Estimation of Power Spectrum by Using M-transform andWavelet Shrinkage

Abstract

The authors have recently proposed a new signal processing technique called M-transform. By using the M-transform, an impulsive noise is converted into a small-amplitude random signal. We also proposed a new method to remove mixed impulsive noise and white noise simultaneously by applying the wavelet shrinkage to the M-transformed signal. The proposed method was very efficient to remove mixed impulsive and white noise. In this paper, we apply the noise reduction method to estimation of a power spectrum. Frequency transfer function of a linear system can be obtained by using the power spectrum of the input signal and the output signal. In the actual measurement of the frequency transfer function, we must use a periodogram instead of the cross-spectrum and the power spectrum of the input signal. Since the periodogram fluctuates greatly, the estimated frequency transfer function includes impulsive noises. In order to remove these noises, we use the proposed noise reduction method. From the result of the computer simulation, the signal was able to be presumed even when the sinusoidal noise existed