Thursday, 14 August 2008

Ways To Represent Harmonic Frequencies

Maths gives many options to people applying them. It is flexible as such. And it is where the interesting part comes in, the freedom of choice. Read on ....

There are times where we need to observe the harmonics in a signal to analyse and perform some operations on them. So how are these harmonics shown?

There are 2 basic ways to show what harmonics are.

There are advantage and disadvantage to both presentation. And which presentation to use is subjected to the application objective.

Presentation method:

1) Using time base axis (or domain)
2) Using frequency axis (or domain)

The diagrams below show what I meant.

Diag 1 Time base presentation

This method shows clearly the relationship between the various frequency components in a single graph. We can compare the relative timing between them all.

(Note: Timing is proportional to the angle of the wave).

However, as the number of harmonics get larger, the presentation gets messy and may not reflect clearly the timing relation. So this style of presentation is only suitable for showing small number of harmonic frequencies.

Next is the Frequency domain method.

Diag 2 Frequency presentation

There is another name for this presentation. It is sometimes called the Frequency Spectrum or Frequency Response.

Here the harmonics are marked by the individual vertical lines representing their particular frequencies. The height of each lines identifying their amplitude. The presentation is not as messy as the time base presentation which has many overlapping waves (in a single graph). This method is good if there are many harmonics to be shown.

However, the disadvantage is that we are not able to see the actual shape or profile of these harmonic frequencies, and their relative timings.

Here the concern focuses more on the numerical frequency value as opposed to their shape which is better managed by the time base presentation.

Thus, which presentation method to use depends on the application objective, whether is it waveform shape or frequency value.


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