# Integration and derivative of Signals in Simulink | Simulink Tutorial

### Introduction:

Integration and Derivative of signals are both important parts used in many engineering and scientific applications. These applications include examples like signal processing, communication systems, control and measurement applications etc.

**Integration** is a process of finding the integral of an input quantity. This is done over a defined time period. Thus, Integrator block in Simulink calculates the integral of the input signal with respect to time. Simulink uses different numerical approximation methods to compute the output of the integrator. Thus, providing great precision in the results. It works on Laplace Representation of integration.

>> Simulink library>>Simulink>>Continuous>>Integrator

Whereas, **differentiation** is a process to find the rate at which the input changes with respect to some parameter, mostly time. Therefore, Derivative block in Simulink computes the derivative of an input signal with respect to the simulation time.

>> Simulink library>>Simulink>>Continuous>>Derivative

### Model:

** Example**:

The input to the integrator block is the square wave. The output of the integrator is then given to a derivative block. Finally, to observe all the waveforms, we connect all the signals to scope.

Now let’s look at the application of these blocks in the most fundamental part of any communication.

### Modulation:

This** **is a process of changing the properties of a periodic signal (carrier signal). The properties change according to the changes in the message signal. Modulation helps remove most of the errors in transmission and makes the process more efficient. Thus, it is the most fundamental part of any type of communication.

**AM modulation in Simulink:**

Amplitude Modulation is a type of modulation in which the amplitude of the periodic signal i.e. the carrier signal changes according to changes in the amplitude of message signal.

*F(t)=(1+m(t))*c(t)*

*m(t)=Am*sin(2*pi*fm*t)*

*c(t)=Ac*sin(2*pi*fc*t)*

**FM modulation in Simulink:**

A modulation technique in which the frequency of the periodic signal i.e. the carrier signal is changed according to the changes in the amplitude of the message signal is called Frequency modulation.

*F(t)=Ac*cos(2*pi*fc*t + 2*pi*fd*integral(Am*sin(2*pi*fm*t)))*

*m(t)=Am*sin(2*pi*fm*t)*

*c(t)=Ac*sin(2*pi*fc*t)*

The carrier signal is approximated to work as per the simulation time. This is done by creating a linearly increasing variable to represent time using a ramp block.

P.S. There is a use of approximation with time. Thus, the output of FM modulation is not as desired.

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