The phase response of analog and digital all-pass chains remains closely matched except near the Nyquist frequency, where the digital phase response reaches zero at half the sampling rate while the analog response approaches zero asymptotically—an important consideration when emulating analog phasers in digital environments.
If you pass a sharp, sudden click (an impulse) through an allpass filter, it no longer looks like a sharp click on an oscilloscope. The high frequencies might pop through instantly, while the mid-range frequencies lag behind. The result is a short, sweeping frequency sound, often described as a "chirp" or a "laser" sound.
An all-pass filter is a linear, time-invariant (LTI) system designed to have a constant magnitude response across the entire frequency spectrum. If you pass a signal through an ideal all-pass filter, the output signal will contain the exact same frequency components at the exact same volumes, but the timing—or phase—of those frequencies will be shifted. Mathematically, the frequency response of an ideal all-pass filter satisfies:
If you are looking for the "paper" behind the math or the project itself, here are the most relevant resources:
An all-pass filter is exactly what it sounds like: a filter that allows all frequencies to pass through at equal gain. If you look at a frequency response graph, it’s a perfectly flat line.
[b0, b1, b2] = [k, α, 1] [a0, a1, a2] = [1, α, k]
In mastering, all-pass filters are sometimes used to "smear" the phase of a waveform. By shifting the phase of various harmonics, the sharp peaks of a waveform can be redistributed. This reduces the peak level of the audio without changing its perceived loudness or frequency balance, effectively creating more "headroom" for the final limiters. 3. Creative Sound Design
is a specialized, open-source audio processing tool designed to alter the phase relationship of a sound wave without changing its volume. Developed by enummusic on GitHub , this Virtual Studio Technology (VST) plugin serves as a powerful, free alternative to premium software like Kilohearts Disperser.
Humans are remarkably sensitive to phase at low frequencies. Here is what allpassphase does to perception:
Creating that classic "whooshing" guitar effect by sweeping phase shifts against a dry signal [4].
To truly grasp the power of an allpass filter, one must first understand the concept of in the context of audio. A complex audio signal, such as a drum hit or a spoken word, is composed of dozens or hundreds of individual sine waves, each with its own amplitude (loudness) and frequency (pitch). The phase of a frequency component refers to its specific position within the repeating cycle of its wave—in simple terms, where it is in time relative to a fixed reference point.
In conclusion, the allpass phase is a fundamental concept in audio processing, offering a range of applications and benefits. As the field continues to evolve, we can expect to see new and innovative uses of the allpass phase, pushing the boundaries of what is possible in audio processing.
output[i] = (x0 + y0 * factor) * 0.5; // Variable from bandpass to bandreject
The coefficient a is related to cutoff frequency fc and sample rate fs by: