8954, 0.8568, 0.8091, 0.7510, 0.6818, 0.6008, 0.5075, 0.4020, 0.2847, 0.1566, 0.0194, -0.1245, -0.2720, -0.4192, -0.5614, -0.6932, -0.8089, -0.9022, -0.9672, -0.9981, -0.9901, -0.9397, -0.8452, -0.7074, -0.5297, -0.3186, -0.0837, 0.1623, 0.4043, 0.6256, 0.8087, 0.9371, 0.9970, 0.9785, 0.8779, 0.6985, 0.4518, 0.1572, -0.1588, -0.4646, -0.7266, -0.9127, -0.9970, -0.9634, -0.8096, -0.5491, -0.2111, 0.1616, 0.5174, 0.8026, 0.9702, 0.9879, 0.8457, 0.5600, 0.1736, -0.2491, -0.6323, -0.9017, -1.0000, -0.9003, -0.6148, -0.1960, 0.2705, 0.6827, 0.9443, 0.9880, 0.7949, 0.4037, -0.0939, -0.5730, -0.9055, -0.9959, -0.8104, -0.3923, 0.1445, 0.6439, 0.9522, 0.9671, 0.6743, 0.1591, -0.4140, -0.8520, -0.9988, -0.7935, -0.2997, 0.3091, 0.8072, 1.0000} "Signal to be analyzed";
  input Real[:] scales = {1, 4, 16} "Scales to be transformed";
  input Real[:] w = {1, -1} "Wavelet function for the transform";
  input Real[:] x_w = {0, 1} "Regular grid of the wavelet function";
  output Real[size(scales, 1), size(u, 1)] coefs "A two dimensional matrix of wavelet coefficients. 
    Each column corresponds to one element of the input parameter, scales.";
end cwt;