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.

Automated Polar Measurements with a Rotation Table

For a fully automated polar measurement workflow, connect a motorized turntable (Pololu Tic or GRBL/Arduino) in Settings → Rotation Table. Once connected and a license is active:

• A ▶ Scan button appears in the IR Management window
• Configure the angle range and step (e.g. −90° to +90°, 10° step)
• Click ▶ Scan: the table rotates to each angle, settles, and captures automatically
• Already-measured angles are skipped

See Rotation Table for setup, hardware compatibility, and troubleshooting.

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)

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

Listening Window

The Listening Window curve represents the average frequency response over the angular range that matters most for typical listening positions — the region a listener’s ears are likely to be within.

What is the Listening Window?

The Listening Window is defined as the spatial average of all measured frequency responses within ±30° horizontal and ±10° vertical (inclusive). It captures the sound power arriving at listeners seated slightly off-axis, which is more representative of real-world listening conditions than the strict on-axis response alone.

Display Requirements

The Listening Window curve is shown in the Frequency Responses (Drivers) graph when:

• A valid LinFIR license is active
• At least 2 polar measurements fall within the ±30° horizontal / ±10° vertical window
• The Drivers display mode is selected in the graph toolbar

Visual Appearance

The dashed style allows the Listening Window and the solid Sum (on-axis) curve to be distinguished at a glance on the same plot.

Interpreting the Listening Window

LW ≈ Sum (on-axis):

• The speaker’s balance changes little within the listening window
• Indicates excellent controlled directivity in the ±30°H / ±10°V region
• High confidence that off-axis listeners experience a similar tonal balance

LW rolls off above Sum at high frequencies:

• Normal and expected behaviour (drivers beam at high frequencies)
• The high-frequency roll-off shape indicates how quickly the speaker narrows
• A gentle, smooth roll-off indicates controlled directivity

LW has dips or irregularities not present on-axis:

• Lobing, comb filtering or directivity discontinuities within the listening window
• May indicate a crossover alignment issue affecting near-axis radiation
• A sudden dip at a specific frequency often points to interference between drivers

Comparing LW with DI:

• As DI rises, the LW typically diverges from the on-axis Sum (more directional → more off-axis loss)
• A flat DI with a flat LW indicates a well-controlled constant-directivity design

Directivity Analysis Window

The Directivity Analysis window displays two complementary visualizations of how sound radiates across frequency and angle. It is organized into two tabs:

• Sonogram — colour-mapped 2D heatmap (frequency × angle)
• Overlay Plot — all off-axis curves superimposed on a single frequency-response graph

Accessing the Window

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

Sonogram Tab — 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 = reference level, depending on normalization mode)

-6 dB Directivity Curves:

Thin grey overlay lines trace the -6 dB point on both sides of boresite (positive and negative angles) across frequency. These curves mark the angular width where the response stays within 6 dB of the on-axis maximum — a standard measure of directivity or “beamwidth.”

• Wider grey-line separation at a given frequency → wider dispersion (omnidirectional behaviour)
• Narrower separation → more focused, beamed radiation

These curves make it easy to spot frequency ranges where the speaker narrows its dispersion (beaming) or where directivity becomes asymmetric between left/right and up/down.

Color Scale

Hot colors (red/yellow): Higher magnitude (0 dB and above)

• On-axis or near-axis energy
• Focused radiation
• With normalization modes, values above 0 dB indicate angles/frequencies stronger than the reference

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 and below)

• Heavily attenuated off-axis
• Beaming or nulls

Range clamped to -30 dB by default for clarity (adjustable in settings). Values above the max threshold are saturated to the hottest color (red). The color scale always stops at 0 dB by default — increase the max dB threshold to extend it.

Colormap Range Controls

The Colormap range row in the sonogram toolbar lets you saturate the colour scale to reveal low-amplitude detail without reloading any measurement data.

How to use it:

• Widen the range (e.g. −60 dB to 0 dB) to get a broad overview of the full dynamic range
• Narrow the range (e.g. −15 dB to −5 dB) to zoom in on mid-level detail and expose subtle lobing or diffraction artefacts that would otherwise blend into a unique color
• Changing either value triggers an immediate image regeneration; the previous image remains visible while the new one is computed

The colorbar on the right of each sonogram always reflects the current min/max values and its grid step adapts automatically to the selected range.

Normalization Mode

The Normalization dropdown on the right side of the toolbar controls how sonogram magnitudes are normalised before applying the colour map. Four modes are available:

When to use which:

• Global max. — Quick overview of the full dataset
• Normalize to 0° — Comparing on-axis vs. off-axis directivity with a single reference. Useful for checking dispersion consistency
• Normalize to 0° (per freq) — Detailed analysis of angular directivity patterns per frequency band; removes the dependency on the driver’s frequency response to compare with FEM/BEM simulations
• Normalize to ±10° avg (per freq) — Same as “Normalize to 0° (per freq)” but more robust against narrow on-axis anomalies. Prefer this when the 0° measurement has sharp peaks or nulls from interference patterns (e.g. driver spacing comb filtering) that would distort the per-frequency reference

Note on the 20 kHz cap: The reference maximum is always computed from frequencies at or below 20 kHz. This avoids tweeter resonance peaks in the ultrasonic range from skewing the normalization reference, which would otherwise compress the visible dynamic range in the audible band.

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

Overlay Plot Tab

The Overlay Plot tab shows all measured off-axis frequency responses superimposed on a single graph, one coloured line per angle. It complements the sonogram by making it easier to read precise frequency-domain differences between angles.

Horizontal and vertical directivity are displayed one above the other, each with its own set of controls.

Curve Colours

Angles are mapped to a rainbow colour scale (red → yellow → green → cyan → blue → violet) from the minimum to the maximum angle in the current filter selection.

The angle, frequency, and magnitude are shown in a tooltip when hovering over a curve.

Angle Range Filter

Three preset buttons restrict which angles are plotted:

A drag-value min/max selector allows fine-grained control of the displayed range. The Y-axis auto-scale updates whenever the selection changes.

Normalize to 0°

The Normalize to 0° toggle divides each curve by the on-axis (0°) response (reference computed up to 20 kHz to avoid tweeter resonance peaks):

• The on-axis curve becomes flat at 0 dB
• All other curves show their deviation relative to on-axis at each frequency
• The Y-axis label changes to Relative Magnitude [dB]
• The vertical range is anchored to the configured magnitude lower bound (e.g. −30 dB to +3 dB)
• Curves can show positive dB values where the off-axis response exceeds the on-axis reference at a given frequency

Interpreting the Overlay Plot

Tightly clustered curves:

• Similar response at all angles → well-controlled directivity
• Especially important in the crossover region

Curves spreading at high frequencies:

• Normal behaviour — drivers beam as frequency rises
• A gradual, smooth spread indicates controlled directivity

Sudden divergence at a specific frequency:

• Possible crossover lobing or driver interference at that frequency
• Cross-reference with the sonogram to confirm

With Normalize to 0° enabled:

• Flat normalized curves (near 0 dB) across ±30° indicate a speaker whose tonal balance is consistent within the listening window
• A normalized curve that drops sharply above a certain frequency indicates the onset of beaming
• Positive dB values on off-axis curves indicate angles where the response exceeds the on-axis reference — this can occur with wider dispersion drivers or in crossover regions

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:

1. Physical separation between drivers (geometry)
2. Acoustic path length differences to the measurement point
3. 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:

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

Your license supports:

• Ongoing development
• New features
• Bug fixes and improvements

Related Documentation

• IR Management: Capturing and managing off-axis measurements
• Audio Setup: Configuring audio interface, measurement settings, and timing reference for accurate polar measurements
• 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 colour-mapped heatmaps, frequency × angle)
• Overlay Plot (all off-axis curves superimposed, with angle range filter and normalize to 0° toggle)

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)
• Overlay Plot superimposes all off-axis curves for precise frequency-domain comparison; normalize to 0° shows deviation relative to on-axis
• Crossover optimization based on directivity for consistent off-axis response

Workflow:

1. Configure timing reference (electric loopback recommended)
2. Capture polar measurements for each drivers (preserve time-of-flight)
3. Design crossovers and apply filters
4. View off-axis curves, DI, sonograms, and overlay plots
5. Optimize crossover for desired directivity pattern
6. 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.