Abstract
A new adaptive Packet algorithm based on Discrete Cosine harmonic wavelet transform (DCHWT), (DCAHWP) has been proposed. This is realized by the Discrete Cosine Harmonic Wavelet transform (DCHTWT) which exploits the good properties of DCT viz., energy compaction (low leakage), frequency resolution and computational simplicity due its real nature, compared to those of DFT and its harmonic wavelet version. Hence the proposed wavelet packet is advantageous both in terms of performance and computational efficiency compared to those of existing DFT harmonic wavelet packet. Further, the new DCAHWP also enjoys the desirable properties of a Harmonic wavelet transform over the time domain WT, viz., built in decimation without any explicit antialiasing filtering and easy interpolation by mere concatenation of different scales in frequency (DCT) domain with out any image rejection filter and with out laborious delay compensation required. Further, the compression by the proposed DCAHWP is much better compared to that by adaptive WP based on Daubechies-2 wavelet (DBAWP). For a compression factor (CF) of 1/8, the ratio of the percentage error energy by proposed DCAHWP to that by DBAWP is about 1/8 and 1/5 for considered 1-D signal and speech signal, respectively. Its compression performance is better than that of DCHWT, both for 1-D and 2-D signals. The improvement is more significant for signals with abrupt changes or images with rapid variations (textures). For compression factor of 1/8, the ratio of the percentage error energy by DCAHWP to that by DCHWT, is about 1/3 and 1/2, for the considered 1-D signal and speech signal, respectively. This factor for an image considered is 2/3 and in particular for a textural image it is 1/5.
Highlights
The wavelet transform (WT) provides a frequency dependent resolution so that the high and low frequencies have a coarse and fine frequency resolution
This is realized by the Discrete Cosine Harmonic Wavelet transform (DCHTWT) which exploits the good properties of discrete cosine transform (DCT) viz., energy compaction, frequency resolution and computational simplicity due its real nature, compared to those of DFT and its harmonic wavelet version
Since the performance of DFHWT is inferior to that of Discrete Cosine harmonic wavelet transform (DCHWT) [7], the proposed Discrete Cosine Adaptive Harmonic Wavelet Packet (DCAHWP) has not been compared with those of DFAHWP, the wavelet packet (WP) based on DFT
Summary
The wavelet transform (WT) provides a frequency dependent resolution so that the high and low frequencies have a coarse and fine frequency resolution. To achieve for high frequencies, a finer frequency resolution and for low frequencies, a finer time resolution; the wavelet packet (WP) system is used [1] It allows flexibility of selection of wavelet tree structure that enables the WP to select an optimum time-frequency tiling for a given data. This is achieved by adaptive WP and compared to the normal WT, it is more attractive, for applications like signal compression and transient detection [2,3,4,5]. This is because the adaptive nature of WP facilitates better energy compaction
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