Cross Correlation Between Input-Output Sine Waves I am writing an algorithm to estimate the frequency transfer function of the system. For this, I want to use the Cross-correlation Between Input-Output Sine Waves method. There are a few things I don't understand about method:
I - What does capital N mean?
II - Is and Ic scalar or vector(depend on N)?
These are my thoughts : 
I - N represents the number of outputs I collected for a specific w value with a sampling periode.
II - Scalar.
Could you help?
These formulas are discrete fourier transform.

It's very standard procedure when you analyze wave-alike processes. What it does it transforms the signal from the time-space to the frequencies-space. The idea is that you take sin-wave with specific frequency, multiply it by signal and if the value is big then you have something similar to the wave of this frequency.

$\frac{1}{NT}$ term is just overall time of the sequence (N samples with length T)

The $I_{s}$ and $I_{c}$ is amplitude(intensity) for the sin and cos, respectively. You get them for the specific frequency $\omega$ and it's a single number for each. From this you can get full amplitude (G) and phase $\phi$. Why do you need phase? Because it's important - if you have two waves with similar frequency and $\phi = \pi$, then they would cancel each other, and if they have same phase, they would double.