# How use FIR filter for simulating an integral implemented using the trapezoidal integration?

Suppose I have this equation $$\phi = \frac{60}{T^5} \int_0^T \left( T^2 - 6T \tau + 6\tau^2\right) y(t-\tau) d\tau - \frac{30 \alpha}{T^5} \int(T-\tau)^2\tau^2 u(t-\tau) d\tau$$ and I want to use digital Filter for calculating this integral.

How I can do this? What is the relationship between low pass filter and digital filter in this case?

• Welcome to SE.DSP! I've made the equation an inline one instead of an image. Please try to use LaTeX for equations on this site. Digital filters cannot implement integration in continuous-time, though they can get very good approximations. Do you have any background as to how $y$ and $u$ are converted to discrete-time signals? – Peter K. May 24 '17 at 15:15
• @PeterSmith in reality i use simulink but i don't have background about the best way to convert this signals to continuous time. – Maroua HADDAR Jun 12 '17 at 11:48