In this lesson you will learn about the two primary approaches to estimating the power spectrum. The parametric approach assumes the data is generated according to a model, while the nonparametric approach makes no assumptions about the origin of the data. Understanding the advantages of each approach will enable you to choose the appropriate method […]
Estimation of Power Spectra and Coherence
The Periodogram
The periodogram is one of the simplest and oldest – dating back to the late 1800s – nonparametric estimates of the power spectral density. In this lesson you will learn how the periodogram estimates the power spectral density and evaluate the bias and variance properties of the periodogram. Although the periodogram has a serious deficiency […]
The Averaged Periodogram: Welch's Method
The averaged periodogram addresses the limitations of the periodogram by using averaging to reduce variance. Use of averaging to reduce variance is a common theme in many nonparametric spectrum estimators. In this lesson you will learn how the averaged periodogram estimates the power spectral density. You will also learn how choices for window, segment length, […]
Power Spectrum Estimation Examples: Welch's Method
Multiple algorithm parameters must be chosen when using Welch's method, that is, the averaged periodogram. Understanding how to select these parameters to obtain an estimator with desired characteristics is an important step in properly applying Welch's method. In this lesson you will learn how the window, segment length, overlap, and number of segments affect the […]
Estimation of Coherence and Cross Spectra
Coherence and cross spectra are powerful tools for evaluating the relationships between different signals. In practice they must be estimated from measured data. In this lesson you will learn how to estimate coherence and cross spectra using the principles of Welch's method for power spectrum estimation. You will also gain an understanding of how parameters […]
