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Edinburgh Speech Tools
2.1-release
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Functions | |
int | slowFFT (EST_FVector &real, EST_FVector &imag) |
Basic in-place FFT. More... | |
int | FFT (EST_FVector &real, EST_FVector &imag) |
Alternate name for slowFFT. | |
int | slowIFFT (EST_FVector &real, EST_FVector &imag) |
Basic inverse in-place FFT. | |
int | IFFT (EST_FVector &real, EST_FVector &imag) |
Alternate name for slowIFFT. | |
int | power_spectrum (EST_FVector &real, EST_FVector &imag) |
Power spectrum using the fastFFT function. More... | |
int | power_spectrum_slow (EST_FVector &real, EST_FVector &imag) |
Power spectrum using the slowFFT function. | |
int | fastFFT (EST_FVector &invec) |
Fast FFT An optimised implementation by Tony Robinson to be used in preference to slowFFT. | |
int | fastlog2 (int) |
These are the low level functions where the actual FFT is performed. Both slow and fast implementations are available for historical reasons. They have identical functionality. At this time, vectors of complex numbers are handled as pairs of vectors of real and imaginary numbers.
The Fourier transform of a signal gives us a frequency-domain representation of a time-domain signal. In discrete time, the Fourier Transform is called a Discrete Fourier Transform (DFT) and is given by:
where is the DFT (of order
) of the signal
, where
are the n complex nth roots of 1.
The Fast Fourier Transform (FFT) is a very efficient implementation of a Discrete Fourier Transform. See, for example "Algorithms" by Thomas H. Cormen, Charles E. Leiserson and Ronald L. Rivest (pub. MIT Press), or any signal processing textbook.
int slowFFT | ( | EST_FVector & | real, |
EST_FVector & | imag | ||
) |
Basic in-place FFT.
There's no point actually using this - use fastFFT instead. However, the code in this function closely matches the classic FORTRAN version given in many text books, so is at least easy to follow for new users.
The length of real and imag must be the same, and must be a power of 2 (e.g. 128).
int power_spectrum | ( | EST_FVector & | real, |
EST_FVector & | imag | ||
) |