Equalization (filter types, Q, slopes, phase)

Definition

An equalizer is a linear filter that modifies the amplitude, and generally the phase as well, of the signal as a function of frequency: H(f) = |H(f)| · e^(jφ(f)).

Filter types:

• high-pass / low-pass: attenuate below or above the cutoff frequency f_c; the slope is 6 dB/octave per order (1st order 6, 2nd 12, 3rd 18, 4th 24, 8th 48 dB/octave). Butterworth: maximally flat response, −3 dB at f_c; Linkwitz-Riley: −6 dB at f_c, used in crossovers; Bessel: more gradual slope and nearly constant group delay;
• low and high shelving: raise or lower all frequencies below or above a point;
• bell (peaking): raises or lowers a band around f_0, with a width defined by Q;
• notch: very narrow, deep cut;
• band-pass, tilt (rotation of the spectrum around a point), all-pass (modifies only the phase).

Q and bandwidth: Q = f_0 / BW, where BW is the distance in Hz between the −3 dB points (some manufacturers use the half-gain points). Conversion from width in octaves N: Q = √(2^N) / (2^N − 1): 2 octaves → 0.67; 1 octave → 1.41; 1/3 octave → 4.32; 1/6 octave → 8.65.

Phase: minimum-phase filters (analog and digital IIR) introduce a phase shift and a group delay concentrated around the modified frequencies; a 2nd-order Butterworth high-pass has +90° at the cutoff frequency. Linear-phase filters (FIR) have constant group delay: no phase distortion, but latency and pre-ringing (energy before the transient) with narrow or steep filters at low frequencies. IIRs obtained with the bilinear transform show cramping near Nyquist (the bell narrows); analog-matched models or oversampling correct it.

Parameters and units

Musical function

Corrective equalization removes what is disturbing: rumble below the fundamental, mud at 200–400 Hz, narrow resonances, harshness at 2–5 kHz, sibilance. Tonal equalization defines the character: body, presence, air. Complementary equalization creates space between instruments that occupy the same zone (a cut on the guitar where the vocal has presence). In mastering the EQ balances the overall spectrum with broad moves of ±0.5–2 dB. The choice of phase matters when several correlated tracks are equalized differently (multiple drum microphones) and in steep corrections at low frequencies.

Practical example

• Vocal: high-pass 80 Hz, 12 dB/octave; bell −3 dB at 300 Hz with Q 1.41 (1 octave: −3 dB points at 212 and 425 Hz); bell +2 dB at 3.5 kHz with Q 1; high shelf +2 dB from 10 kHz.
• Slopes: a 4th-order Butterworth high-pass at 30 Hz attenuates by 24.1 dB at 15 Hz (one octave below) and by 3 dB at 30 Hz; a 2nd-order one attenuates by 12.3 dB at 15 Hz.
• Phase: high-pass at 40 Hz, 48 dB/octave on the kick. With minimum phase, the 50 Hz fundamental undergoes a large phase shift and the transient changes shape; with linear phase the transient stays intact, but the latency is tens of milliseconds and pre-ringing appears: for a kick, the most suitable choice is a minimum-phase filter with a 12–24 dB/octave slope.

Common mistakes

• Equalizing in solo and judging the result without the mix.
• Narrow, strong boosts (+6 dB, Q > 4): they emphasize resonances and sound artificial; boosts should be wide, cuts can be narrow.
• High-pass filters set too high on all tracks: the mix loses body and warmth.
• Linear phase on drums and bass with steep filters: audible pre-ringing before the hits.
• Equalizing two microphones on the same source differently with minimum-phase filters and ignoring the resulting cancellation.
• Comparing EQ on and bypass at different loudness.

How to check it

• App analysis: the energy per band (Sub 20–60, Bass 60–120, Upper bass 120–250, Low mids 250–500, Mids 500–2000, Upper mids 2000–4000, Presence 4000–8000, Air 8000–16,000, Ultra highs 16,000–20,000 Hz) and the spectral curve show the effect of the EQ on the file; compare before and after and against a reference. For correlated tracks check the Stereo correlation and the Mono sum drop.
• EQ analyzer: FabFilter Pro-Q and Fruity Parametric EQ 2 show the spectrum before and after the intervention.
• Sweep: a narrow bell (Q 6–8) at +10 dB swept across the spectrum to find a resonance, then turned into a cut.
• Level-matched bypass: compensate the output gain before judging.