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

LabVIEW 2010 Advanced Signal Processing Toolkit Help

Edition Date: June 2010

Part Number: 371419D-01

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The power cepstrum is an efficient tool for finding different harmonic families in the power spectral density (PSD) of a time series. A power cepstrum is the inverse FFT transform of the natural logarithm of the PSD. You can compute the power cepstrum of a time series as follows:

C(τ) = FFT–1(log(PSD))

The power cepstrum C(τ) is a real-valued time series.

The following figure shows the PSD and power cepstrum of a gearbox vibration signal, respectively.

The PSD graph suggests that the signal contains both periodic and non-periodic components. In the Power Cepstrum graph, you can see that the power cepstrum gives a more clear indication of harmonic peak families than the PSD.

You can modify, or lifter, the power cepstrum and then transform it back to the PSD. The word lifter is an anagram of the word filter, formed by reversing the first three letters. By liftering the unnecessary harmonic peak families, you can remove an individual peak family from the PSD. The following figure shows the PSD of the gearbox vibration signal after you lifter all the harmonic peak families. Notice that the harmonic peaks in the liftered PSD have disappeared.

To lifter the harmonic families, complete the following steps:

1. Compute the power cepstrum of the vibration signal from the PSD.
2. Remove harmonic peaks of individual harmonic family that you want to discard from the power cepstrum.
3. Reconstruct the PSD from the liftered power cepstrum.

If a PSD contains several harmonic families, use the TSA Lifter PSD VI to separate harmonic peaks in the PSD by computing the power cepstrum and filtering the unnecessary harmonic peaks in the cepstrum.