A new spectral estimator based on discrete cosine transform and modified groupdelay

Abstract

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.

A New OFDM System Based on Discrete Cosine Harmonic Wavelet Transform (DCHWT) for PSK and QAM

“…Further, the WT coefficients get affected by the leakage effect of DFT because of abrupt signal truncation. The DFHWT is very attractive, provided no processing of the components is involved prior to inverse transformation [11][12][13]. However, for a signal segment obtained without using any smoothing window function, there may be a severe leakage effect from one frequency region/wavelet scale of the signal into another.…”

“…The grouped coefficients for each scale have to be treated as if they are DCT coefficients of that scale in time domain [13]. In view of these advantages, DCHWT has been successfully employed for spectral estimation, compression [11,12]. Due to reduced leakage and computational simplicity of DCHWT, it is of interest to explore its application for OFDM system [14].…”

“…HWT approach, recently the discrete cosine harmonic wavelet transform (DCHWT) has been introduced [11][12][13] and uses DCT instead of DFT. This paper proposes a new OFDM system based on DCHWT for BPSK, QPSK and 16-QAM modulated signals.…”

Discrete cosine harmonic wavelet transform and its application to signal compression and subband spectral estimation using modified group delay

“…4, the general procedure of deriving DCT by taking the DFT of a symmetrically extended signal was considered. The equivalent DFT which has the desired properties of the DCT can only be computed using the analytic DCT [6]. It is not possible to get a DFT equivalent to a DCT, from the DCT, just by applying the inverse DCT and further computing the DFT of the one sided signal of the symmetric signal as this does not exploit the properties of the DCT and it is same as the DFT of the original signal.…”

“…The symmetrical extension reduces the abruptness of truncation significantly and results in a smooth transition from one period to another (due to built in periodicity of DFT), as if there is no windowing and no side lobes to enhance the Gibbs and leakage effects [2], resulting in a significant reduction in the leakage effect or variance. In view of this, the analytic DCT [6] which is the DFT that has the desired properties of DCT, is explored. Such a DFT derived from DCT has a smaller magnitude and frequency bias.…”