Spectral Decay Reverb — v0.2 User Guide

Convolution reverb with a Poisson‑based impulse response featuring exponential decay, chirp (sweeping) modulation, and bandpass filtering. The IR is generated from a Poisson point process (simulating sparse reflections) with an amplitude envelope decay_base^(-t/impulse_dur) and a sinusoidal chirp: 1 + 0.7·sin(2π·t·150 + t·20). A Hann bandpass filter (100–4000 Hz) shapes the final tone.

Author: Shai Cohen Affiliation: Department of Music, Bar‑Ilan University, Israel Version: 0.2 (2025) – Stereo, wet/dry, visualisation License: MIT License Repo: GitHub

Contents:

What it does Quick start Presets (4 archetypes) Impulse response design Parameters Visualization FAQ / troubleshooting

What this does

Spectral Decay Reverb is a convolution‑based reverb with a custom‑designed impulse response (IR). The IR is generated from a Poisson point process (random impulses with a given density), then shaped with:

An exponential decay envelope: decay_base^(-t / impulse_dur) (higher decay_base = faster decay).
A chirp (frequency‑sweeping) modulation: 1 + 0.7·sin(2π·t·150 + t·20) – this creates a shimmering, evolving texture.
A Hann bandpass filter (default 100–4000 Hz) to focus the reverb on the spectral range of most interest.

Key features v0.2:

Poisson‑based IR – sparse, randomised impulses (density controls “graininess”).
Exponential decay with adjustable base.
Chirp modulation for evolving, non‑static timbre.
Hann bandpass filter with smooth transitions (smoothing parameter).
Stereo decorrelation: right channel uses slightly different IR parameters (duration, density, decay, filter).
Wet/dry mix and visualisation of bandpass shape and IR envelope.

Quick start

In Praat, select exactly one Sound object (mono or stereo).
Run script… → Spectral_Decay_Reverb.praat.
Choose a Preset:
- Subtle Decay, Medium Decay, Heavy Decay, Extreme Decay
For custom mode (preset = Custom), adjust parameters as desired.
Set Wet_dry_percent (0 = dry only, 100 = wet only).
Click OK. The script creates a Poisson‑based IR, convolves it with the input (extended with a silent tail), filters, applies wet/dry mix and fadeout, and imports the result as originalname_spectral_preset.

Tip: Start with Medium Decay (IR 3 s, density 2000, decay base 110) to hear the characteristic chirp modulation. For a more grainy, diffuse texture, increase Poisson_density. For a brighter reverb, raise the high cutoff.

Important: This reverb uses Praat’s Convolve command, which can be slow for long IRs. The IR length is determined by Impulse_duration_s – keep it reasonable (2–4 s) for faster processing.

The 4 presets (+ Custom)

Preset	IR dur (s)	Density	Decay base	Bandpass (Hz)	Description
Subtle Decay	2.0	1200	150	120–3500	Light, gentle decay.
Medium Decay	3.0	2000	110	100–4000	Balanced, clear reverb.
Heavy Decay	4.5	3000	80	80–4500	Dense, prominent tail.
Extreme Decay	6.5	4500	50	60–5000	Extreme, cavernous decay.

Each preset also sets wet_dry_percent appropriately (35–80 %).

Impulse response design

📐 Poisson point process

Creates a train of impulses with an average density of poisson_density events per second. Each impulse is a short pulse (width 0.035 s, frequency 2800 Hz). This sparse structure gives the reverb a grainy, diffused character unlike dense noise‑based IRs.

📐 Decay envelope

amp(t) = decay_base^(-t / impulse_dur)

decay_base controls the steepness: higher values = faster decay (e.g., 150 decays quickly, 50 decays slowly).

📐 Chirp modulation

mod(t) = 1 + 0.7·sin(2π·t·150 + t·20)

This adds a frequency‑sweeping (chirp) component: the sine frequency increases over time (the term t·20 in the phase). The result is a shimmering, evolving timbre that never sounds static.

📐 Hann bandpass filter

After convolution, the wet signal is passed through a Hann bandpass filter with low and high cutoffs and a smoothing parameter that controls the transition steepness. This restricts the reverb to a chosen frequency range (default 100–4000 Hz), focusing energy on the most audible part of the spectrum.

The right channel uses slightly different parameters (IR duration ×0.93, density ×0.95, decay ×0.95, modulation frequency 140 Hz instead of 150 Hz, and shifted bandpass cutoffs) to decorrelate the stereo image.

Parameters & defaults

IR parameters

Parameter	Range	Default	Description
Tail_duration_s	any positive	2.0 s	Length of silent tail added after the original sound (allows reverb to ring out).
Impulse_duration_s	any positive	3.0 s	Length of the generated impulse response (determines reverb length).
Poisson_density	integer	2000	Average number of Poisson impulses per second. Higher = denser, smoother reverb.
Decay_base	positive	110	Base of the exponential decay envelope. Higher = faster decay.

Spectral filtering

Parameter	Range	Default	Description
Low_cutoff_Hz	any positive	100 Hz	Lower frequency of the Hann bandpass filter.
High_cutoff_Hz	any positive	4000 Hz	Upper frequency of the bandpass filter.
Smoothing_Hz	any positive	100 Hz	Transition width of the filter skirts (Hann window).

Mix & output

Parameter	Range	Default	Description
Wet_dry_percent	0–100	50	0 = dry only, 100 = wet only.
Fadeout_duration_s	any positive	1.2 s	Cosine fade‑out applied at the end of the tail to avoid clicks.
Draw_visualization	yes/no	yes	Show waveforms, bandpass shape, IR envelope, and summary.
Play_result	yes/no	yes	Auto‑play after processing.

Visualization (Praat picture)

When Draw_visualization = 1, the script draws:

Original waveform (grey).
Result waveform (blue) with wet/dry percentage.
Bandpass filter shape (left panel) – idealised Hann bandpass response (gain vs. frequency). The passband is shaded, and the smooth transitions are shown.
IR envelope with chirp (right panel) – the generated impulse response envelope over time, showing both the raw modulated signal (purple) and the underlying exponential decay (dotted brown).
Parameter summary – IR duration, density, decay base, bandpass range.

Tip: The IR envelope plot clearly shows the effect of the decay base and the chirp modulation. Notice how the amplitude oscillates (due to the sine modulation) while the overall trend follows the exponential decay.

FAQ / troubleshooting

Convolution is very slow

Praat’s Convolve can be slow for long IRs. Reduce Impulse_duration_s (e.g., to 1.5 s) for faster preview. Also, lower Poisson_density reduces the number of impulses, which may speed up the IR generation (but not the convolution itself).

Output is silent / no reverb heard

Check that Wet_dry_percent is not 0. Also verify that the IR was created correctly – the Info window shows the parameters used. If the IR is extremely short or dense, it may produce an inaudible result. Try increasing Impulse_duration_s or decreasing Decay_base (slower decay).

Reverb sounds too “grainy”

Increase Poisson_density – this creates more impulses per second, smoothing out the graininess. You can also increase the pulse width (the script uses 0.035 s – edit 0.035 in the To Sound (pulse train) line).

Understanding decay_base

The decay envelope is decay_base^(-t/impulse_dur). This is equivalent to an exponential with time constant τ = impulse_dur / ln(decay_base). For example:

decay_base = 150 → τ ≈ 0.6 s (fast decay)
decay_base = 50 → τ ≈ 1.7 s (slower decay)

So higher decay_base = faster decay, which may be counter‑intuitive – but the formula is chosen for numerical convenience in Praat.

Stereo decorrelation

The right channel uses a slightly different IR (duration ×0.93, density ×0.95, decay ×0.95, etc.) to ensure left and right are not identical. This creates a wider, more immersive image. If you need a narrower image, you can reduce the differences in the script.