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This paper proposes a new harmonic wavelet transform (HWT) based on discrete cosine transform (DCTHWT) and its application for signal or image compression and subband spectral estimation using modified group delay (MGD). Further, the existing DFTHWT has also been explored for image compression. The DCTHWT provides better quality decomposed decimated signals, which enable improved compression and MGD processing. For signal/ image compression, compared to the HWT based on DFT (DFTHWT), the DCTHWT reduces the reconstruction error. Compared to DFTHWT for the speech signal considered for a compression factor of 0.62, the DCTWHT provides a 30% reduction in reconstruction error. For an image, the DCTHWT algorithm due to its real nature, is computationally simple and more accurate than the DFTHWT. Further compared to Cohen-Daubechies-Feauveau 9/7 biorthogonal symmetric wavelet, the DCTHWT, with its computational advantage, gives a better or comparable performance. For an image with 6.25% coefficients, the reconstructed image by DFTHWT is significantly inferior in appearance to that by DCTHWT which is reflected in the error index as its values are 3.0 and 2.65%, respectively. For spectral estimation, DCTHWT reduces the bias both in frequency (frequency resolution) and spectral magnitude. The reduction in magnitude bias in turn improves the signal detectability. In DCTHWT, the improvement in frequency resolution and the signal detectability is not only due to good quality DCT subband signals but also due to their stretching (decimation) in the wavelet transform. The MGD reduces the variance while preserving the frequency resolution achieved by DCT and decimation. In view of these, the new spectral estimator facilitates a significant improvement both in magnitude and frequency bias, variance and signal detection ability; compared to those of MGD processing of both DFT and DCT fullband and DFT subband signals.

This paper proposes a new spectral estimator based on Discrete Cosine Transform (DCT) and modified group delay function (MGD) (DCTMGD). The new estimator provides a significant reduction in variance and bias, better signal detection ability and frequency resolution compared with those o f based on DFT (DFTMGD). The DCT provides reduced bias and hence enables good signal detection ability. The M G D enables better variance reduction without any loss in frequency resolution. For two sinusoids in noise, it has an improvement in variance o f about 63% for SNR= 20dB and 57% for SNR=OdB, over those o f DFTMGD. For the clean Autoregressive(AR) process, the root mean square error (RMSE) reduces by 35% over that of DFTMGD. Further it i s able to detect a sinusoid which is about 25 dB below AR spectral peaks.

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