Designing FIR Filters by Windowing

To design a FIR filter by windowing, you start with an ideal frequency response, calculate its impulse response, and then truncate the impulse response to produce a finite number of coefficients. To meet the linear-phase constraint, maintain symmetry about the center point of the coefficients. The truncation of the ideal impulse response results in the effect known as the Gibbs phenomenon — oscillatory behavior near abrupt transitions (cutoff frequencies) in the FIR filter frequency response.

You can reduce the effects of the Gibbs phenomenon by smoothing the truncation of the ideal impulse response using a smoothing window function. By tapering the FIR coefficients at each end, you can diminish the height of the side lobes in the frequency response. The disadvantage to this method, however, is that the main lobe widens, resulting in a wider transition region at the cutoff frequencies. The selection of a window function, then, is similar to the choice between Chebyshev and Butterworth IIR filters in that it is a trade-off between side lobe levels near the cutoff frequencies and width of the transition region.

Designing FIR filters by windowing is computationally inexpensive. It is therefore the fastest way to design FIR filters. It is not necessarily, however, the best FIR filter design method.