What should I do know to know the frequency from complex signal?

Now I'm trying to digging the DFT function. But nobody tell about the what do we need it at least to solve the dft from the complex signal- a signal with many frequencies

If I got the complex signal as the below,

then what should we have to know at the first time to do DFT? Especially, What kind of things should I have to know to solve a signal with many frequencies?

I've seen some parameter from example as the below when I googling. sampling rate, N, nyquist rate, ..., sort of things. In the practically field for engineer, if they got a that kind signal, how do they do at the first time?

as I know the below image is DFT equation.

then how do we decide the "N" and "m"?

• Welcome to DSP.SE! Why do you say the signal is complex? Do you mean complicated? Here, "complex" means having real and imaginary components. – Peter K. Nov 9 '17 at 20:59
• @PeterK. sorry I give you some misunderstanding. yes exactly your are right. I mean that is a signal with many frequencies. – start01 Nov 10 '17 at 0:25
• capital $N$ is the number of values your signal has (the length of $x(n)$), lowercase $n$ is just the variable, used in the summation to solve for $X(m)$. – goldrik Nov 10 '17 at 2:43
• @goldrik As you know the real world's signal is continuous not discrete. so we need to discrete it from continuous signal. but I don't know how do we decide length of signal? – start01 Nov 10 '17 at 4:29
• Yes, if you're starting with a continuous signal, then it should be discretized before applying the DFT. However, the number of samples you use is entirely up to you; this decision will not change the way you apply the transform (of course, you should follow the Nyquist Sampling Theorem when discretizing, but that's a different problem). I do believe your example signal is already discretized, since there is clearly a value at each time step (the plot just connects the points). – goldrik Nov 10 '17 at 5:11

When you say "complex" signal, I assume you mean just a signal with many frequencies, and not a "complex-valued" signal, in which the the signal values themselves are complex numbers. Let me know if I am incorrect in this assumption. (Actually, computation of DFT is the same in either case).

I'm also assuming your signal is discrete.

The discrete Fourier Transform, $F(\omega)$, can be found by solving the following equation (where N is the number of samples your signal, $f[n]$, contains)

$$F(\omega) = \sum_{n=0}^{N-1} f[n] e^{\frac{-j 2\pi \omega n}{N}}$$

Alternatively, you could use the function fft() on MATLAB.

• sorry I give you some misunderstanding. yes exactly your are right. I mean that is a signal with many frequencies. – start01 Nov 10 '17 at 0:20

In the practically field for engineer, you should at least get into a summary of all signal processing concepts you have mentioned.

As an example, sample frequency refers to the frequency at which your are obtaining a sample from an continuous signal (i.e Electric signal from a sensor).