The FourierTransform class is used to calculate the forward and inverse fourier transform. User can select different algorithm implementation, like discrete fourier (DF), split radix (SR) fast fourier transform, etc. The input data and output data are stored in vector objects. The input data can be of either real or complex types.
The Discrete Cosine Transform (DCT) is widely used for speech and image processing, since the DCT has the energy compaction capability and also approaches the statistically orthogonal transformation in decorrelating a signal. The DCT is a close relative of the DFT, but is more computationally efficient for signals that are real and even. For example, in a typical MFCC frontend for speech recognition, we apply an IDCT_II transformation to filterbank coefficients to get an approximation of the cepstrum, which in reality simply represents an orthogonal and compact representation of the log magnitude spectrum.
Since these algorithms have numerous options, we list them separately. The options available for the algorithm choice denoted DFT are:
The options available for the algorithm choice denoted FFT are:
The options available for the algorithm choice denoted DCT are:
The references for the algorithms described in the previous three tables are:
- S. Orfanidis,
Introduction to Signal Processing,
Prentice-Hall, Upper Saddle River, New Jersey, USA, pp. 495,
ISBN 0-13-209172-0, 1996.
- This technique is a variation of the Goertzel algorithm.
A good starting point for details is this description
of the
Goertzel algorithm,
located within the
Ptolemy
toolkit.
- J.G.Proakis, D.G.Manolakis,
Digital Signal Processing - Principles, Algorithms, and
Applications, 2nd Edition,
Macmillan Publishing Company, New York, pp. 727-730, 1992.
- J.G.Proakis, D.G.Manolakis,
Digital Signal Processing - Principles, Algorithms, and
Applications, 2nd Edition,
Macmillan Publishing Company, New York, pp. 727-730, 1992.
- C.S. Burrus and T.W. Parks,
DFT/FFT and Convolution Algorithms - Theory and Implementation,
2nd Edition,
John Wiley and Sons, New York, New York, USA, 1985.
- R.N.Bracewell,
"The Fast Hartley Transform,"
Proceedings of the IEEE,
vol. 72 no. 8, pp. 1010-1018, August 1984.
- H. Guo, G.A. Sitton and C.S. Burrus,
"The Quick Discrete Fourier Transform,"
Proceedings of the International Conference on Acoustics,
Speech, and Signal Processsing,
pp. 453-456, Adelaide, Australia, April 1994.
- A. Saidi, "Decimation In Time Frequency FFT Algorithm," Proceedings of the International Conference on Acoustics, Speech, and Signal Processsing, pp. 453-456, Adelaide, Australia, April 1994.
- K. Rao, and P. Yip,
Discrete Cosine Transform: Algorithms, Advantages
and Applications,
Academic Press, San Diego, California, USA, pp. 15, 1990.
- X. Huang, A. Acero, and H. Hon, Spoken Language Processing, Prentice Hall PTR, Upper Saddle River, New Jersey, USA, pp. 228, 2001.
See the programming examples below for more insight into how to configure these options. We recommend users being by using the default settings, and then explore options systematically from there.