MIT 21M.380 Session 8: Filters and EQs

21m.380 · Music and Technology Recording Techniques & Audio Production Filters & eqs Session 8 Figure 1. The basic four-band division of the audible frequency spectrum (after Izhaki 2011, fig. 14.3) Highs High mids Low mids Lows 20 50 200 100 500 1k 2k 5k 10k 20k 𝑓 (Hz) Solidity Power Rumble 20 50 Body Thickness Warmth Definition Brightness Air Loudness Clarity Presence Sparkle Crispness Brilliance Edge Sizzle Color Fattness Natural Tone 100 200 500 1k 2k 5k 10k Figure 2. Qualitative descriptions of various frequency ranges (after Izhaki 2011, fig. 14.4) 20k 𝑓 (Hz) 1 Student presentation (pa1) • 2 Announcement: Recording sessions • Still looking for volunteering musicians for 11/14 and 11/30 sessions • Ideas are welcome! 1 of 6 3 Filtering the frequency spectrum • Waveforms are great to visualize and edit sound in the time domain. • But what about editing the spectrum (frequency content) of sound? • Filters selectively amplify or attenuate certain frequencies ranges. • Filters don’t add frequencies that are not already present in the source! They are sound processors rather than generators. • A filter is best described by its frequency response:1 1 The frequency response of a filter de- – Constant frequency response at 0 dB … equivalent to piece of wire scribes its gain as a function of frequency. – Constant frequency response at +3 dB … +3 dB amplification – But we’re primarily interested in treating frequencies differently! • E.g., combination of filters can be used to equalize uneven response • But ironically, eqs are often used to deliberately unequalize frequencies! • Everything is a filter! eqs, rooms, analog circuits, speaker cabinets, … 4 Filter types & parameters Filter type Parameter Cut Cut-off frequency Slope (or roll-off) Shelving Peaking Symbol Unit Definition 𝑓𝑐 — Hz dB/octave at −3 dB point — Gain Center frequency 𝑔 𝑓𝑐 dB Hz max. amplification or attenuation at 𝑔/2 Gain Center frequency Bandwidth Quality (or Q factor) 𝑔 𝑓𝑐 Δ𝑓 𝑄 dB Hz Hz 1 max. amplification or attenuation at 𝑔𝑚𝑎𝑥 between −3 dB (or +3 dB) points 𝑄 = 𝑓𝑐/Δ𝑓 Table 1. Filter parameters 2 of 6 4.1 Cut filters • Low-cut (or high-pass) vs. high-cut (or low-pass) filters 2 Remember that an octave is defined • Cut-off frequency 𝑓𝐶 at −3 dB (not −6 dB!) by definition as the frequency ratio 𝑓1 ∶ 𝑓2 = 1 ∶ 2, e.g, there is an octave between 30 and 60 Hz or between 1 and 2 kHz. • Slope or roll-off (dB per octave)2 18 gain (dB) Figure 3. Frequency response of a low-cut (high-pass) filter Cut-off frequency 𝑓𝑐 = 70 Hz 12 6 0 −3 dB −6 Slope: −12 dB/octave −12 −1820 50 100 200 500 1k 2k 5k 10k 20k 𝑓 (Hz) 18 gain (dB) Figure 4. Frequency response of a high-cut (low-pass) filter Cut-off frequency 𝑓𝑐 = 700 Hz 12 6 0 −3 dB −6 Slope: −6 dB/octave −12 −1820 50 100 200 500 1k 2k 5k 10k 20k 𝑓 (Hz) 4.2 Shelving filters • Gain 𝑔 > 0 (boost) or 𝑔 < 0 (cut) with regards to 0 dB response • Center frequency 𝑓𝐶 at 𝑔/2 4.3 Peaking filters • Gain 𝑔 > 0 (boost) or 𝑔 < 0 (cut) with regards to 0 dB response • Peaking filters with 𝑔 < 0 are also called notch filters • Center frequency 𝑓𝐶 at 𝑔𝑚𝑎𝑥 • Bandwidth Δ𝑓 defined by −3 dB (not −6 dB!) points • But quality 𝑄 = 𝑓𝐶 Δ𝑓 relates better to sound perception (why?) 3 of 6 18 Center frequency 𝑓𝑐 = 100 Hz gain (dB) 12 Figure 5. Frequency response of a low-frequency shelving filter 6 Gain 0 𝑔 = −12 dB 𝑔 2 𝑔 2 −6 −12 −1820 50 100 200 500 1k 2k 5k 10k 20k 𝑓 (Hz) 18 Center frequency 𝑓𝑐 = 5 kHz gain (dB) 12 6 Figure 6. Frequency response of a high-frequency shelving filter Gain 𝑔 = +6 dB 0 −6 −12 −1820 50 100 200 500 1k 2k 5k 10k 20k 𝑓 (Hz) 18 Center frequency 𝑓𝑐 = 1 kHz gain (dB) 12 −3 dB 6 0 −6 Quality 𝑄 = −12 −1820 50 𝑓𝑐 Δ𝑓 = 100 200 2 3 Bandwidth Δ𝑓 = 1.5 kHz 500 1k 2k Gain 𝑔 = +9 dB 5k 𝑓 (Hz) 4 of 6 10k 20k Figure 7. Frequency response of a peaking filter 5 Equalizers (eqs) Combination of multiple filters, commonly: • Shelving or cut filters (sometimes switchable) for lf and hf bands HI U 12k • Peaking filters for variable number of mid bands (often 1 or 2) 5.1 -15 Typical applications +15 MID U • Remove low-frequency rumble: low-cut filter • Noise reduction: hf shelving filter -15 • Remove ac hum: notch filter at multiples of 60 Hz (us) or 50 Hz (eu) • Reduce unpleasant resonances at specific pitch(es): notch filters +15 800 200 2k 100 • Remove dc offset: steep low-cut at ca. 5 Hz 8k LOW U 80Hz • Separate instruments across audible spectrum (e.g., reduce leakage) • Add ‘brilliance’: hf shelving filter 5.2 -15 Parametric eqs • Controlled by parameters outlined in table 1 • Really first choice for eqing individual instruments! • Recommended daw plugins: – Reaper: Reaeq (comes with Reaper) – Ardour: x42-eq (6 Band; mono & stereo versions) by Robin Gareus Installation on Debian/Ubuntu: sudo apt-get install x42-plugins 5.3 +15 LOW CUT 75 Hz 18dB/OCT Figure 8. Parametric eq in an input channel strip of a Mackie cr1604-vlz mixing desk (© Loud Technologies Inc. With edits. All rights reserved. This content is excluded from our Creative Commons license. For more information, see http : / / ocw . mit . edu/help/faq-fair-use/) Graphic eqs • Many frequency bands (say, 31), with one fader per band • Initially more intuitive, but in many ways also less flexible – why? 1 2 Band № 3 4 20 25 32 – – – • Center frequencies of bands are spaced logarithmically, not linearly! – Idea: each band covers a constant frequency interval – Typical example: 10 octave bands (1 ∶ 21 ) from 31.5 Hz to (ca.) 16 kHz 1 – Or: 31 1⁄3-octave bands (1 ∶ 2 /3 ) from 20 Hz to (ca.) 20 kHz • Typically applied to a stereo mix (rather than an individual instrument) • Often used to compensate room acoustics in live engineering – Suppress feedback & undesirable resonances – Frequently static settings (sometimes fixated with screws) 5 of 6 … … 31 0 dB 40 / 1 3 ≈1∶2 Center frequency/Hz Figure 9. Principle of a graphic eq with 31 1⁄3-octave bands 20k 5.4 Eqing techniques & recommendations • Rule of 👍: Favor cutting over boosting! • Aim to retain peak level (might require adjusting overall output gain) • Eqing almost always requires a compromise: – A high-cut filter to remove tape noise might also affect piano sound – A low-cut filter to remove rumble might also affect kick drum ‘oomph’ • Eqing bass instruments traditionally challenging for novice engineers3 • Demo in Reaper: Sweeping the frequency range4 1. Instantiate peak filter in a parametric eq recommendations by different sound engineers on how to eq bass instruments. 4 The purpose of this technique is 2. Set peak filter to high 𝑔 and high q (or small bandwidth) 3. Slowly sweep 𝑓𝑐 through frequency range 4. When you have found the frequency, adjust 𝑔 and q to taste 6 3 Senior (2011a, p. 176) has collected Preview ed2 assignment References & further reading Ariza, Christopher (2012). 21m.380 Music and Technology. Filters and Filter Parameters. url: http://ocw.mit.edu/courses/music-and-theaterarts/21m-380-music-and-technology-recording-techniques-andaudio - production - spring - 2012 / lecture - notes / MIT21M _ 380S12 _ lec07.pdf (visited on 09/30/2015). Izhaki, Roey (2011). “Equalizers.” In: Mixing Audio. Concepts, Practices and Tools. 2nd ed. Focal Press. Chap. 14, pp. 202–57. isbn: 978-0240522227. mit library: 002302617. url: http://libproxy.mit.edu/login?url= http : / / search . ebscohost . com / login . aspx ? direct = true&db = nlebk&AN = 454037&site = ehost - live&ebv = EB&ppid = pp _ 202 (visited on 11/22/2014). Requires mit library login (max. 1 reader at a time). Katz, Bob (2014). “Equalization techniques.” In: Mastering Audio. The Art and the Science. 3rd ed. Burlington, ma: Focal Press. Chap. 4, pp. 55–71. isbn: 978-0240818962. mit library: 002307049. On course reserve at the Lewis Music Library. Senior, Mike (2011a). “Beyond eq.” In: Mixing Secrets for the Small Studio. 1st ed. Focal Press. Chap. 12, pp. 191–202. isbn: 978-0240815800. mit library: 002092991. Electronic resource. Accompanying information and sound examples: http://www.cambridge-mt.com/ms-ch12.htm. — (2011b). “Equalizing for a reason.” In: Mixing Secrets for the Small Studio. 1st ed. Focal Press. Chap. 11, pp. 171–90. isbn: 978-0240815800. mit library: 002092991. Electronic resource. Accompanying information and sound examples: http://www.cambridge-mt.com/ms-ch11.htm. 6 of 6 to locate frequencies in the spectrum that require adjustment by deliberately exaggerating them.