Filtering with the DFT

February 2, 2019 by 3200 Creative

Filtering with the DFT

Question 1 of 2

1. Question
Why are we interested in using the DFT to implement filtering by multiplying DFT coefficients and then taking the inverse DFT?
- It is more complicated than ordinary convolution and thus looks more impressive
- It is more computationally efficient than ordinary convolution under certain conditions
- It makes an interesting exam problem
- The only reason is because multiplication is more insightful than convolution
Correct

Incorrect
Question 2 of 2

2. Question
Which of the following best describes the overlap and add procedure for filtering a signal $x[n]$ with a system having finite duration impulse response $h[n]$ ?
- Multiply DFT coefficients $X[k]$ and $H[k]$ and take the inverse DFT
- Break $x[n]$ up into blocks, take the DFT of each block, multiply with $H[k]$ , take the inverse DFT and sum a shifted version with the combined time domain signal due to previous blocks
- Overlap a shifted version of $x[n]$ with $h[n]$ and add up the product
Correct

Incorrect