# sketching frequency domain representation

I've been given this signal and asked to sketch a frequency domain representation how do i do that? how do you know which frequency components are present in the signal?

This is a classical example of beat. This means that the signal (assuming that it is periodic and extends to plus and minus infinity) contains only two frequencies with the same amplitude. The frequency of the sine wave which seems to enclose the signal will be equal to the difference between the two frequencies. The frequency of the sine wave which seems to be modulated by the enclosing wave will be the mean of the two frequencies which are present in the signal.

• In other words: the signal has the form $\cos(A)\cos(B)$, which is equal to $\cos(A+B)+\cos(A-B)$ (ignoring a scale factor).
– MBaz
May 24, 2016 at 1:01
• so how would you go and estimate the frequency components? May 24, 2016 at 15:14
• @MauriceMoh What is the frequency of the wave which encloses the signal (from where to where does one period occur)? And what is the frequency, which is modulated by this enclosing wave (how many periods can you see of this frequency in this graph)? May 24, 2016 at 16:31

Fourier transform is one of possible tools to use in order to see what is the frequency content of the time domain signal and the other way around (in this case we use inverse Fourier transform). The Fourier transform decomposes a function of time (a signal) into the frequencies that make it up (c/p from Wikipedia)-> there is a lot of material, just google it.

• is there a way that we can just estimate the frequency components since the question is just to sketch a frequency domain graph May 23, 2016 at 15:04
• Well, yes of course. You can see two periodicites in the graph. Which are these two? how are they connected, @MauriceMoh ? May 23, 2016 at 15:08
• i am afraid i don't know May 23, 2016 at 15:21
• so this is what i think between the range of 0.5 to 1.5 there are 11 oscillations hence one of the frequency components would be 11 hz and in the range of 1.5 to 2 there are 5 oscillations hence the other frequency component is 10 hz is this correct? i also don't know what the amplitudes for these frequencies are though. May 23, 2016 at 15:27