All Pass Filter
From ControlTheoryPro.com

1 Introduction to All Pass Filters
An all pass filter is a filter with a completely flat magnitude response across all frequencies. However, the phase is shifting by 180 °. This is accomplished by a pole zero pair where the real part of the pole equals 1 times the real part of the zero.
2 Basics of an All Pass Filter
For an all pass filter in the sdomain the transfer function is simple.
where
 for a stable filter.
In MATLAB an all pass filter with a 180 ° phase shift at 1 Hz would be formed with the following commands
>> a = 1 * (2*pi); % Convert 1 Hz into rad/sec >> F_AP = tf([1 a], [1 +a]);
3 MATLAB Related Books