Continue studying DFT.
Important things to know: We implement linear convolution by doing circular convolution. Assume we have 2 sequences \(x_{1}\) and \(x_{2}\), both of same length, say \(N\). We can use circular convolution to implement linear convolution. but need \(2N-1\) as the length to do it using circular.
But why do we do this? because circular convolution can then be found in a fast this way: Multiply the DTF of the 2 sequences, then find the inverse DFT.
This is the circular convolution of the 2 sequences. Which is also the linear convolution (if we have the \(2N-1\) length sorted out first). We can always append zeros to the end of the sequences to make the length be \(2N-1\).
Since we have fast algorithm to do DFT and inverse DFT (example, FFT), then this is a way to quickly find linear convolution of 2 sequences.
We had examples showing how to do circular convolution. Make sure to practice this more as it will be on exam.
HW 6 assigned today. We are now going over Handout E on DFT.