Phase Frequency Analyzer

Phase response tells you the time offset that every frequency in your signal sees as it passes through a system. Group delay is the audible consequence — it's how long a wave-packet around each frequency is delayed in seconds (or milliseconds). Together they describe everything about a system's behaviour that isn't its magnitude response.

Wrapped vs unwrapped

FFT-derived phase is wrapped to ±180° (or ±π radians) because atan2 only produces values in that range. As you scan up the spectrum, the true phase often passes through ±180° boundaries and "wraps" to the other side — producing the saw-tooth look on the wrapped plot. The Unwrap phase toggle detects those jumps and adds ±360° to subsequent points so the underlying continuous phase trajectory becomes visible. Unwrapped phase is what you need to compute group delay.

Group delay = −d(phase) / d(ω)

Group delay is the negative slope of unwrapped phase vs angular frequency. A flat (constant) phase slope gives flat group delay — meaning all frequencies are delayed by the same amount, which preserves a transient's shape. A varying group delay smears transients differently across the spectrum: a sharp drum hit's high-frequency components arrive at a different time than its low-frequency components.

The before/after workflow

Start the mic with a clean signal — pink noise played through your monitors, a sine sweep, or even just music. Click Capture snapshot (A). The current magnitude, phase, and group delay are stored as a yellow dashed overlay on all three plots. Now insert an EQ or filter in your signal chain and watch how the live curves move relative to the snapshot. A minimum-phase EQ will shift phase smoothly without introducing extra delay; a linear-phase EQ will produce constant group delay but possibly with pre-ringing; an analogue-modelled EQ will show its characteristic phase shift around each band.

Why is the phase plot so noisy?

Phase is only well-defined where there's energy. At frequencies with very low magnitude, the bin's complex value is essentially zero plus noise, and its angle is random. The Smoothing control averages the complex spectrum across frames (smoothing in the complex domain avoids the wraparound artefacts you'd get from averaging phase directly). 75 % smoothing is a good default; for transient material drop it to 30 % so you don't blur fast changes.

Why isn't my phase changing when I move my hand?

Phase only changes meaningfully when the spectrum's energy moves between frequencies, or when something is delaying or shifting the signal. A steady tone has a constant phase per bin. Voice and music have rapidly-varying phase that's mostly noise-like — phase analysis is most useful on responses to controlled stimuli (pink noise sweeps, impulses), not on arbitrary content.