How is the average of spectra calculated?

Spectrum averages are classified into two types, [1] power spectrum average and [2] Fourier spectrum average.


The main purpose for executing the average of power spectra under 1ch measurement is improvement of the average of the fluctuating spectrum values in the case of determined signals (for instance, cyclic signals) or statistical spectrum estimated precision in the case of irregular signals. The available averaging methods include [1] arithmetic average, [2] exponential average, [3] peak average, and [4] sweep average.


Arithmetic average is simple average (ensemble average) of power values of each frequency band and is also referred to as RMS average. Exponential average is weighted power average and the average frequency is equivalent to the time constant. Peak average is a technique for keeping the maximum value (N mean count) of power values in the frequency band and strictly speaking, it is not average processing. Sweep average is a technique that uses sine wave signals and determines the spectrum by sweeping (that is changing the frequencies sequentially) the sine wave signals. This  method is classified into an internal signal mode and an external signal mode. In internal signal mode, sine waves that completely synchronize with the FFT resolution are used by using the oscillator that is incorporated in the FFT analyzer, thereby improving the measurement precision.


It must be noted that power spectrum is average processing of power values (that is, EU2 values). Refer to the related item for the actual average method.


Fourier spectrum average, which is an average of complex numbers, is the synchronous average that is concurrently used with the trigger function, and has the same effect as the temporal waveform. This method has a disadvantage of requiring trigger signals. Its advantages include [1] reduction of noise components and [2] average of phase spectra.


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