13.2. Definition of Convolution

Try these first

1. 1.

   What is the definition of convolution?

   Hint

   Think about how functions interact with each other.

2. 2.

   Write the formula for convolution as defined in this section.

   Hint

   Recall the limits of integration and functions involved.

3. 3.

   What is convolution primarily used for?

   • Combining functions
   • Differentiation
   • Finding roots

   Hint

   Focus on the operation combining functions.

4. 4.

   True or False: The convolution of f and g is dependent on the order of functions used.

   • True
   • False

   Hint

   Remember the properties of convolution.

5. 5.

   Assuming f(t) = cos(t) and g(t) = sin(t), calculate (f * g)(t) using convolution and state its physical significance.

   Hint

   Think about trigonometric identities or integration techniques.

6. 6.

   In a filtering system represented by h(t), the input signal is f(t) = e^(-at). Show how convolution of these two functions would provide the output signal.

   Hint

   Refer back to the impulse response concept in system theory.