Chapter - 1

Key Words: Equalization, Q-FActor, Tonal Balance

Equalization

🎯 Learning Objectives

By the end of this topic, you should be able to:

  • Understand the principles of equalization (EQ) in audio.
  • Identify different filter types: low-pass, high-pass, band-pass, shelving, and parametric.
  • Apply EQ to shape the tonal balance of instruments and vocals.
  • Recognize the effect of Q-factor and gain on frequency bands.

Introduction:

Equalization (EQ) is the process of adjusting the balance of frequency components in an audio signal. It is used to correct, enhance, or creatively shape the sound.

Example Analogy: Adjusting bass, mid, and treble controls on a stereo to suit a room’s acoustics.

Physical Principles of EQ:

Frequency Spectrum

Audio signals can be represented in the frequency domain using Fourier transform:

X(f)=βˆ«βˆ’βˆžβˆžx(t)eβˆ’j2Ο€ftdtX(f) = \int_{-\infty}^{\infty} x(t) e^{-j 2 \pi f t} dt
  • Low frequencies (< 250 Hz): Bass and subbass
  • Mid frequencies (250–4000 Hz): Vocals, melody, body of instruments
  • High frequencies (> 4000 Hz): Clarity, brightness, air
Frequency spectrum illustration
Figure 1. Typical audio frequency spectrum with bass, mid, and treble bands.

Types of EQ Filters

Filter TypeDescriptionFrequency Effect
Low-Pass (LPF)Allows frequencies below cutoff to passAttenuates high frequencies
High-Pass (HPF)Allows frequencies above cutoff to passAttenuates low frequencies
Band-Pass (BPF)Passes frequencies in a bandAttenuates outside band
Notch / Band-StopCuts a narrow frequency bandRemoves hums or resonances
ShelvingBoosts or cuts frequencies above/below cutoffTreble/bass control
ParametricAdjustable center frequency, gain, and QPrecise control of any band

EQ Parameters

Center Frequency

  • Denoted as f0f_0
  • The frequency at which a peaking EQ or shelf is applied.

Gain

  • Denoted as GG
  • Amount of boost or cut in decibels (dB).

Quality Factor (Q)

  • Measures bandwidth relative to center frequency.
Q=f0BQ = \frac{f_0}{B}

Where BB is the bandwidth in Hz.

  • High Q β†’ narrow band
  • Low Q β†’ wide band

Common EQ Types with Mathematical Forms

1. High / Low Pass Filter

  • Removes low/high frequencies
  • First-order transfer function:
H(s)=Ο‰cs+Ο‰cH(s) = \frac{\omega_c}{s + \omega_c}
  • Fourth-order: cascade of first-order or second-order sections

2. Peaking / Bell EQ

  • Boost or cut around f0f_0
H(s)=1+G1+jQ(ff0βˆ’f0f)H(s) = 1 + \frac{G}{1 + j Q (\frac{f}{f_0} - \frac{f_0}{f})}

3. Shelving EQ

  • Low shelf: boosts/cuts below f0f_0
  • High shelf: boosts/cuts above f0f_0
  • Example: 6 dB boost low shelf: +6Β dBΒ @Β 150Β Hz+6 \text{ dB @ 150 Hz}

4. Notch / Band Stop

  • Very narrow cut:
H(s)=s2+Ο‰02s2+Ο‰0Qs+Ο‰02H(s) = \frac{s^2 + \omega_0^2}{s^2 + \frac{\omega_0}{Q} s + \omega_0^2}
Frequency spectrum illustration
Frequency spectrum illustration
Figure 2. Tiefpass, Hochpass, Notch – Betrag (oben), Phase (unten)
Frequency spectrum illustration
Frequency spectrum illustration
Figure 3. Tiefpass, Hochpass, Notch – Betrag (oben), Phase (unten)

Example EQ Settings

  • Peaking EQ: +6 dB @ 1 kHz, Q = 1
  • Low Shelf: +4 dB @ 150 Hz
  • High Shelf: –3 dB @ 5 kHz

Observation:

  • Uniform scales for magnitude: βˆ’6…+6 dB
  • Phase: βˆ’60…+60Β°
  • Shelving filters affect broadband phase
  • Peaking EQ shows localized phase rotation around f0f_0

Problem-Oriented Editing

  • Remove resonances, impact noise, hum
  • Use broadband boost for tonal shaping
  • Use narrowband cut for specific problems
  • Monitor in a treated room or with reference tracks
  • Dynamic EQ can act like multiband compression for frequency-specific dynamics

Visual Demonstration

Octave Band Equalizer

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πŸ“˜ Explanation of EQ Parameters:

Frequency

The central frequency of the band to adjust (Hz).

  • Bass: 20–250 Hz
  • Midrange: 250–4000 Hz
  • Treble: 4000–20000 Hz

Gain

The amount of boost or cut applied (dB).

  • Positive gain: boost
  • Negative gain: cut

Q-Factor / Bandwidth

Controls the width of the affected frequency band.

  • Narrow Q: precise surgical adjustments
  • Wide Q: gentle tone shaping

Filter Type

Determines how frequencies are shaped (LPF, HPF, BPF, shelving, notch).

🎀 Applying EQ to Specific Audio Sources

Vocals

  • Use HPF to remove low rumble (< 80 Hz)
  • Slight boost at 2–5 kHz for presence
  • Apply narrow cuts for resonances

Drums

  • Kick: boost 50–100 Hz, cut 300–500 Hz
  • Snare: boost 200 Hz for body, 3–5 kHz for snap
  • Overheads: smooth highs with gentle shelving

Guitar / Piano

  • Adjust mids to sit in the mix
  • Cut muddy low-mids 200–400 Hz
  • Brighten high-end for clarity

πŸ” Advanced EQ Techniques

  • Dynamic EQ: Gain changes depending on input amplitude (like a multiband compressor).
  • Mid/Side EQ: Separate processing for center (vocals) and sides (stereo width).
  • Surgical EQ: Use narrow Q to remove resonances or unwanted frequencies without affecting the rest.

🧠 Key Takeaways

  • EQ shapes the spectrum: cut for clarity, boost for vibe.
  • Key types: shelving, peaking, high/low pass, notch, graphic.
  • Parameters: center frequency f0f_0, gain GG, Q factor QQ.
  • Phase response is important: wide vs narrow, shelf vs bell.
  • Problem-oriented EQ enhances clarity, removes unwanted resonances, and improves tonal balance.

🧠 Quick Quiz

1) Which EQ parameter controls the width of the frequency band affected?

2) What filter type would you use to remove low-frequency rumble?

3) Which EQ is most suitable for precise removal of resonances?

4) Boosting 3–5 kHz in vocals usually affects what aspect?

5) A low Q-factor in a parametric EQ produces what kind of adjustment?