On Wed, Jun 24, 2020 at 7:46 PM Russell Wedelich <wedel...@gmail.com> wrote:
> Respectively Eric, I think you may be confusing two different use cases > for windows. Your recent reference is referring to constructing FIR filters > via the Windowing method of ideal brickwall filters. This is different from > a frequency domain convolution implementation of an FIR filter (which may > or may not explicitly apply a smooth window) which as far as I can tell is > the origin of this part of the discussion. > And for the convolution implementation of a FIR filter if you were to compare _correct_ implementations of each approach which had adequate(*) internal precision relative to the output, the results would be _bit identical_. (*) In practice, digital implementations of *both* time domain FIR and convolution typically lack enough internal precision such that their output is exact, and as a result they won't be bit identical. Though I wouldn't be surprised if, for a given internal precision, a WOLA implementation using FFTs wasn't *more* faithful to a infinite precision FIR than the same FIR implemented with limited precision, due to the smaller circuit depth for the frequency domain approach.
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