### Example Zero-Phase Filter Design

Figure 10.1 shows the impulse response and frequency response
of a length 11 zero-phase FIR lowpass filter designed using the Remez
exchange algorithm.^{11.2} The matlab code for designing this filter is as
follows:

N = 11; % filter length - must be odd b = [0 0.1 0.2 0.5]*2; % band edges M = [1 1 0 0 ]; % desired band values h = remez(N-1,b,M); % Remez multiple exchange designThe impulse response

`h`is returned in linear-phase form, so it must be left-shifted samples to make it zero phase.

Figure 10.2 shows the amplitude and phase responses of the FIR
filter designed by `remez`. The phase response is zero
throughout the passband and transition band. However, each
zero-crossing in the stopband results in a phase jump of
radians, so that the phase alternates between zero and in the
stopband. This is typical of practical zero-phase filters.

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Elementary Zero-Phase Filter Examples

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Summary of Series/Parallel Filter Sections