APPLICATION of the DFT: Convolution of Finite Sequences. In filtering applications we need to implemenent a linear convolution between the input signal and the impulse response of the filter. zero when

To have all sequences of the same length N-M-1, we pad them with zeros DFT IDFT zero pad DFT

Convolution of Long Data Streams Problem: in general one of the sequences (the data) is much longer than the other sequence (the impulse response of the filter). In this case we do block processing by subdividing the data into smaller sections. There are two methods to perform this operation: Overlap and Save and Overlap and Add. L L L

it depends on the boundary of the block See the convolution of every block by itself: it depends on the boundary of the block

Overlap and Add. Convolve each section and add the “tail” to the next section L L L add add

NOT affected by sectioning of the data See a different way: saved from NOT affected by sectioning of the data

Overlap and Save save L L L Since we disregard the “transient” response we can just use circular convolution discard M-1 values