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.