The dft, fft, and practical spectral analysis

OpenStax

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The discrete fourier transform

Dft definition and properties

0.3 Dft and idft properties

0.4 Periodicity

0.5 Circular shift

0.6 Time reversal

0.7 Complex conjugate

0.8 Circular convolution property

0.9 Multiplication property

0.10 Parseval's theorem

1 Fast convolution

2 Chirp-z transform

3 Ffts of prime length and rader's conversion

4 Efficient fft algorithm and programming tricks

5 Choosing the best fft algorithm

Spectrum analysis

Spectrum analysis using the discrete fourier transform

0.1 Discrete-time fourier transform

0.2 Discrete fourier transform

0.3 Relationships between dft and dtft

0.4 Dft and discrete fourier series

0.5 Dft and dtft of finite-length data

0.6 Dft as a dtft approximation

0.7 Relationship between continuous-time ft and dft

0.8 Zero-padding

0.9 Effects of windowing

1 Classical statistical spectral estimation

1.1 Periodogram method

1.2 Auto-correlation-based approach

2 Short time fourier transform

Fast fourier transform algorithms

Overview of fast fourier transform (fft) algorithms

2 Goertzel's algorithm

3 Multidimensional index maps

4 The prime factor algorithm

4.1 General index maps

4.2 Conditions for one-to-oneness of general index map

4.5 Conditions for arithmetic savings

4.6 Conditions for short-length transforms to be dfts

Source: OpenStax, The dft, fft, and practical spectral analysis. OpenStax CNX. Feb 22, 2007 Download for free at http://cnx.org/content/col10281/1.2

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