A
Note About Periodic Signals - What is the frequency of a periodic signal.
(If
the frequency is 50 Hz, why is there no component at 50 Hz?)
There are many cases where you examine periodic signals, and you make certain
assumptions. Some years ago, a student did a project with some chimes
and examined the frequency content of the tones that they produced.
There were some surprises in the signals he recorded, and the phenomenon
that he found there is what this note is about. There are always
a few surprises in this business, so here we go.
Here is an expression for a signal.
-
f(t) = 10 sin(2p*100t)
+ 10 sin(2p*150t)
+ 10 sin(2p*200t)
This signal is periodic.
The question is "What is the frequency of this signal?"
The Answer To The Question
At first you might want to say that the frequency of the signal is 100
Hz since that is the lowest frequency sine wave in the signal. However,
150 Hz is not a harmonic of 100 Hz, and you have to be careful. It
helps if you graph the signal. Here is a graph from Mathcad.
-
Notice that the repetition
period is .02 seconds, implying a 50 Hz repetition rate.
-
Also notice that 100,
150 and 200 Hz are all harmonics of 50 Hz.
-
The conclusion is that
you can have a signal that is periodic with a fundamental frequency, but
that there does not need to be a signal at the fundamental frequency.
What we can conclude is
that we don't have to have any component at the fundamental of a signal.
If we have a signal that repeats every T seconds, there is no guarantee
that the signal will have a component at a frequency of 1/T.