Saturday, 16 August 2008

Difference Between Frequency And Phase Change

In mathematics, trigonometric expression is represented by y = a sin (bx + c).

The 3 parameters are amplitude (a), period / frequency factor(b) and phase (c).

All 3 parameters, defined by the trigonometric equation, affect the profile of the sine wave.

While the "a" parameter affects the height or amplitude of the sine wave, how does the frequency and phase parameter affects the profile of the wave since they belong to the angular portion of the sine expression?

Let's look at the diagrams below to understand the difference between frequency change and phase change.

We will use a sine wave as reference, and plot another wave with slight frequency change after 2 cycles of the reference sine wave. (diagram 1).

Diagram 1 showing Frequency change as compare to a reference sine wave.

In diagram 1, we can see that frequency change, after 2 cycles into the reference wave, consists of gradual compression (in this case for higher frequency) from longer cycle duration (period) to smaller cycle duration. The blue dashed line, in diagram 1, shows the path to be taken if there is no change to the frequency.

How about phase change?

Diagram 2 shows Phase change compared to a reference sine wave.

In diagram 2, we see that after 2 cycles into the reference sine wave, a drastic twist to the original path occurred. This twist or sudden transition is caused by the phase change that is performed at the same location to reflect the difference between change in frequency and phase parameter.

In diagram 1, the frequency change is 2.5 times the original.
In diagram 2, the phase change is 2.4 radian lagging from the original.

Though frequency and phase are both angular parameter of trigonometric equation, they react differently when there is a change. Phase change is more drastic and will supposedly cause more frequency harmonics to be generated as a result. This is less so for frequency change.


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