[ H(z) = H_mp(z) \cdot S(z) ]
When an audio signal passes through an all-pass filter, different frequencies are shifted in time relative to one another. When multiple all-pass filters are stacked sequentially, this effect becomes heavily magnified. This phenomenon is known as or transient smearing .
An all-pass filter has a completely flat volume response. It lets every single frequency through without making it quieter or louder. However, it forces certain frequencies to slow down slightly. This timing delay changes the of those specific frequencies. The resulting change in timing across the frequency spectrum is what audio engineers call the allpassphase response. The Two main Types of All-Pass Filters allpassphase
To understand how an allpass phase behaves, we look at the transfer function in both the continuous-time (Laplace transform, -domain) and discrete-time (Z-transform, -domain) systems. 1. Continuous-Time (Analog) All-Pass Filters
By applying slightly different allpassphase shifts to the left and right channels of a stereo mix (using a "phase shuffler"), you can alter the perceived width of an instrument. It doesn't sound like a slapback delay; it sounds like the instrument has moved forward or backward in the stereo field. This is a secret trick of mastering engineers for widening pad sounds or background vocals. [ H(z) = H_mp(z) \cdot S(z) ] When
// Update delay lines x2 = x1; x1 = x0; y2 = y1; y1 = y0;
The phase response of a stable, causal all-pass filter is strictly . This means that as frequency increases, the phase angle continuously drops. An all-pass filter has a completely flat volume response
For embedded and real-time applications, a second-order all-pass filter can be implemented efficiently in C using difference equations:
A phase shift is a tiny delay measured in degrees (from 0 to 360) relative to a wave's cycle.
Create rising or falling "whoosh" effects by modulating the filter frequency with an LFO.