Computational Signal Processing with Wavelets
A. Teolis, Naval Research Laboratory, Washington D.C.
0-8176-3909-8 * 1997-Spring * $59.95. * Hardcover * 330 pages
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1-Dimensional Signal Noise Suppression

Here is an example of suppressing noise in a synthetic signal named "opacket". Noiseless wavelet processing of this signal is discussed elsewhere. The processing steps involved are

  1. create the noisy signal (SNR=5dB)
  2. specify a wavelet filter bank (Morlet, CF=40, BW=10)
  3. wavelet transform the noisy signal
  4. threshold and inverse wavelet transform the result and compare with clean original

These steps are outlined in the following.

Create the noisy signal

From the main window of the WSPW select 5 in the SNRdB menu and select opacket in the Signal menu. Depressing the Make button results in the noisy "opacket" signal to be loaded and displayed as shown below.

Specify the wavelet fitler bank

In the Wavelet Interface window (if one does not exist specify cwt in the Transform menu of the main WSPW window) select Morlet in the Family menu and set the (bandwidth) parameter to 10 and the CF (center frequency) parameter to 40 with the #filters menu set to 64. Depress the button Morlet to create the Morlet wavelet filter bank. This results in the display that follows.

Wavelet Transform

Selecting the xform button in the main WSPW window shown above causes the wavelet transform to be computed and displayed in a new window. The cwt of the opacket signal is shown below.

Note that the signal features are well preserved in the wavelet domain and that the effect of the noise is distributed throughout the time-frequency plane.

Threshold Wavelet Transform

Setting the Threshold menu to a value of 20% and depressing the Apply button thresholds the wavelet transform so that only the largest 20% of the transform is retained. The result of the thresholding operation is displayed below.

Invert Thresholded Wavelet Transform

Finally, depressing the invert button performs the inverse wavelet transform on the thresholded version of the wavelet transfrom. This action causes a new window to be spawned with the following plots (counter-clockwise from upper right hand plot)

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