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APPLICATION of the DFT: Convolution of Finite Sequences .

zero when . 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 pad. zero pad.

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APPLICATION of the DFT: Convolution of Finite Sequences .

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  1. zero when 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.

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

  3. 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

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

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

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

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

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