A new spectral estimator based on discrete cosine transform and modified group delay

TLDR: In this paper, the authors proposed a new spectral estimator based on discrete cosine transform (DCT) and modified group delay function (MGD) for the clean autoregressive (AR) process.

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 of based on DFT (DFTMGD). The DCT provides reduced bias and hence enables good signal detection ability. The MGD enables better variance reduction without any loss in frequency resolution. For two sinusoids in noise, it has an improvement in variance of about 63% for SNR= 20 dB and 57% for SNR=0 dB, over those of DFTMGD. For the clean autoregressive (AR) process, the root mean square error (RMSE) reduces by 35% over that of DFTMGD. Further it is able to detect a sinusoid which is about 25 dB below AR spectral peaks.