Showing papers on "Twiddle factor published in 1978"

z-transform DFT filters and FFT's

Abstract: The paper shows how discrete Fourier transformation can be implemented as a filter bank in a way which reduces the number of filter coefficients. A particular implementation of such a filter bank is directly related to the normal complex FFT algorithm. The principle developed further leads to types of DFT filter banks which utilize a minimum of complex coefficients. These implementations lead to new forms of FFT's, among which is a \cos/\sin FFT for a real signal which only employs real coefficients. The new FFT algorithms use only half as many real multiplications as does the classical FFT.

On Computing the Discrete Cosine Transform

Abstract: Haralick has shown that the discrete cosine transform of N points can be computed more rapidly by taking two N-point fast Fourier transforms (FFT's) than by taking one 2N-point FFT as Ahmed had proposed. In this correspondence, we show that if Haralick had made use of the fact that the FFT's of real sequences can be computed more rapidly than general FFT's, the result would have been reversed. A modified algorithm is also presented.

Two-dimensional zoom FFT

Abstract: The concept of the zoom FFT (a more efficient algorithm which allows zooming in on a narrow segment of the spectrum while preserving its frequency content) is extended to the two-dimensional case. The technique is further expanded to allow zooms over a specified segment within both the time and the frequency domains. Comparisons are also made as to the computational efficiency of this technique compared to the conventional two-dimensional FFT algorithms.