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Pitch Extraction
Published in Randy Goldberg, Lance Riek, A Practical Handbook of Speech Coders, 2019
The cepstrum is defined as the inverse discrete Fourier transform of the log of the magnitude of the discrete Fourier transform of the input signal s(n). The inverse DFT and DFT are defined in Equations 3.21 and 3.20. In symbolic notation, the cepstrum is expressed as: () Cepstrum(d)=IFFT(log10|FFT(s(n))|)
Speech Recognition
Published in Sadaoki Furui, Digital Speech Processing, Synthesis, and Recognition, 2018
The Bark and Mel scales are nearly proportional to the logarithmic frequency scale in the frequency range above 1 kHz.Cepstrum method
Industry 4.0-Based Fault Diagnosis of a Roller Bearing System Using Wave Atom Transform and Artificial Neural Network
Published in Pankaj Agarwal, Lokesh Bajpai, Chandra Pal Singh, Kapil Gupta, J. Paulo Davim, Manufacturing and Industrial Engineering, 2021
Rakesh Kumar Jha, Preety D. Swami
Rolling bearings that are used in rotating machinery bear axial and radial loads. Any discrepancy occurring in the bearing element may affect machine operations and lead to machinery disintegration and breakdown over a period of time. Due to the bearing faults generated during machine operations, the failure rate in machines is 40%–50% (Henriquez et al., 2014; Rai and Upadhyay, 2016). Problems in lubrication and component mounting and severe loading are some of the reasons behind the occurrence of the pit and crack formation on the surface of the bearing element. These defective bearings not only affect machine performance but also brings about a partial to complete shutdown of the production system in the long run. The results may turn out to be catastrophic, not only in terms of economical loss because this may endanger the life of the operator as well. It is good to know the machine’s health condition well in advance to avoid such failures. For this purpose, vibration-based machine condition schemes are widely adopted and employed, and these rely on the principle that in standard conditions, rotating machines acquire certain vibration patterns. Any alteration in the pattern indicates that there may be certain irregularities arising in the machine. After the time-frequency-based vibration analysis methods, the envelope spectrum analysis (Yang, 2014; Tyagi and Panigrahi, 2017) comes into the equation. This method is based on the selection of the optimum band for the demodulation of an envelope which is quite crucial. A few years later, fault diagnosis using spectral kurtosis (Antoni, 2006; Randall and Antoni, 2011) was suggested in order to utilise the short-time Fourier transform. Later methods employing cepstrum analysis (Li et al., 2009) were introduced in which the cepstrum would split the harmonics of fault frequencies over a wide frequency range for analysis. Empirical Mode Decomposition (EMD) (Han et al., 2019; Hoseinzadeh et al., 2019), Ensemble EMD (EEMD) (Yu et al., 2017; Wu et al., 2019) and wavelet transform (WT) (Wang et al., 2010) based signal analysis methods were proposed by researchers. WT (Konar and Chattopadhyay, 2011) is a multiresolution transform and decomposes the signals into different frequency sub-bands called levels and, unlike Fourier transform, it simultaneously provides time-frequency information of the signal. Signal processing techniques combined with Artificial Neural Network (ANN) (Amar et al., 2015) and deep learning techniques are the latest trend and are proving to be more effective and reliable.
Condition monitoring systems: a systematic literature review on machine-learning methods improving offshore-wind turbine operational management
Published in International Journal of Sustainable Energy, 2021
Innes Murdo Black, Mark Richmond, Athanasios Kolios
Cepstrum involves taking the inverse Fourier transform of the logarithmic power spectrum. This methodology has been applied in auto-correction ANSIs, which is just performed on the logarithm of the power spectrum, In Cepstrum the correction is mainly focused on the lower harmonics (Geropp 1997).