Convolutions

Question 1

Describe the typical steps needed to find the result of convolution of signal with a response function in DT?

Answer 1

1. Identify your signal and function
2. Invert one of them (which is easyer) and try to slide it through the other
3. Identify your bounds of full/partial overlap (bit more annoying for DT)
4. Take convolution sum in those bounds for the corresponding values of your signal and response function and calculate it probably using geometric series formula
5. Well thats it :D

Question 2

Geometric series formula

Answer 2

Question 3

Geometric series formula convergence for n -> infinity

Question 4

If you have u[n-3]-u[n-9] as a DT signal at what time n is the first and last non-zero point of the signal?

Answer 4

3 and 8

Question 5

How do you evalueate a convolution sum of two block functions if you know your overlap bounds?

Answer 5

Take the sum from the first to last bound points of your block functions value product. Transform the sum so you can express it as sums from 0 so you can evalueate more easily (maybe geometric series)

Question 6

how do you evaluate sum of 1s from 7 to 12?

ez question

Answer 6

12- 6 = 6

Question 7

Describe the process of convolution of signal through a response function in CT

Answer 7

1. Identify your signal and response functions
2. Reverse one and scroll through the other
3. Find overlap boundaries
4. Take convolution integral with the found bounds and evaluate integral.
5. Thats it