title: The Fft, Fundamentals and Concepts
author:  Robert W. Ramirez 
description: Simple and concise discussion of both Fourier Theory and the FFT (fast fourier transform) are provided. Math is held to a minimum: concepts are illustrated in detail with over 100 drawings and waveform photographs. For jr/sr or grad level courses in Signal Processing or courses on Fourier Analysis in Electrical Engineering and Electronic Technology departments.
zlib_text: A history of cepstrum analysis and its application to mechanical
  problems
  Robert B. Randall
  School of Mechanical and Manufacturing Engineering, University of New South Wales, Sydney 2052, Australia
  a r t i c l e
  i n f o
  Article history:
  Received 9 August 2016
  Received in revised form 13 December 2016
  Accepted 20 December 2016
  Available online 30 December 2016
  Keywords:
  Cepstrum analysis
  History
  Gear diagnostics
  Machine diagnostics
  Operational modal analysis
  a b s t r a c t
  It is not widely realised that the ﬁrst paper on cepstrum analysis was published two years
  before the FFT algorithm, despite having Tukey as a common author, and its deﬁnition was
  such that it was not reversible even to the log spectrum. After publication of the FFT in
  1965, the cepstrum was redeﬁned so as to be reversible to the log spectrum, and shortly
  afterwards Oppenheim and Schafer deﬁned the ‘‘complex cepstrum”, which was reversible
  to the time domain. They also derived the analytical form of the complex cepst