Frequency- and Time-Localized Reconstruction from the Continuous Wavelet Transform
Reconstruct a frequency-localized approximation of Kobe earthquake data. Extract information from the CWT for frequencies in the range of [0.030, 0.070] Hz.
Obtain the CWT of the data.
[wt,f] = cwt(kobe,1);
Reconstruct the earthquake data, adding the signal mean back into the transformed data.
xrec = icwt(wt,,f,[0.030 0.070],'SignalMean',mean(kobe));
Plot and compare the original data and the data for frequencies in the range of [0.030, 0.070] Hz.
subplot(2,1,1) plot(kobe) grid on title('Original Data') subplot(2,1,2) plot(xrec) grid on title('Bandpass Filtered Reconstruction [0.030 0.070] Hz')
You can also use time periods, instead of frequency, with the CWT. Load the El Nino data and obtain its CWT, specifying the time period in years.
load ninoairdata [cfs,period] = cwt(nino,years(1/12));
Obtain the inverse CWT for years 2 through 8.
xrec = icwt(cfs,,period,[years(2) years(8)]);
Plot the CWT of the reconstructed data. Note the absence of energy outside the band of periods from 2 to 8 years.
Compare the original data with the reconstructed data for years 2 through 8.
figure subplot(2,1,1) plot(nino) grid on title('Original Data') subplot(2,1,2) plot(xrec) grid on title('El Nino Data - Years 2-8')