Abdulnasir Hossen and Ulrich Heute
The WaveletBased DFT A New Interpretation, Extensions and Applications
3325 - 3329
2007
1
10
International Journal of Computer and Information Engineering
https://publications.waset.org/pdf/6859
https://publications.waset.org/vol/10
World Academy of Science, Engineering and Technology
In 1990 1 the subbandDFT (SBDFT) technique was proposed. This technique used the Hadamard filters in the decomposition step to split the input sequence into low and highpass sequences. In the next step, either two DFTs are needed on both bands to compute the fullband DFT or one DFT on one of the two bands to compute an approximate DFT. A combination network with correction factors was to be applied after the DFTs. Another approach was proposed in 1997 2 for using a special discrete wavelet transform (DWT) to compute the discrete Fourier transform (DFT). In the first step of the algorithm, the input sequence is decomposed in a similar manner to the SBDFT into two sequences using wavelet decomposition with Haar filters. The second step is to perform DFTs on both bands to obtain the fullband DFT or to obtain a fast approximate DFT by implementing pruning at both input and output sides. In this paper, the waveletbased DFT (WDFT) with Haar filters is interpreted as SBDFT with Hadamard filters. The only difference is in a constant factor in the combination network. This result is very important to complete the analysis of the WDFT, since all the results concerning the accuracy and approximation errors in the SBDFT are applicable. An application example in spectral analysis is given for both SBDFT and WDFT (with different filters). The adaptive capability of the SBDFT is included in the WDFT algorithm to select the band of most energy as the band to be computed. Finally, the WDFT is extended to the twodimensional case. An application in image transformation is given using two different types of wavelet filters.
Open Science Index 10, 2007