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More General FIR Filter Design

We have looked at more than just FIR filter design by the window method and frequency-sampling technique. The general steps were

  1. Prepare a desired frequency-response that ``seems achievable''
  2. Inverse FFT
  3. Window the result (time-limit it)
  4. FFT that to see how it looks
In general, the end result will be a somewhat smoothed version of what we originally asked for in the frequency domain. However, this smoothing will be minimal if we asked for a truly ``doable'' desired frequency response. Because the above steps are fast and non-iterative, they can be used effectively in response to an interactive user interface (such as a set of audio graphic-equalizer sliders that are interpolated to form the desired frequency response), or even in a real-time adaptive system.

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Comparison to Optimal Chebyshev FIR Filter
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Filtering and Windowing the Ideal Hilbert-Transform Impulse Response