Convoluted Alternatives

The questions below are due on Thursday April 03, 2025; 02:00:00 PM.
 
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Each of the following parts of this question defines a new function. Your task is to determine if that new function can be expressed as the convolution of two of the following three signals.

Notice that there are ten possible answers. The new function may be equal to any of the following: (a*a), (a*b), (a*c), (b*a), (b*b), (b*c), (c*a), (c*b), (c*c), or none of these options. If the answer is not unique, you will receive full credit for any one of the correct answers.

Part a. Which two functions (if any) can be convolved to produce the following function.

Part b. Which two functions (if any) can be convolved to produce the following function.

Part c. Which two functions (if any) can be convolved to produce the following function.

Part d. Which two functions (if any) can be convolved to produce the following function.

Part e. Which two functions (if any) can be convolved to produce the following function.

Part f. Which two functions (if any) can be convolved to produce the following function.

Please upload a single pdf file that contains your answers to all parts of this problem:

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