Classic IIR Filter Bank — User Guide

Design and apply lowpass or highpass IIR filters using Bessel, Butterworth, or Chebyshev Type I prototypes. The audio renderer, response plots, and Z-plane diagram all use the same second-order-section (SOS) cascade.

Author: Shai Cohen Affiliation: Department of Music, Bar-Ilan University, Israel Version: 0.5.1 (2026) License: MIT License Repo: Praat AudioTools

Contents:

What this does Quick start Presets Filter families Controls Rendering & output Visualization Notes & limits

What this does

The script builds a cascade of biquadratic IIR sections from one of three classical lowpass prototypes, optionally transforms it to highpass, and can then apply that exact cascade to the selected Sound. The same coefficients are used for the magnitude response, wrapped phase response, and Z-plane plot, so the visualization describes the filter that actually renders the audio.

Current filter bank: Bessel, Butterworth, and Chebyshev Type I. Earlier simplified Chebyshev-II and pseudo-Elliptic entries were removed because they did not implement the transmission zeros and rational approximations required by those filter families.

Quick start

Select exactly one Sound object.
Choose a preset, or leave Preset = Custom.
Select Bessel, Butterworth, or Chebyshev I.
Choose Lowpass or Highpass, then set the order and cutoff.
For Chebyshev I, set Passband_ripple_db.
Leave Plot_responses and Plot_zplane enabled if you want the diagnostic Picture page.
With Apply_filter enabled, the filtered Sound is created and normalized to Scale_peak.

Cutoff meaning: Butterworth and the calibrated Bessel implementation place the requested cutoff at approximately −3.0103 dB. For Chebyshev I, the cutoff is the edge of the equiripple passband, not a −3 dB point.

Presets

Presets override the filter family, mode, order, and cutoff shown below. They do not change Scale_peak, plotting switches, Apply_filter, or playback.

Preset	Filter	Mode	Order	Cutoff
Custom	Uses the values entered in the form.
Speech Lowpass (3.5 kHz)	Butterworth	Lowpass	4	3500 Hz
Music Lowpass (8 kHz)	Butterworth	Lowpass	4	8000 Hz
Rumble Filter (80 Hz HP)	Butterworth	Highpass	4	80 Hz
Presence Reduction (2 kHz LP)	Butterworth	Lowpass	4	2000 Hz

Filter families

Bessel is not linear phase. It is an IIR family chosen for relatively flat group delay. The phase plot remains frequency-dependent.

Controls

Control	Default	Behavior
Preset	Custom	Selects one of the fixed setups above or leaves the manual values unchanged.
Filter_type	Butterworth	Bessel, Butterworth, or Chebyshev Type I.
Filter_mode	Lowpass	Lowpass or Highpass.
Order	4	Must be 2, 4, 6, or 8. Internally this creates order/2 SOS sections.
Cutoff_frequency	1000 Hz	Must be below Nyquist. Butterworth/Bessel: approximately −3.0103 dB point. Chebyshev I: passband edge.
Passband_ripple_db	0.5 dB	Used only by Chebyshev I.
Scale_peak	0.95	Target peak applied after filtering. This is normalization, not a ceiling or limiter.
Plot_responses	Yes	Draws magnitude and wrapped phase response from the designed SOS cascade.
Plot_zplane	Yes	Draws poles, zeros, and the unit circle from the same SOS coefficients.
Apply_filter	Yes	Creates and processes a copy of the selected Sound. If disabled, the script can be used for plotting only.
Play_after_processing	Yes	Plays the filtered output when one has been created.

Rendering & output

The filter is implemented as a cascade of second-order sections. Each channel is loaded directly from the Sound into a script vector, processed through the same SOS cascade with independent filter state, and written back with a compiled Formula pass.

Channel count: preserved. Mono, stereo, and higher multichannel Sounds are processed channel-by-channel with identical coefficients.
Duration and sample count: unchanged; IIR filtering does not append a convolution tail.
Sample rate and Sound time domain: preserved because processing is performed on a copy of the original Sound.
Output level: after filtering, Scale peak always scales the created output to the requested target peak. Values above 1.0 can therefore create an unsafe peak for integer PCM export.
Output name: <original>_Bessel_LP, <original>_Butterworth_HP, <original>_ChebyshevI_LP, etc.
No dry/wet mix: the created output is fully filtered before target-peak normalization.

Highpass mapping: v0.5.x designs the lowpass prototype at the complementary digital frequency before the z → −z reflection. The reflected transition therefore lands at the cutoff entered by the user instead of near Nyquist minus that value.

Visualization

If either plotting switch is enabled, the script creates an 8 × 8.7 inch Picture page with a title and summary strip. The page reports the selected filter family, LP/HP mode, order, cutoff, target peak, and sample rate.

Magnitude response

The red response is evaluated directly from the SOS coefficients at 512 frequency points from 0 Hz toward Nyquist. The panel uses a −80 to +10 dB display range, a dotted −3 dB reference, and a vertical line at the requested cutoff.

Phase response

The blue curve is the wrapped phase in degrees, displayed from −180° to +180°. Large wrap discontinuities are not connected. It should not be interpreted as an unwrapped phase or as proof of linear phase.

Z-plane

The unit circle is shown with zeros as green circles and poles as red X marks. Lowpass sections place their finite zeros at z = −1; after the highpass transform they move to z = +1. Stable filters have poles inside the unit circle.

The plots describe the designed SOS cascade whether or not Apply_filter is enabled. When audio is created, it uses those same coefficients.

Notes & limits

Only even orders 2, 4, 6, and 8 are supported.
The cutoff must be below Nyquist.
Very low or very high cutoffs, high order, or aggressive Chebyshev ripple can place poles close to the unit circle and increase numerical sensitivity; use the Z-plane plot as a diagnostic.
Passband_ripple_db is ignored by Bessel and Butterworth.
The script does not implement Chebyshev Type II, Elliptic, bandpass, or bandstop modes in v0.5.1.