Signal and System : Convolution problem

Thread starter lazyaditya
Start date Mar 10, 2013
Tags

Convolution Signal System

In summary, convolution is a mathematical operation used in signal and system analysis to combine two signals and determine the output of a linear system. Its purpose is to understand how a system responds to different inputs. To perform convolution, one signal is time-reversed and shifted, and then multiplied and integrated with the other signal. The properties of convolution include commutativity, associativity, distributivity, and time shifting. In frequency domain analysis, convolution is equivalent to multiplication, making it useful for analyzing systems in the frequency domain.

Mar 10, 2013

lazyaditya

I have given the question and my attempt in the image that i have loaded please tell me that am i doing it right ?

Physics news on Phys.org

Mar 10, 2013

rude man

Homework Helper

Insights Author

Gold Member

I would if I could read it ...

Mar 10, 2013

lazyaditya

rude man said:

I would if I could read it ...

I have added a new image

Mar 11, 2013

rude man

Homework Helper

Insights Author

Gold Member

I want to double-check this today but right now it looks good.

Mar 18, 2013

lazyaditya

Ok :)

What is convolution in signal and system?

Convolution is a mathematical operation that combines two signals to produce a third signal representing the output of a linear system. It involves multiplying one signal by a time-reversed and shifted version of the other signal, and then integrating the product over time. It is commonly used to analyze the output of a system when the input is known.

What is the purpose of solving convolution problems?

The purpose of solving convolution problems is to understand how a system responds to different inputs. By convolving an input signal with the impulse response of the system, we can determine the output of the system for that particular input. This is useful in fields such as signal processing, communication systems, and control systems.

How do you perform convolution in signal and system?

To perform convolution, you first need to time-reverse and shift one of the signals. Then, you multiply the two signals together at each time point and integrate the product over time. This process is repeated for each time shift of the signal. The resulting output signal is the convolution of the two input signals.

What are the properties of convolution?

The properties of convolution include commutativity, associativity, distributivity, and time shifting. Commutativity means that the order of the inputs can be switched without affecting the output. Associativity means that the order in which convolutions are performed can be changed without altering the result. Distributivity means that convolution is distributive over addition. Time shifting means that convolving a signal with a shifted version of another signal produces the same output as convolving the original signals and then shifting the result.

How is convolution related to frequency domain analysis?

In frequency domain analysis, convolution is equivalent to multiplication. This is known as the convolution theorem, and it states that convolving two signals in the time domain is equivalent to multiplying their Fourier transforms in the frequency domain. This property allows us to analyze systems in the frequency domain, which can sometimes be easier than in the time domain.