On the Grunbaum Commutor Based Discrete Fractional Fourier Transform
نویسنده
چکیده
The basis functions of the continuous fractional Fourier transform (FRFT) are linear chirp signals that are suitable for time-frequency analysis of signals with chirping timefrequency content. Efforts to develop a discrete computable version of the fractional Fourier transform (DFRFT) have focussed on furnishing a orthogonal set of eigenvectors for the DFT that serve as discrete versions of the Gauss– Hermite functions. Analysis of the DFRFT obtained from Grunbaum’s tridiagonal commuter and the kernel associated with it reveals the presence of both amplitude and frequency modulation in contrast to just frequency modulation seen in the continuous case. Furthermore the instantaneous frequency of the basis functions of the DFRFT are sigmoidal rather than linear.
منابع مشابه
Erratum to "On discrete Gauss-Hermite functions and eigenvectors of the discrete Fourier transform" [Signal Processing 88 (11) (2008) 2738-2746]
1. Page 2741, caption of Fig. 2: three occurrences of ‘‘commutator’’ instead of ‘‘commutor’’, i.e. the caption should read Fig. 2. Eigenvalue decomposition of the commutor for the CDFT: (a) sorted eigenvalues of the commutor T1 for N 1⁄4 128. (b) Selected symmetric and skew-symmetric eigenvectors of the commutor for k 1⁄4 0,1, 2, 3. 2. Page 2743, fourth sentence after Eq. (14): ‘‘commutator’’ i...
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