How to prove this convolution problem?

In summary, the conversation discusses various tips and strategies for solving and proving convolution problems. It is recommended to have a strong understanding of the concept and its properties, as well as using algebraic manipulation and known identities to simplify the problem. Common mistakes to avoid include forgetting to include limits of integration and not carefully applying mathematical properties. Resources such as textbooks, online tutorials, and software programs can also aid in solving convolution problems.
  • #1
clw
2
0

Homework Statement


How do I prove that sinc(t) * sinc(t) = sinc(t)?


Homework Equations





The Attempt at a Solution


I converted it to frequency domain and got that rect(f) rect (f) = rect (f) which then converts back to sinc (t). But I'm just curious as how would I go about doing this if I don't convert to frequency domain? I get

[itex]\int ^{\infty} _{-\infty} sinc(\tau) sinc( t- \tau) dt [/itex]

I get stuck at this integral. Any help would be very much appreciated!
 
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  • #2
Tall order, I think.
 

FAQ: How to prove this convolution problem?

How do I approach solving a convolution problem?

The first step in solving a convolution problem is to understand the concept of convolution and its properties. This involves knowing the definition of convolution, understanding how it is represented mathematically, and being familiar with common examples. It is also important to have a strong grasp of basic mathematical operations and techniques.

What is the best way to prove a convolution problem?

The best way to prove a convolution problem is to use algebraic manipulation and properties of convolution to simplify the problem. This often involves breaking down the problem into smaller, more manageable parts and using known identities and properties to solve each part. It is also helpful to have a clear understanding of the end goal and to work backwards from the desired solution.

Are there any common mistakes to avoid when proving a convolution problem?

One common mistake when proving a convolution problem is to forget to include the limits of integration in the final solution. It is also important to correctly set up the integrals and to pay attention to the order of the functions being convolved. Additionally, it is important to carefully apply mathematical properties and not make assumptions without proper justification.

How can I check my solution for a convolution problem?

One way to check your solution for a convolution problem is to plug in a few different values for the variables and see if the result matches the expected output. It is also helpful to compare your solution to known solutions for similar problems. Additionally, it is a good idea to double check all steps and calculations to ensure that no mistakes were made.

Are there any resources or tools that can assist in proving convolution problems?

There are several resources and tools that can be helpful in proving convolution problems. These include textbooks and online tutorials that provide explanations and examples of convolution, as well as software programs and calculators that can perform convolution calculations. Additionally, seeking assistance from a math professor or tutor can also be beneficial in understanding and solving convolution problems.

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