All-Pass → Phase → Phaser

A filter that appears to do nothing? An all-pass filter passes every frequency at the same magnitude — but changes their phase relationships.

HEAR IT → SEE IT → MANIPULATE IT → NAME IT → SHOW THE MATHS
Watch magnitude stay flat while phase moves. Then add the dry signal and hear why that matters.

1. Same magnitude, different phase

Move the all-pass frequency. The first graph remains at 0 dB; the second graph changes.

Magnitude response

Ideal all-pass chain: 0 dB across frequency.

Phase response

Cascading stages accumulates phase rotation.
Filtering does not have to mean changing level. An all-pass changes phase as a function of frequency.

2. Make phase visible

Dry and processed test sines have the same amplitude. Their relative position changes.

DRYALL-PASS
Phase difference: —

Different frequencies receive different phase shifts: this is not simply one fixed delay applied to everything.

3. Hear it

Try ALL-PASS ONLY, then DRY + ALL-PASS. Noise exposes the notches; saw makes the phaser musically obvious; sine isolates one frequency.

Listen for the trick: all-pass alone retains a flat magnitude response. Sum it with dry and phase differences become reinforcement and cancellation.

4. Add dry → notches appear

Move the frequency here and watch the cancellation notches move. This is the same all-pass frequency control as Section 1.

1.00 kHz
1.00 kHz
With the LFO on, this shows the instantaneous sweep frequency.

All-pass only

Flat magnitude.

Dry + all-pass

Phase cancellation creates notches.
DRY ───────────────────────────┐ ├── Σ ── OUTPUT INPUT → ALL-PASS → ALL-PASS ───┘ ↑ phase changes here

The all-pass does not create these magnitude notches by itself. They appear when the phase-shifted version is summed with dry.

5. Move the phase relationships → Phaser

Modulate the all-pass frequency with an LFO. The phase relationships move, so the cancellation notches move too.

0.35 Hz
75%
LFO │ ▼ DRY ─────────────────────────────────┐ ├── Σ → PHASER IN → ALL-PASS → ALL-PASS → … ───────┘
Fixed all-pass → fixed phase relationships.
Dry + all-pass → notches.
Modulate the all-pass → moving notches.
That is the core of a phaser.

6. Phaser vs Flanger

Flanger

Dry + modulated short delay. The delay creates comb filtering with characteristically regular relationships between peaks and notches.

Phaser

Dry + modulated all-pass chain. Frequency-dependent phase rotation creates the notches when summed with dry.

Same family of idea: alter a signal's phase/time relationship and sum it with the original. Different mechanism.

7. What does the computer see?

A second-order all-pass uses the same familiar biquad structure. Its numerator and denominator coefficients are arranged to give unity magnitude while retaining frequency-dependent phase.

y[n] = b0·x[n] + b1·x[n−1] + b2·x[n−2] − a1·y[n−1] − a2·y[n−2]

Current approximate normalised coefficients:

Same machine — different coefficients. Familiar DELAY, MULTIPLY, ADD and FEEDBACK relationships, rearranged for different behaviour.

Notice the symmetry.

In this all-pass design, the feedforward b coefficients and feedback a coefficients have a deliberately mirrored relationship.

Numerator:     a₂    a₁    1
Denominator:   1    a₁    a₂

That symmetry is what allows the filter to change phase with frequency while keeping its magnitude response flat.

This is a special property of the all-pass design — a and b coefficients do not generally mirror each other in other biquad filters.

8. Why do we care beyond phasers?

All-pass structures are also useful for diffusion. Classic artificial reverberators combine delays, feedback, filtering and all-pass sections to spread energy through time and build dense reflection patterns.

Breadcrumb for later: when we build reverb, this filter comes back.

Phase shift is not inherently bad. It is a normal filter property and a useful tool. It becomes especially audible when signals with different phase relationships are combined.