Directivity Analysis 🔒

License Required: Directivity analysis features require a valid LinFIR license. All other LinFIR features remain free to use.

Directivity analysis tools characterize how your speaker system radiates sound in different directions. These tools predict off-axis behavior, visualize interference patterns between drivers, and help optimize crossover design for consistent directivity.

Overview

Directivity analysis provides:

Off-axis frequency response visualization at any measured angle
Directivity Index (DI) prediction across the frequency spectrum
Directivity sonograms (2D frequency vs. angle heatmaps)
Crossover optimization insights based on radiation patterns

Key Applications:

Identify directivity errors, beaming and dispersion characteristics
Optimize crossover design for consistent off-axis response
Assess room interaction based on directivity patterns
Visualize interference patterns between drivers

Polar Measurements

Measurement Requirements

To use directivity tools, you need impulse responses at multiple angles:

Horizontal Axis:

Measurements with vertical angle = 0°, varying horizontal angle
Example: -90°, -60°, -30°, 0°, +30°, +60°, +90°
More angles provide better accuracy (5° or 10° increments recommended)

Vertical Axis:

Measurements with horizontal angle = 0°, varying vertical angle
Example: -60°, -40°, -20°, 0°, +20°, +40°, +60°
Particularly important for speakers with vertical array configurations

On-axis Reference:

The (0°, 0°) measurement is the on-axis reference
Must be captured first before off-axis measurements
Appears in both horizontal and vertical columns in the IR Management window

⚠️ Critical: Time of Flight Must Be Preserved

DO NOT:

Apply windowing that removes the acoustic delay
Time-align measurements to the same start point
Remove the relative delay between drivers

WHY:

The relative delay between angles encodes interference patterns
This delay represents the acoustic path length to the microphone
Off-axis measurements have different path length ratios between drivers
These delays create the directivity patterns we analyze

What happens if you remove time-of-flight:

DI calculation assumes drivers are co-located (incorrect)
Predicted interference patterns don’t match reality
Off-axis nulls and peaks won’t appear
Directivity sonograms show incorrect lobing patterns

⚠️ Critical: Use Proper Timing Reference

Configure a timing reference method in Audio Settings before capturing polar measurements:

Electric (loopback) - RECOMMENDED:

Most reliable method
Connect output to input with a cable
Eliminates software scheduler variability
See Reference Timing for setup

Acoustic (chirp):

Uses another driver as timing reference microphone
Good for setups where loopback is impractical
Requires careful positioning

Avoid “None” timing mode:

Relies on system audio scheduler (unreliable on Windows)
Timing jitter corrupts phase relationships between drivers
Can produce incorrect directivity analysis

💡 Tip: Stable timing is essential for accurate phase relationships between drivers. See Reference Timing for detailed setup instructions.

Measurement Tips

General Guidelines:

Keep microphone-to-speaker distance constant for all angles
Rotate the speaker (not the microphone) when possible
Ensure consistent room conditions for all measurements
Use high SNR settings to capture clean off-axis data

Distance Recommendations:

Farfield measurements (>1 meter) work best
Distance should be at least 2-3× the largest driver spacing
Too close = nearfield effects, inaccurate directivity
Too far = room reflections dominate

Microphone Positioning:

Ensure microphone height matches speaker acoustic center
Keep microphone axis perpendicular to speaker front baffle
Avoid obstructions in the measurement path

Off-Axis Curve Visualization

View off-axis frequency responses directly in the main graph window.

Accessing Off-Axis Display

Location: Main graph toolbar (Drivers/Speakers display mode only)

Angle Selector

Axis Selection:

Toggle between h (horizontal) and v (vertical) axis buttons
Only available when viewing individual drivers or summed system
Not available in Room Calibration modes

Angle Dropdown:

Select from available measurement angles
Only angles with actual measurement data are shown
0° always represents the on-axis reference

Interpreting Off-Axis Curves

Compare off-axis to on-axis:

Smooth transitions across angles = good dispersion control
Large deviations at certain angles = beaming or nulls
Crossover region consistency = proper driver integration

What to look for:

Beaming: Response drops off rapidly at off-axis angles (high-frequency issue)
Comb filtering: Peaks and dips that vary with angle (driver interference)
Crossover lobing: Nulls or peaks appearing at specific off-axis angles near crossover frequency
Baffle diffraction: Ripples that change with angle at mid-to-high frequencies

Example Interpretation:

Good directivity:

Off-axis curves smoothly roll off at high frequencies
No sudden dips, peaks or steps through crossover region
Consistent shape across ±30° angles

Poor directivity:

Deep nulls appearing at ±20° near crossover frequency
Off-axis step in frequency response near a crossover frequency, indicating directivity mismatch between drivers
Dramatic level changes between neighboring angles
Comb filtering visible at mid frequencies

Directivity Index (DI) Prediction

The Directivity Index (DI) quantifies how directional your speaker is across the frequency spectrum.

What is DI?

Definition:

\[ \text{DI} = 10 \times \log_{10}(Q) \]

where \(Q\) is the directivity factor

\(Q\) is calculated by spherical integration:

\[ Q = \frac{4\pi}{\int_0^{2\pi} \int_0^{\pi} |H(\theta,\phi)|^2 \sin(\theta) , d\theta , d\phi} \]

Interpretation:

0 dB = omnidirectional (radiates equally in all directions)
Higher values = more directional (sound focused forward)

Typical DI Values

0-3 dB: Wide dispersion

Subwoofers
Large woofers at low frequencies
Most speakers below 200 Hz

3-6 dB: Moderate directivity

Most drivers at mid frequencies
Typical 2-way speakers at 1-4 kHz

6-12 dB: Controlled directivity

Waveguides and horns
Well-designed constant directivity systems
Ideal for controlled room interaction

12+ dB: Very directional

Narrow dispersion (potential beaming issues)
Extreme horns
May sound disconnected from room in typical listening spaces

How DI Reflects Filtering

The DI curve shows:

Combined effect of driver placement and crossover filtering
Interference between drivers creates peaks/dips in the DI
Crossover slopes affect how quickly directivity changes
Time-of-flight differences encode driver spacing in the DI pattern

Example DI Behaviors:

Smooth DI transition:

Gradual increase from 3 dB at 500 Hz to 6 dB at 4 kHz
Indicates good driver integration through crossover

DI spike at crossover:

Peak to 8-10 dB at 2.5 kHz, then drops to 6 dB at 3 kHz
Indicates on-axis summing peak (lobing) at crossover frequency
Off-axis response likely has nulls

DI dip at crossover:

Dip to 0 dB at crossover frequency
Indicates on-axis null (destructive interference)
May sound better off-axis than on-axis

Using DI for Design

Target smooth DI transition:

Avoid sudden changes (>3 dB) in DI through crossover region
Gradual transitions indicate good driver integration

Avoid sudden DI changes:

Peaks = on-axis lobing (hot spot)
Dips = on-axis null (cancellation)
Both indicate poor crossover alignment

Consider desired room interaction:

Wider DI (3-6 dB) = more room sound (spacious, diffuse)
Narrower DI (6-12 dB) = less room sound (direct, focused)
Match DI to listening environment and preference

Match DI to listening environment:

Near-field (desktop, mixing): Moderate DI acceptable (3-8 dB)
Far-field (living room, theater): Wider DI preferred (3-6 dB) to engage room
Treated rooms: Higher DI acceptable (6-10 dB) due to controlled reflections

Directivity Sonograms

The Directivity Sonogram window displays 2D visualizations of how sound radiates across frequency and angle.

Directivity Sonogram

Accessing Sonogram Window

Menu: View → Directivity Sonogram
Requires: Valid LinFIR license and polar measurements loaded

Window Layout

Two separate sonogram plots:

Horizontal directivity: Vertical angle = 0°, varying horizontal angle
Vertical directivity: Horizontal angle = 0°, varying vertical angle

Axes:

X-axis: Frequency (Hz, logarithmic scale)
Y-axis: Measurement angle (degrees)
Color: Normalized magnitude in dB (0 dB = global maximum)

Color Scale

Hot colors (red/yellow): Higher SPL (0 to -6 dB)

On-axis or near-axis energy
Focused radiation

Warm colors (orange): Moderate attenuation (-6 to -12 dB)

Moderate off-axis output
Typical dispersion

Cool colors (blue/purple): Significant attenuation (-12 to -30 dB)

Heavily attenuated off-axis
Beaming or nulls

Range clamped to -30 dB for clarity (adjustable in settings)

Interpreting Sonograms

Horizontal bands:

Similar spectral balance across angles
A band remaining coherent from about −60° to +60° indicates a well-designed driver with controlled directivity and no excessive beaming

Angular width and color spread:

Warm colors extending from −90° to +90° in the bass / low-midrange are normal (low frequencies are inherently near-omnidirectional)
Progressive narrowing at high frequencies is expected, but confinement to < −45° to +45° suggests excessive beaming

Symmetry around 0°:

Geometrical and acoustical symmetry
Proper driver placement and reliable measurements

Asymmetric patterns:

Potential baffle diffraction
Room reflections contaminating measurements
Driver offset or asymmetric waveguides (intentional in most 3 way monitor designs)

Interference patterns (diagonal/complex):

Driver interaction visible
Crossover region summing effects
Time-of-flight encoding driver spacing

What to Look For

Good Patterns:

Smooth color transitions:

Gradual change from hot (on-axis) to cool (off-axis)
Indicates controlled directivity

Symmetric patterns:

Equal radiation to left/right (horizontal) or up/down (vertical)
Indicates Symmetric design

Horizontal bands in crossover region:

Consistent radiation pattern through crossover
Good driver integration

Bad Patterns:

Narrow bright vertical regions:

Beaming (concentrated energy on-axis)
Excessive directivity at that frequency
Often caused by large drivers at high frequencies

Dark spots off-axis / Diagonal stripes:

Nulls or cancellations between drivers
Indicates poor crossover alignment or lobing
May be acceptable if smooth and symmetric
Often caused by driver spacing and time-of-flight
Crossover regions with insufficient acoustic slope, producing off-axis lobing

Crossover Design Insights

Compare on-axis and off-axis patterns:

Check for consistent summing across all angles
Look for lobing (bright spots appearing at off-axis angles)

Verify driver summing:

Crossover frequency should show smooth transition in sonogram
Moderate nulls or peaks appearing at specific angles

Adjust crossover if needed:

Lobing visible: Try different crossover slopes or frequency
Nulls visible: Check driver polarity and time alignment

Example Adjustments:

Problem: Bright and wide lobe at +30° near crossover frequency
Solution: Lower crossover frequency or increase slope to reduce overlap

Problem: Null at 0° (on-axis) at crossover frequency
Solution: Check driver polarity, adjust time delay, or change crossover type

Problem: Vertical bright bands alternating with dark bands
Solution: Driver spacing issue (comb filtering) - may require physical redesign

Why Time-of-Flight Matters

Physics of Multi-Driver Interference

When multiple drivers reproduce the same frequency range, their outputs combine in space. The phase relationship between drivers depends on:

Physical separation between drivers (geometry)
Acoustic path length differences to the measurement point
Crossover filter phase shifts

How Time-of-Flight Encodes This

Each driver’s impulse arrives at a slightly different time:

This delay represents the acoustic path length to the microphone
At the on-axis position, path lengths may be similar
At off-axis positions, path length ratios change

Off-axis measurements capture geometry:

Driver A might be 1.0 meters away on-axis
Driver B might be 1.05 meters away on-axis (5 cm path difference)
At +30° off-axis, Driver A might be 0.95 m and Driver B might be 1.15 m (20 cm difference)
This changing path length ratio creates interference patterns

These delays create directivity:

At some frequencies, drivers sum constructively (in phase)
At other frequencies, drivers sum destructively (out of phase)
The frequency where this happens depends on the angle (because path lengths change with angle)
This is the fundamental physics of directivity

What Happens If You Remove TOF without keeping relative delays

Time-aligning removes geometric delay information:

All drivers appear to arrive at the same time
DI calculation assumes drivers are co-located (all at the same point in space)
This is physically incorrect for real speakers

Predicted interference patterns don’t match reality:

Off-axis nulls and peaks won’t appear
Directivity sonograms show incorrect lobing
DI curve does not reflect actual radiation pattern

Example:

With TOF preserved:

Tweeter and woofer are 15 cm apart vertically
At 2.3 kHz (wavelength ≈ 15 cm), expect null at certain off-axis angles
DI curve shows this correctly

With TOF removed (time-aligned):

Software thinks drivers are co-located
Predicts no null at 2.3 kHz
DI curve is smooth (incorrect)
Real speaker still has null at 2.3 kHz off-axis

Proper Workflow

1. Capture IR with full time-of-flight intact

Use proper timing reference (electric loopback or acoustic chirp)
Do not apply windowing that removes acoustic delay
Preserve the natural arrival time differences

2. Import into LinFIR preserving the delay

Keep the raw impulse peak positions as captured or remove the same amount of time across all measurements
Each angle will have slightly different delay values (this is correct)

3. Apply crossover filters

Crossovers add their own phase shifts
These combine with geometric delays

4. LinFIR predicts directivity

Calculation includes both geometry (TOF) and filtering (crossover phase)
Spherical integration over all measured angles
Result: realistic DI and sonograms

5. Sonogram shows realistic interference

Interference patterns reflect both driver spacing and crossover design
Allows optimization of crossover for desired directivity

Limitations and Best Practices

Measurement Density

More angle measurements = more accurate prediction

Minimum recommended: 7 angles per axis (±90° in 30° steps)
Good: 13 angles per axis (±90° in 15° steps)
Ideal: 19 angles per axis (±90° in 10° steps) or finer

Why density matters:

DI calculation uses spherical integration
Sparse measurements = poor integration accuracy
Fine measurements = more accurate directivity prediction

Room Reflections

Directivity analysis is most accurate in anechoic conditions

Room reflections distort off-axis measurements
Early reflections appear as interference in the sonogram
Can create false lobing patterns

Mitigation strategies:

Measure outdoors (less reflections)
Measure in large room with speaker away from walls
Use gating/windowing carefully:
- Remove late reflections (>10 ms after main arrival)
- Use Adaptive Window to preserve bass while gating reflections

Microphone Position

Keep measurement distance constant:

Same distance for all angles
Ensures consistent SPL normalization
Eliminates distance-related level variations

Farfield measurements (>1 meter) work best:

Avoids nearfield effects
Drivers behave as coherent sound sources
More accurate directivity prediction

Microphone height:

Should match speaker acoustic center
For 2-way speaker, typically between tweeter and woofer
Ensures symmetric vertical measurements

Computational Notes

DI calculation uses spherical integration:

Computationally intensive (integrates over all angles and frequencies)
May take a few seconds for dense polar data

Sonogram generation:

Creates high-resolution 2D images (frequency × angle)
Parallel processing used for speed
Results are cached to improve performance

Getting a License

To unlock Directivity Analysis tools:

Visit the LinFIR website: https://linfir.demaudio.com
Purchase a license key
Enter your e-mail and key in LinFIR: Settings → License
All directivity features will be enabled immediately

Your license supports:

Ongoing development
New features
Bug fixes and improvements

IR Management: Capturing and managing off-axis measurements
Reference Timing: Setting up timing reference for accurate polar measurements
Audio Setup: Configuring audio interface and measurement settings
Driver Processing: Crossover design and optimization

Summary

Directivity Analysis tools characterize how your speaker radiates sound in different directions:

Features:

Off-axis frequency response visualization at any angle
Directivity Index (DI) prediction across the spectrum
Directivity sonograms (2D frequency vs. angle heatmaps)

Requirements:

Valid LinFIR license
Polar measurements at multiple angles (horizontal and vertical)
Preserved time-of-flight
Proper timing reference (electric loopback or acoustic chirp)

Key Concepts:

Time-of-flight encodes driver geometry (must be preserved)
DI quantifies how directional the speaker is (0 dB = omni, higher = more directional)
Sonograms visualize radiation patterns (hot colors = on-axis energy, cool = off-axis attenuation)
Crossover optimization based on directivity for consistent off-axis response

Workflow:

Configure timing reference (electric loopback recommended)
Capture polar measurements for each drivers (preserve time-of-flight)
Design crossovers and apply filters
View off-axis curves, DI, and sonograms
Optimize crossover for desired directivity pattern
Iterate based on measurements

Use directivity analysis to understand and optimize your speaker’s radiation pattern for better room interaction and consistent sound across the listening area.

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