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"Linear Phase EQ: What It Costs and When to Pay It"

When you boost 8 kHz with a minimum-phase EQ, the filter shifts phase at and around that frequency. The phase response is non-linear: frequencies near the boost center are shifted more than frequencies farther away. This is unavoidable. For a minimum-phase filter, the magnitude response and phase response are linked through the Hilbert transform, and you cannot alter one without altering the other. Linear-phase EQ breaks this link by using a different filter architecture, one where every frequency is delayed by the same amount. The result is a filter that adjusts gain without touching phase relationships at all. This seems straightforwardly better. It is not, and the reason why has to do with how human hearing masks sound in time.

What Minimum Phase Actually Means

The term "minimum phase" is not marketing language. It describes a specific mathematical property. A discrete-time filter is minimum phase if all its zeros lie strictly inside the unit circle in the z-plane. This constraint ensures that the filter has the smallest possible phase response for its given magnitude response. It also means the filter's energy is concentrated maximally toward time zero: the filter starts responding immediately when a signal arrives rather than looking ahead.

The Hilbert transform connects the log magnitude spectrum and the phase spectrum of a minimum-phase system:

arg[H(jω)] = -H{ log|H(jω)| }

This is an exact identity, not an approximation. If you know the magnitude response of a minimum-phase filter, you can derive its phase response completely, and vice versa. The two are not independent design parameters. When a manufacturer describes their analog EQ emulation as modeling both the magnitude and phase of the original hardware, they are describing minimum-phase behavior: the phase naturally follows from the magnitude response of the circuit.

The practical consequence is that minimum-phase EQ processes audio causally. The output at time t depends only on the input at time t and earlier, never on future samples. No lookahead required. Zero added latency.

Group Delay and Frequency-Dependent Timing

Group delay is the negative derivative of phase with respect to frequency. A filter with constant group delay delays all frequencies by the same amount. A filter with varying group delay delays different frequencies by different amounts.

Minimum-phase filters have frequency-dependent group delay because their phase response is derived from their magnitude response. A boost at 200 Hz imposes more group delay at 200 Hz than at 2 kHz. The low-frequency components of a transient arrive later than the high-frequency components. Sharp attacks become slightly blurred, with bass content lagging behind the treble.

For moderate boosts in the midrange, this effect is largely inaudible. Psychoacoustic research suggests group delay differences below roughly 1 to 2 ms in the midrange fall beneath the threshold of audibility under typical listening conditions. The threshold is higher at low frequencies, where the ear is less sensitive to phase, and lower for listeners using headphones in controlled conditions. Heavy processing at low frequencies, steep filter slopes, and large magnitude boosts push the effect further into audible territory.

Linear-phase EQ eliminates frequency-dependent group delay. Every frequency is delayed by the same amount. A sharp transient comes out sharp, with all frequency components arriving simultaneously. This is what "phase coherent" means in practice.

The Pre-Ringing Problem

A linear-phase filter achieves its constant group delay through a symmetric FIR design. The filter's impulse response is symmetric around its center point: if the filter uses N coefficients, the first N/2 samples mirror the last N/2 samples. The filter must process future samples to produce current output, which requires lookahead. That lookahead is the source of the latency you see in plugin headers when linear-phase mode is active.

The symmetry has a second consequence. When a transient passes through a linear-phase filter, the symmetric impulse response causes the filter to ring both before and after the transient. Post-transient ringing is expected from any resonant filter. Pre-transient ringing is not: it produces a faint ghost of the transient that appears before the event itself.

On a snare hit boosted at 5 kHz through a steep linear-phase filter, this pre-ringing manifests as a brief high-frequency artifact in the milliseconds before the shell attack. Its amplitude is typically well below the transient, often 30 to 50 dB quieter depending on filter slope and boost amount. Whether this is audible depends on the filter's steepness, the magnitude of the boost, and the material.

The counterintuitive part: this pre-ringing is often more audible than the transient smearing from an equivalent minimum-phase filter, even at lower absolute amplitude. The reason is temporal masking asymmetry.

Temporal Masking and Why Pre-Ringing Is Special

Human hearing uses temporal masking to suppress artifacts that appear near loud sounds. A transient creates two masking windows: forward masking (suppressing sounds that arrive after the transient) and backward masking (suppressing sounds that arrive before it). Forward masking is substantially stronger and lasts much longer. After a loud transient, quieter sounds are masked for 50 to 150 ms. Before a loud transient, backward masking covers roughly 5 to 20 ms at most, and at considerably lower efficiency.

Minimum-phase EQ produces post-transient ringing, which falls inside the forward masking window. The transient itself suppresses the artifact. Linear-phase EQ produces pre-transient ringing, which falls outside the weaker backward masking window. The artifact has less masking working in its favor.

This asymmetry explains a result that confuses many engineers: a minimum-phase EQ with visible phase non-linearity on a phase analyzer can sound cleaner on drum material than a linear-phase EQ showing a flat phase trace. The phase distortion from minimum-phase processing is hidden by the forward masking of the transient it is distorting. The pre-ringing from linear-phase processing escapes the weaker backward mask and becomes audible at lower absolute levels. Phase accuracy on a screen does not predict audibility in the mix.

Latency as a Design Parameter

FabFilter Pro-Q offers several linear-phase modes with different latency settings. The underlying tradeoff is FIR filter length. A longer filter achieves a steeper transition band with less passband ripple, but it requires more lookahead and increases both the latency and the duration of the pre-ringing window.

At lower-latency linear-phase settings, the filter is shorter: frequency resolution is coarser and pre-ringing is brief but more concentrated. At maximum-latency settings, the filter is longer: frequency resolution is accurate but pre-ringing extends over a longer window before each transient. Neither setting eliminates the tradeoff. They redistribute it between frequency accuracy and temporal artifacts.

Pro-Q 3 and Pro-Q 4 also offer Natural Phase mode, which does not correspond to either minimum or linear phase. It matches the phase behavior of an analog circuit, combining causal response with phase relationships derived from the circuit model rather than from the symmetric FIR constraint. The result has the low latency of minimum-phase with a phase character that tracks analog behavior rather than the minimum-phase mathematical optimum. For engineers who want analog EQ behavior without the overhead of linear-phase processing, this is a practical middle ground. It illustrates a broader point: the choice between minimum phase and linear phase is not binary. Phase response can be designed along a continuous spectrum between the two extremes, with different audibility tradeoffs at each point.

When to Use Which

Minimum-phase EQ is the practical default for tracking and most mixing applications. It processes causally, adds no latency, and its phase distortion is masked by the transients it is processing. On kick, snare, vocals, and bass, minimum-phase EQ preserves the timing of attacks in a way that matches how the ear processes those sources.

Linear-phase EQ earns its place in two specific contexts. First, mastering, where multiple already-mixed signals need EQ applied without introducing differential phase shifts between elements that were balanced in the stereo image at mix time. Second, parallel processing, where a filtered copy of a signal is blended back with the dry signal. Minimum-phase coloring on the filtered copy will introduce comb filtering at the blend point because the copy is delayed differently at different frequencies. Linear-phase EQ ensures the filtered copy is exactly phase-aligned with the original.

Steep linear-phase high-pass filters at low frequencies deserve particular caution. Pre-ringing from a linear-phase high-pass at 80 Hz occurs at 80 Hz, where backward masking is weakest and the ear is sensitive to timing artifacts in bass content. Minimum-phase high-pass filters at the same frequency produce post-transient ringing that is more effectively masked by the transients being high-passed.

The choice is not between phase accuracy and phase distortion. It is between two types of distortion with different audibility profiles under different conditions. The option that looks phase-correct on a display is not automatically the option that sounds correct in a mix.