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 EU2/Hz. In practice, if the vertical axis is voltage (V), it becomes V2/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/s2), and is referred to as ASD (Acceleration Spectral Density), and is expressed in (m/s2)2/Hz or m2/s3.
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.


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