Periodogram and Welch Method Revisited
SPECTRAL ANALYSIS OF NONPARAMETRIC METHODS & IMPROVED WELCH METHOD VIA CIRCULAR OVERLAP
Svs Gopala Krishna, S.Mujassim, Prof.D.Ramachandra Reddy School of Electronics Engineering, VIT University, Vellore- 632014, Tamilnadu, India. gopal.svsemails@gmail.com; mujassim@rediffmail.com
Abstract The objective of this paper is to overcome the drawback in the Welch method. The major problem with the Welch method is that the variance is not monotonically decreasing with respect to the amount of fraction of overlap. It is difficult to choose the fraction of overlap which gives optimum variance value as its dependent on the type of the window used. By replacing the regular overlap mechanism of the Welch method with a circular overlap we can achieve the monotonic decrease in variance as the fraction of overlap increases. This paper is analyzed in two fold manner. The first part gives preface to all non-parametric methods and comparison of all the methods in terms of two statistical parameters viz. variance and resolution. The second part of this literature deals with the modification of the standard Welch method to get a monotonic decrease in variance. Index Terms— Non-Parametric, Periodogram, Variance, Resolution, Windowing, Power Spectrum, Bartlett method, Welch method. I. INTRODUCTION SPECTRUM ESTIMATION is an important application of the Digital Signal Processing. Spectral analysis is used in many applications such as to get the target location and its velocity information in the radar applications [9]. In general many practical applications such as Ocean noise, Wind speed give a time series data [10]. This data can be analyzed using spectral analysis. Spectrum estimation is a problem that involves estimating the power spectrum of the signal from a finite number of noisy measurements of the signal. The techniques adopted for the analysis of power spectrum estimation (PSE) are classified into two classes: 1.Parametric and 2.Non-parametric methods. In our literature, we
Svs Gopala Krishna, S.Mujassim, Prof.D.Ramachandra Reddy School of Electronics Engineering, VIT University, Vellore- 632014, Tamilnadu, India. gopal.svsemails@gmail.com; mujassim@rediffmail.com
Abstract The objective of this paper is to overcome the drawback in the Welch method. The major problem with the Welch method is that the variance is not monotonically decreasing with respect to the amount of fraction of overlap. It is difficult to choose the fraction of overlap which gives optimum variance value as its dependent on the type of the window used. By replacing the regular overlap mechanism of the Welch method with a circular overlap we can achieve the monotonic decrease in variance as the fraction of overlap increases. This paper is analyzed in two fold manner. The first part gives preface to all non-parametric methods and comparison of all the methods in terms of two statistical parameters viz. variance and resolution. The second part of this literature deals with the modification of the standard Welch method to get a monotonic decrease in variance. Index Terms— Non-Parametric, Periodogram, Variance, Resolution, Windowing, Power Spectrum, Bartlett method, Welch method. I. INTRODUCTION SPECTRUM ESTIMATION is an important application of the Digital Signal Processing. Spectral analysis is used in many applications such as to get the target location and its velocity information in the radar applications [9]. In general many practical applications such as Ocean noise, Wind speed give a time series data [10]. This data can be analyzed using spectral analysis. Spectrum estimation is a problem that involves estimating the power spectrum of the signal from a finite number of noisy measurements of the signal. The techniques adopted for the analysis of power spectrum estimation (PSE) are classified into two classes: 1.Parametric and 2.Non-parametric methods. In our literature, we