Estimating the Complex Cepstrum of a Time Series (Advanced Signal Processing Toolkit)

LabVIEW 2014 Advanced Signal Processing Toolkit Help

Edition Date: June 2014

Part Number: 372656C-01

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Unlike the real cepstrum, the complex cepstrum of a time series preserves the phase information of the original time series. Therefore, you can reconstruct the original time series from the power cepstrum. The complex cepstrum is useful in noise reduction, signal separation, and cepstral filtering.

Use the TSA Complex Cepstrum VI to compute the complex cepstrum of a time series. Use the TSA Inverse Complex Cepstrum VI to reconstruct a time series from the complex cepstrum.

The following figure shows an example of removing echoes from a time series by processing the complex cepstrum. In this example, the original signal consists of three signal components: a decaying sinusoid starting at time 0, added with two distinct echoes of that signal later in time, as shown in the Signal with Echoes graph.

As the previous figure shows, you can remove echoes from a time series using the following steps:

  • Compute the complex cepstrum of the original time series using the TSA Complex Cepstrum VI. The peaks appearing in the Complex Cepstrum graph indicate the echo locations.
  • Remove the peaks corresponding to the echoes from the complex cepstrum by setting the peak values to zero. The Peak-Removed Complex Cepstrum graph shows that the peaks have been removed.
  • Reconstruct the original time series from the modified complex cepstrum using the TSA Inverse Complex Cepstrum VI. In the Reconstructed Signal graph, you can see that the reconstructed time series does not contain echoes.

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