# Amplitude value after a Discrete-Time integration calculation?

I am using Matlab block Discrete-Time Integrator on Simulink and I would like to know in advance, what output of that block regarding to its amplitude and the current sampling frequency would be.

For instance, I am setting as input a $${\tt Reference} (t) = A \sin(\omega t)$$ where $A = 0.4$ and $\omega = 2\pi\cdot 2KHz$, the outcome of Discrete-Time Integrator is my ${\tt Reference} (t)$ integrated a cosine function as expected $$ve[n] = -B \cos[\Omega n]$$ with $B=2.55*10^4$

However, as shown in the picture the amplitude $B$ is quite large, which puzzles me. I am aware that the integrator scales the output with $K T_s$, being my $f_s = 200MHz$. So I was wondering whether or not there is an expression that allows me know that scale factor in the amplitude that is happening after the integration, I am aware that is related to my sampling time but I cannot figure out how or what is.

## 1 Answer

I figured it out coming back to basic maths, I was making a mistake when integrating my sin function that Matlab block wasn't doing, I was missing behind the $\omega$ variable

$$ve[n] = -B \cdot \cos[\Omega\cdot n] = \int A\sin(\omega\cdot t) = (A/\omega)(-\cos(\omega\cdot t)) + Const$$ $$\mathbf {B = (A/\omega) }$$