Phase Distortion Visualizer

What is Phase Distortion?

Phase distortion is a synthesis method that modifies the phase (timing) of a waveform rather than its amplitude. By distorting how quickly we read through a sine or cosine wave, we can create complex harmonic content without using traditional filters or multiple oscillators.

In terms of phase modulation, this approach shares the same fundamental principle as Yamaha’s DX series FM synthesis—both manipulate phase to generate harmonics. Beyond the algorithms presented here, many modern digital synthesizers implement similar techniques under names like “warp” or “phase shaping” each applying various transformations to the phase domain to sculpt timbre.

The Mathematical Foundation

All phase distortion algorithms follow this common formula:

y = A(φ) · W(2π(φ + Δ(φ)))

Where:

• φ (phi) = Input phase, progressing linearly from 0 to 1
• Δ(φ) (delta) = Phase offset function, unique to each algorithm
• W = Base waveform (sine or cosine)
• A(φ) = Amplitude envelope (optional, used in CZ Reso)
• y = Output signal

Phase Transfer Function Explained

The Phase Transfer graph (upper visualization) shows how the input phase φ is transformed into the distorted phase Φ = φ + Δ(φ):

• Diagonal line: Represents undistorted phase (no modulation)
• Curved/bent line: Shows the actual phase transformation. Even simple operations like raising the phase to a power (φⁿ) can dramatically alter the waveform—higher exponents compress the early portion of the cycle and stretch the later portion, creating saw-like characteristics
• Steep sections: Phase moves quickly → compressed cycle → higher pitch perception
• Flat sections: Phase barely moves → stretched cycle → lower pitch perception
• Vertical jumps: Instantaneous phase shift → discontinuities that add harmonics

“While PD uses piecewise linear functions for Δ(φ), FM implementation uses a sine wave as Δ(φ), creating the classic digital metallic clang.”

How to Use

1. Select an Algorithm: Click on any algorithm button to switch between different modulation types
2. Adjust Amount: Use the slider to control the intensity of phase distortion (0-100%)
3. Observe Changes: Watch the upper graph show how input phase is transformed, and the lower graph display the resulting audio waveform
4. Download: Click “Download Wavetable” to generate a complete wavetable that smoothly morphs through the entire modulation range

Technical Details

Each algorithm applies a unique phase offset function Δ(φ) to transform the input phase φ into a distorted phase Φ = φ + Δ(φ). The output signal is then calculated as y = sin(2πΦ) or y = cos(2πΦ), creating rich harmonic content through phase manipulation alone.

The exported wavetable contains 256 frames that sweep the modulation amount from 0% to 99%, allowing for smooth timbral transitions when used with wavetable-compatible synthesizers.