Does alternating two frequencies create an intermediate one?

[CyberByte]

I'm kind of new to signal processing and I was wondering what the frequency of a signal of alternating frequencies would be. The signal would contain full periods of two different frequencies, let's say 1 and 2 Hz to keep things simple. The signals can be represented like this:

time:   0 1 2 3 4 5 6 7 8 9 10 11
signal: + - + + - - + - + + -  -

where the signal repeats and each time unit lasts 0.25 seconds, so the signal at times 0 and 1 is 2 Hz and between 2 and 5 is 1 Hz (also see image).

Now, do I just have two signals of 1 and 2 Hz respectively, or did I somehow create a signal of 1.333 Hz?* According to Wikipedia I'm supposed to determine frequency by dividing the number of periods by the time passed. If I do this after 0.5 seconds (2 time units), the frequency is 2 Hz, after 1.5 seconds it would be 1.333 Hz and if I ignore the first 2 time units (or I would have started the signal with the 1 Hz sequence) it should be 1 Hz. So I guess it may not be very clear cut and it depends on the application...

I basically want to make part of my computer screen flicker at a certain frequency, but my hands are tied by the refresh rate and I was wondering if I could just get the desired frequency by alternating between frequencies that the monitor can natively generate. I need to know if people would perceive the above case as a flicker of 1.333 Hz, or something else (but this is not important enough to warrant a full-blown experiment).

Thanks for your time!


* It's 1.333, because the 1 Hz period lasts twice as long as the 2 Hz period. In order to get 1.5 Hz you would need a signal like this: + - + - + + - -.

 

[biff44]

Re: Does alternating two frequencies create an intermediate

Well, kind of. If you look over a long time average, say in a frequency counter, then yes, it will look like a single frequency. And the longer the averaging time, the better it will look.

If you are looking at a very short interval, the instantaneous frequency will appear to hop, though. One thing you could do in the analog world is to lowpass or bandpass filter the composite signal. By eliminating the frequency harmonics, it will look more "sinusoidal".

Maybe a better way to do what you are trying to do is to take a single frequency and step through 4 discrete phase shifts. It is called serrodyne frequency translation.