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Power Spectrum Estimation Techniques

A power spectrum demonstrates the distribution of energy in a time series relative to its frequency domain. As a time series might contain irregularly sampled periods of signal, the power spectrum is generally considered continuous, which requires a representation of that frequency̵7;s values to be proportional to its frequency interval. In order to remove that dependence on interval, the power spectrum can be normalized to represent its power spectral density, or PSD.

What is PSD?
- PSD is defined as measuring the signal power of a spectrum per each unit in its bandwith, as measured in volts driving a 1 ohm feed, or V^2/Hz. If your PSD value is represent in decibel format (dB), the unit for the PSD changes to dB ref V/sqrt(Hz). In order to calculate the PSD of a time series, you̵7;ll need to make sure to convert your units to whatever unit you are measuring for that span.
Parametric vs. Nonparametric Methods
- The two major methods of PSD estimation are parametric and nonparametric. Parametric methods involve using parametric models of a time series based on a series of finite numbers, using gathered to form a single vector. These methods take for granted that the time series is part of a linear system that can be measured in response to white noise. In order to estimate a PSD using parametric methods, you will need to gather the model parameters of the series, one that reflects the behavior of the contained system.
Nonparametric Methods
- Finite vs. Infinite Systems.
  
  Nonparametric methods are based on a time series that are considered infinite, and thus do not require you to gather the parameters or a model of the system before proceeding. These methods are instead based on a process called data windowing, where a selection of data is used in place of the entire system. This results in a slight distortion of the results, due to the constrained sample, but also allows the estimation period to avoid peaks where the data goes far outside its expected behavior.
Examples of Nonparametric Methods
- Nonparametric methods are based on the discrete Fourier transform, which is an algorithm designed to transform samples of a time period into its frequency domain. It is used commonly for spectral analysis, telecommunications, acoustics, medical imaging and so on. Common examples of nonparametric methods include the periodogram method (which is the most common), Welch method (which divides its sequences into subsequences) and Capon method (which uses output power through a bandpass filter to limit the response).

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