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I read Digital Signal Processing of author G.Proakis and see this FIR Filter Structure. I understand all about this but I wonder that what is purpose of classification to 4 structures? Here is this section: enter image description here

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These are just different ways to implement FIR filters. In theory these structures are all equivalent in the sense that they compute exactly the same output signal for a given input signal (under ideal circumstances, i.e., infinite precision), but in practice they behave differently. The differences are mainly the following:

  1. their behavior when implemented with finite word-length
  2. computational complexity
  3. memory requirements

I'm sure that if you continue reading the book, these structures will be explained in more detail, and their relative merits will be discussed.

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