Microphone Simulation — User Guide

Physically accurate microphone modeling: simulates polar patterns (omni, figure-8, cardioid, hypercardioid), stereo configurations (XY, AB, ORTF, MS, Blumlein, Decca Tree), and spatial positioning (azimuth, distance) with fractional-sample ITD and distance attenuation.

Author: Shai Cohen Affiliation: Department of Music, Bar-Ilan University, Israel Version: 2.3 (2025)

What this does

This script simulates realistic microphone recording by applying polar pattern responses (omnidirectional, figure-8, cardioid, hypercardioid), stereo configurations (XY, AB, ORTF, Mid-Side, Blumlein, Decca Tree), and spatial cues (interaural time difference, distance attenuation). Takes mono source, positions it in 3D space (azimuth, distance), processes through microphone model(s), outputs mono or stereo result. Uses fractional-sample sinc interpolation for accurate ITD, corrected M/S polarity, and validated configurations. Useful for understanding microphone techniques, virtual mic placement, spatial audio simulation.

Coordinate system (top view): Front (0°) | Source (azimuth) | Left --+-- Right (-90°) Mic (+90°) | Back (±180°)

Quick start

Select one mono Sound object in Praat (stereo auto-converted to mono).
Run script… → Load Microphone Simulation script.
Choose Preset (13 presets covering common recording scenarios) OR select "Custom".
If Custom: Set Pattern (Omni/Fig-8/Cardioid/Hypercardioid), Stereo_config, Azimuth (0-360°), Distance_cm.
For AB/ORTF: Adjust Mic_spacing_cm if needed.
Enable Apply_near_field_distance for 1/r amplitude attenuation (optional).
Enable Play_result to auto-play output.
Click OK — processing instant, result appears as new Sound object.

Quick tip: Start with ORTF Standard preset (most versatile stereo technique). Try Studio Vocal for mono, Mid-Side for adjustable width. All presets use physically accurate models with corrected polarity and fractional-sample delays.

Polar Patterns

What are Polar Patterns?

Directional sensitivity of microphones:

Polar pattern: Graph showing mic sensitivity vs. angle
On-axis (0°): Maximum sensitivity direction
Off-axis: Reduced sensitivity at other angles
Null points: Directions with zero/minimum sensitivity

Four Pattern Types

🌐 Omnidirectional

Formula: gain = 1.0 (uniform)

Sensitivity: Equal in all directions

Null: None

Use: Room ambience, classical music, Decca Tree, AB stereo

∞ Figure-of-Eight (Bidirectional)

Formula: gain = cos(θ)

Sensitivity: Maximum front (0°) and back (180°), equal opposite polarity

Null: Sides (±90°)

Use: Mid-Side (Side mic), Blumlein pair, room rejection

♥ Cardioid (Heart-Shaped)

Formula: gain = 0.5 + 0.5×cos(θ)

Sensitivity: Maximum front (0°), reduced sides, minimum back

Null: Back (180°)

Use: Most common (vocals, XY, ORTF, MS Mid), stage/studio

▶ Hypercardioid

Formula: gain = 0.25 + 0.75×cos(θ)

Sensitivity: Narrower pickup than cardioid, some rear lobe

Null: ~120° (sides-rear)

Use: Focused spot pickup, rejection of sides, stage monitors

Stereo Configurations

Configuration	Pattern	Spacing	Angle	Character
Mono	Any	—	—	Single mic, no stereo
Mid-Side (MS)	Card + Fig-8	Coincident	M:0°, S:90°	Adjustable width, mono-compatible
XY	Directional	Coincident	±45°	Coincident stereo, good imaging
Blumlein	Fig-8	Coincident	±45°	Natural room sound, figure-8 XY
AB	Omni	50-200cm	0°	Spaced omnis, ITD-based, spacious
ORTF	Cardioid	17cm	±55°	French standard, ITD+ILD, versatile
Decca Tree	Omni	L-C-R 2m	Various	Orchestral, 3-mic classical

Configuration Details

Mid-Side (MS):

M (Mid): Cardioid facing forward
S (Side): Figure-8 facing left/right
Decode: L = M+S, R = M-S (corrected polarity)
Width adjustable in post by changing S level

XY Pair:

Two directional mics (cardioid, hypercardioid, or fig-8)
Coincident (same point, no spacing)
Angled ±45° from center
ILD (level difference) based stereo

AB Pair:

Two omnidirectional mics only (validated)
Spaced 50-200cm apart
ITD (time difference) based stereo
Wide, spacious image

ORTF:

Two cardioid mics, 17cm spacing
Angled ±55° (110° total angle)
Both ITD and ILD cues
French broadcasting standard

Decca Tree:

Three omni mics: L, C, R
L/R: ±1m lateral, C: 1.5m forward
Mix: L+0.7C, R+0.7C
Classical orchestral standard

13 Recording Presets

Preset	Pattern	Config	Position	Use Case
Studio Vocal	Cardioid	Mono	0°, 30cm	Close vocal recording
Blumlein Pair	Fig-8	Blumlein	0°, 1m	Natural room stereo
ORTF Standard	Cardioid	ORTF	0°, 1m	Versatile stereo (recommended)
Spaced Omnis	Omni	AB 50cm	0°, 2m	Moderate spacing, warm
Mid-Side	Card+Fig-8	MS	0°, 1m	Adjustable width
Classical Decca Tree	Omni	Decca	0°, 3m	Orchestra, far-field
Close XY	Cardioid	XY	0°, 50cm	Close stereo, focused
Hypercardioid Spot	Hyper	Mono	0°, 1.5m	Focused mono pickup
ORTF Right Side	Cardioid	ORTF	+90°, 1m	Source from right
ORTF Left Side	Cardioid	ORTF	-90°, 1m	Source from left
ORTF Behind	Cardioid	ORTF	180°, 1m	Rear capture
AB Wide Spacing	Omni	AB 100cm	0°, 2m	Very spacious stereo
XY Figure-8	Fig-8	XY	0°, 1m	Blumlein variant

Spatial Parameters

Azimuth (Horizontal Angle)

Azimuth: 0° to 360° (or ±180°) 0° = Front (straight ahead) +90° = Right -90° = Left ±180° = Back (behind microphone) Effect on recording: Omnidirectional: No effect (equal all directions) Directional mics: Reduced gain off-axis Stereo pairs: Creates L/R balance and ITD

Distance

Distance: Centimeters from microphone Effect (if near-field enabled): Amplitude attenuation: gain = 1/distance 30cm (close): +10 dB vs 1m reference 100cm (1m): 0 dB (reference) 200cm (far): -6 dB vs 1m reference ITD effect (spaced mics): Closer sources = larger ITD (more delay difference) Far sources = smaller ITD (approaching plane wave)

Mic Spacing (AB, ORTF)

Spacing affects ITD (Interaural Time Difference): ITD = (spacing × sin(azimuth)) / speed_of_sound Example: 17cm spacing (ORTF), source at 90° ITD = (0.17 × sin(90°)) / 343 = 0.495 ms Wider spacing = larger ITD = more spacious Narrower spacing = smaller ITD = tighter image Typical values: ORTF: 17cm (standard) AB: 50-100cm (moderate-wide) Decca: 200cm L-R spacing (very wide)

Parameters

Parameter	Type	Default	Description
Source_sound	positive	1	Which selected sound to process
Preset	choice	Custom	13 presets or manual configuration
Custom Settings (if Preset=Custom)
Pattern	choice	Cardioid	Omni / Fig-8 / Cardioid / Hypercardioid
Stereo_config	choice	None (Mono)	Mono / MS / XY / Blumlein / AB / ORTF / Decca
Azimuth_degrees	real	0°	Source horizontal angle (0-360° or ±180°)
Distance_cm	real	100cm	Source distance from microphone
Mic_spacing_cm	real	17cm	Spacing for AB/ORTF (ignored for others)
Apply_near_field_distance	boolean	no	Enable 1/r amplitude attenuation
Play_result	boolean	yes	Auto-play output

Technical Implementation

Fractional-Sample Delays

Accurate ITD using sinc interpolation:

ITD often fractions of samples (e.g., 0.3 samples at 44.1kHz = 6.8µs)
Integer-sample delays create audible quantization
Script uses Praat's sinc interpolation for sub-sample accuracy
Result: Smooth, artifact-free spatial imaging

Corrected M/S Polarity

CORRECTED Mid-Side implementation: Side microphone: gain = cos(θ + 90°) = -sin(θ) (Positive-left convention) Decode matrix: L = (M + S) / √2 R = (M - S) / √2 This matches standard M/S decode: S positive = more left S negative = more right

Validation

Configuration constraints enforced:

XY pair: Requires directional mics (Cardioid/Fig-8/Hyper) — omni blocked
AB pair: Omnidirectional only (as documented)
Source count: Must select at least one sound

Output

New Sound object (mono or stereo):

Naming: "originalname_ConfigPattern" (e.g., "voice_ORTF", "drums_XY_Cardioid")
Mono configs: Single channel output
Stereo configs: Two-channel output (L/R)

Info window displays:

Preset used (if applicable)
Pattern and configuration
Source position (azimuth, distance)
Mic spacing (for AB/ORTF/Decca)
Near-field status
Applied corrections list

Version 2.3 corrections:

✓ M/S polarity corrected (S positive = left)
✓ Fractional-sample delays (sinc interpolation)
✓ AB pair omni-only enforcement
✓ XY pair directional-mic validation
✓ Distance attenuation option (1/r)

Applications

Education:

Teaching microphone techniques
Understanding polar patterns
Comparing stereo configurations
Demonstrating ITD vs ILD

Virtual mic placement:

Testing mic positions without physical setup
Comparing techniques on same source
Auditioning spacing/angle variations

Spatial audio simulation:

Creating stereo from mono sources
Positioning elements in stereo field
Simulating recording sessions

Research:

Psychoacoustic spatial perception
Mic technique comparison studies
ITD/ILD trade-off analysis

Limitations

Physical modeling limitations:

Horizontal plane only: No elevation (assumes source at ear height)
No head shadowing: Simplified ITD/ILD (no HRTF)
No room acoustics: Anechoic model (no reflections, reverb)
Ideal patterns: Perfect polar responses (no real-world imperfections)
Far-field default: Distance attenuation optional (enable for close-mic realism)
No proximity effect: Directional mics have bass boost up close (not modeled)
Mono input required: Stereo sources converted to mono first

Usage Tips

Choosing configurations:

ORTF: Best all-around stereo (ITD+ILD balance)
MS: When width adjustment needed in post
AB: Spacious, natural for classical/jazz
XY: Tight, focused, good mono compatibility
Mono Cardioid: Solo instruments, vocals

Comparing techniques:

Process same source with different presets
Compare ORTF vs XY vs AB for your material
Test azimuth variations (-90°, 0°, +90°)
Try different distances to hear proximity effect simulation

Parameter experimentation:

AB spacing: Try 50cm, 100cm, 150cm for spaciousness comparison
Azimuth: Test 0° (center), ±45° (off-center), ±90° (side)
Distance: Close (30cm), Medium (1m), Far (3m)
Near-field: Enable for close-mic realism (distance attenuation)