Cepstrum
- A cepstrum is a time history defined as the power spectrum of the logarithm of the Power spectrum. This, you can interpret as the spectrum of a spectrum. It extracts periodicities in the spectrum, such as harmonic families and sidebands. The imaginary part is the Hilbert transform.
- If a spectrum contains several sets of sidebands or harmonic series, they can be confusing because of overlap. But in the cepstrum, they will be separated in a way similar to the way the spectrum separates repetitive time patterns in the waveform. Gearboxes and rolling element bearing vibrations lend themselves especially well to cepstrum analysis.
- The cepstrum is closely related to the autocorrelation function.
- Applications
- If a spectrum contains several sets of sidebands or harmonic series, they can be confusing because of overlap. But in the cepstrum, they will be separated in a way similar to the way the spectrum separates repetitive time patterns in the waveform. Gearboxes and rolling element bearing vibrations lend themselves especially well to cepstrum analysis.
- Gearbox analysis
- Bearing analysis
- The cepstrum also has weighting functions, called lifters. The purpose of the lifters is to eliminate a part of the information in the cepstrum before the transformation. For instance, the comb lifter can remove a whole harmonic family.
- Application examples:
- The cepstrum also has weighting functions, called lifters. The purpose of the lifters is to eliminate a part of the information in the cepstrum before the transformation. For instance, the comb lifter can remove a whole harmonic family.
- Echo removal
- Speech analysis
- Gearbox analysis
- Bearing analysis
See also: Autocorrelation, Echo, Echo Location.
Subjects: Mathematics Noise & Vibration Signal Processing