Harmonic analysis vs. Spectral analysis (Part 2 of 4)

Spectral analysis

In Part 1 of this article we discussed harmonic analysis, which is concerned with periodic signals. It was indicated that the analysis interval for the Fourier transform should contain exactly an integer number of periods.

Spectral analysis is mostly concerned with non-periodic signals such as, for example, sound or vibration signals. Although such signals may have periodic components, such as the hum of a motor or a vibration in a gearbox, they are not periodic because there are other components in the signals that are not periodic. Quite often, the periodic components are not easy to see in the time domain because they are hidden in other strong, non-periodic signals and there is no clear periodic repetition in the time signal. This is illustrated in the left time signal below, where the signal is constructed from a single sine signal and a noisy signal. The signal is obviously not periodic and although the sine component in the signal may be recognized, it is not very clear.

In such cases, the Fourier transform is done over a fixed time interval, rather than over a time interval determined by the duration of a single period, as is done with harmonic analysis. It is also common in spectral analysis to use time-domain windowing: the time signal in the analysis interval is first weighted by a dedicated bell-shaped weighting function (like a Hanning or Blackman window) before a Fourier transform is done. Using overlapping time intervals for determining the frequency domain representation is also commonly done.

Spectral analysis is very useful as it makes it possible to determine approximately what the strong frequencies components in the signal are. For example, the periodic components mentioned above (i.e., the sine signal) is hardly distinguishable in the time domain but shows up much more clearly in the frequency domain after spectral analysis (see picture above). Looking at how the strength and frequency of such periodic components change with, for example, the RPM of an electrical machine, may hint at which physical effects are responsible for causing a certain sound or vibration. This dependency between, for example, RPM and periodic components is typically shown in a 3D or Campbell diagram, depicting the changing spectrum as a function of time or RPM.

In #HBK's Perception, real time spectral analysis is available in the Spectral display, where various parameters can be chosen, such as the length of the analysis interval, the percentage overlap, the type of windowing function, etc. More extended analysis functionality is available from #HBK in the BK Connect solution.

In the next part of this article, we will discuss what will happen if you apply spectral analysis to periodic signals. What will be the result in the frequency domain? Will you still get the harmonics of your signal, or not quite?

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