# PSD Analysis

Power refers to the magnitude of the PSD is the mean-square value of the signal being analyzed. Spectral refers to a PSD being a function of frequency. Density refers to the power in a band of frequencies under the PSD curve in that band.

### PSD Defined

In the term Power Spectral Density, each word is chosen to represent an essential component of the PSD.

Power refers to the fact that the magnitude of the PSD is the mean-square value of the signal being analyzed. It does not refer to the physical quantity power (as in watts or horsepower). But since power is proportional to the mean-square value of some quantity (such as the square of current or voltage in an electrical circuit), the mean-square value of any quantity has become known as the power of that quantity.

Spectral refers to the fact that the PSD is a function of frequency. The PSD represents the distribution of a signal over a spectrum of frequencies just like a rainbow represents the distribution of light over a spectrum of wavelengths (or colors).

Density refers to the fact that power in a band of frequencies (from a from frequency f1 to a frequency f2) is the area under the PSD curve in that band.

Since the name PSD does not include the quantity being measured, the word power is sometimes replaced by the name of the quantity being measured. For example, the PSD of an acceleration signal is sometimes referred to as the Acceleration Spectral Density.

### Auto Spectral Density (ASD) / Power Spectral Density (PSD)

The PSD plot shows how much power is in a given band of frequencies. In particular, the area under the PSD curve from frequency f1 to frequency f2 is the power (RMS) in that band of frequencies.

The PSD can be used to find resonant frequencies located in a random signal.

### The Statistical PSD Analysis View

PSD shows how correlated (“related”, “statistically connected”, “influenced” by other parts of) a signal is in relation to itself. A signal with “flat” PSD indicates that it is very uncorrelated (“unrelated”, “statistically unconnected”, are not “influenced” by each other, … like consecutive tosses of a fair die). Whereas a signal with some kind of “main lobe” has some degree of correlation. Generally speaking,

• the wider this main lobe is, the more uncorrelated the signal is; and
• the narrower the main lobe is, the more correlated.