EquirippleFilter returns linear-phase FIR filters with a frequency response that is optimal in the sense of minimizing the maximum approximation error [

McC73b]. The approximation error is the difference between the desired and the actual frequency responses. The approximation error is spread evenly across the passbands and stopbands of the filter, resulting in a magnitude response that exhibits equal-sized ripples across the frequency domain (see Figure 9.1.1). The

EquirippleFilter design is a Chebyshev approximation problem and uses the Remez exchange algorithm to find a solution.

FrequencySamplingFilter is a simple linear-phase FIR filter design method that returns a filter with an optimum mean squared error fitted to a set of amplitude values spaced uniformly in the normalized frequency range

. There are two possible sequences of sample positions:

Tables have been published that, for a given filter specification, give the value of the best transition coefficient(s) [Rab70]. These coefficients minimize the maximum deviation of the frequency response of the synthesized filter from the frequency response of the desired filter. This is known as minimax optimization.