A phaser, or phase shifter, is similar to a flanger in that it sweeps notches through the spectrum of an input signal. But while a flanger provides only uniformly spaced notches, a phasor can modulate the frequencies of non-uniformly spaced notches.
A phaser is implemented with allpass filters instead of delay lines, as shown in the block diagram of Fig. 3.
Figure 3:
A digital phaser block diagram.
Second-order allpass filters are particularly convenient to use because each can control a separate notch frequency and bandwidth. Second-order allpass filters have a transfer function given by
where
is the radius of each pole relative to the -plane unit circle (R=1), and the pole angles are . The pole angle can be interpreted as
where is the frequency and is the sampling period.
The phaser will have a notch wherever the phase of the allpass chain is at (180 degrees). This happens close to the complex-conjugate pole pair angles.
The instantaneous frequency response of a phaser created using 4 second-order allpass filters with notch frequencies set at 300, 800, 1000, and 4000 Hz and R = 0.9, 0.98, 0.8, and 0.9 is shown in Fig. 4.
Figure 4:
Instantaneous frequency response of a phaser created with 4 second-order allpass filters and notch frequencies set at 300, 800, 1000, and 4000 Hz.
The depth of the notches can be varied together by changing the feedforward gain parameter .
To achieve the time-varying “phasing” effect, the notch frequencies are modulated with a periodic signal. Note that only a single filter coefficient need be changed in each allpass section to accomplish this.