What are PSD
and ESD? What is the Difference from the Power Spectrum?

**PSD** is a spectral function expressed as a
power value per unit frequency range (1Hz width) which is
independent of the frequency resolution *Δ f* computed with the
FFT, and is frequently used as an unsynchronized signal forming a
continuous spectrum, in other words, for evaluation of irregular
(random) signals. When the signal *x*(*t*) physical unit
is an EU, this unit becomes EU^{2}/Hz. In practice, if the
vertical axis is voltage (V), it becomes V^{2}/Hz or its
square root V/√Hz, and is frequently used as a value for evaluation
of noise in amps, etc.

In the field of random vibration tests, the vertical axis is
acceleration vibration (in m/s^{2}), and is referred to as **ASD (Acceleration Spectral Density)**, and is expressed in (m/s^{2})^{2}/Hz
or m^{2}/s^{3}.

See the following for details of the method of computation.

**ESD** is the function expressing the energy frequency
distribution of the time signal* x*(*t*), and is used for
evaluation of transient signal (e.g. impulse signals) spectra. It is
computed without the averaging operation in the spectrum-related
FAQ [What is Signal Power?], and is therefore obtained by
multiplying the PSD value by the FFT time window length T.

Table 1 Comparison of Three Spectrum Types

Spectrum type | Physical meaning | Relevant signal |
---|---|---|

Power spectrum | Power distribution for each frequency band | Cyclic signal |

PSD | Power distribution for each unit frequency | Continuous random signal |

ESD | Energy distribution for each unit frequency | Transient signal |

Note: PSD and ESD are used primarily in vibration analysis rather than in noise analysis.

Revised:2009/11/16

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