How can I use direct integration to solve for the convolution of two signals?

In summary, the conversation is about the process of convolution and how to calculate it using direct integration. The example given involves convolving two signals, x(t) and h(t), and the question is asking for a method to do this without using graphical methods. The unit step function, u(t), is mentioned and it is causing difficulties in the integration process.
  • #1
Vanush
25
0
Hey guys, I'm having trouble doing ct convolution

i'm trying to convolve two signals together ie, the input x(t) and the impulse response h(t). basically, knowing the impulse response of an LTI system, you can find out the response y(t) to any arbitrary input x(t) using the convolution integral.

in my problem

x(t) = t * ( u(t) - 2*( u(t - 1) + u(t - 2)),
h(t) = u(-t) - u(-t + 1)

So i had a look at examples of calculating the integral using the graphical method, and i get a triangle signal as y(t), convolving the signals above. however, the question wants me to do it using direct integration. I have no idea how to do this! Anyone have any ideas?
 
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  • #2
What is u(t)?
 
  • #3
Unit step function
 
  • #4
He wasn't asking you what that notation meant, but how you should think of interpreting what it means when integrating it.
 
  • #5
THat's the thing, when I put it into the integral I have to work out a bunch of inequalities that really makes my head spin. This question is so much harder than the example :(
 

1. What is continuous time convolution?

Continuous time convolution is a mathematical operation that combines two signals to produce a third signal. It is commonly used in signal processing to analyze and modify signals in continuous time.

2. How is continuous time convolution different from discrete time convolution?

Continuous time convolution involves signals that are defined over a continuous range of time, while discrete time convolution involves signals that are defined at specific time intervals. Continuous time convolution is typically used for analog signals, while discrete time convolution is used for digital signals.

3. What is the mathematical formula for continuous time convolution?

The mathematical formula for continuous time convolution is: f(t) = ∫ x(τ)h(t-τ)dτ, where f(t) is the output signal, x(τ) is the input signal, h(t) is the impulse response of the system, and τ represents the time variable.

4. What are some real-world applications of continuous time convolution?

Continuous time convolution has many applications in various fields, such as audio and video processing, image processing, and telecommunications. It is used to filter out noise from signals, extract useful information from signals, and modify signals to achieve desired effects.

5. What are the limitations of continuous time convolution?

Continuous time convolution assumes that the signals being convolved are time-invariant, meaning that their properties do not change over time. In real-world scenarios, this assumption may not hold true, which can lead to errors in the output signal. Additionally, continuous time convolution can be computationally expensive for large signals or complex systems.

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