The expression for Δf i.e., for the transition band is given as

The estimate is used to carry out the design and if the resulting δ exceeds the specified δ2, then the length can be increased until we obtain a side lobe level that meets the specification.

The design method based on the use of windows to truncate the impulse response h(n) and obtaining the desired spectral shaping, was the first method proposed for designing linear phase FIR filters.

The attractive feature of the frequency sampling design is that the frequency response can take either zero or one at all frequencies, except in the transition band.

In the frequency sampling technique, the transition band is a multiple of 2π/M.

By spreading the approximation error over the pass band and stop band of the filter, this method results in an optimal filter design and using this the maximum side lobe level is minimized.

Frequency sampling design method is particularly attractive when the FIR is realized either in the frequency domain by means of the DFT or in any of the frequency sampling realizations.

The values of the cutoff frequencies of a filter in general by windowing technique depend on the type of the filter and the length of the filter.

The chebyshev approximation method provides total control of the filter specifications, and as a consequence, it is usually preferable over the other two methods.

The major disadvantage of the window design method is the lack of precise control of the critical frequencies.