Graph Interaction & Display

This section covers all interactive features, display controls, and analysis tools available when working with LinFIR’s graphs.

Graph Toolbar

The graph toolbar provides comprehensive controls for selecting which data to display and how to visualize it. The toolbar adapts based on the project mode (Loudspeaker Design vs Room Calibration).

Loudspeaker Design Mode:

Room Calibration Mode:

Display Mode Selection

Purpose: Choose which stage of the signal processing chain to visualize.

Available modes:

• FIR - FIR filter responses only (crossovers, magnitude/phase correction)
• IIR - IIR filter responses only (parametric EQ, shelves, crossovers)
• FIR+IIR - Combined FIR and IIR responses
• Drivers (Loudspeaker Design) / Measurements (Room Calibration) - Full signal chain applied to driver or room measurements (theoretical system response)

Keyboard shortcuts:

• Press F to cycle through filter modes (FIR → IIR → FIR+IIR)
• Press D to switch to Drivers/Measurements mode

Mode behavior:

• Loudspeaker Design mode: Shows individual driver filters plus global filters
• Room Calibration mode: Shows only global filters in FIR/IIR/FIR+IIR modes

See Display Modes section below for detailed explanations of each mode.

Graph Visibility Toggles

Purpose: Show or hide specific graph types.

Available graphs:

• Magnitude (M) - Frequency response in dB
• Phase (P) - Phase response in degrees
• Group Delay (G) - Group delay in milliseconds
• Impulse (I) - Impulse response in time domain
• Step (T) - Step response in time domain
• THD (K) - Total Harmonic Distortion (Loudspeaker Design mode only)

Each button toggles visibility of the corresponding graph. Letters in parentheses indicate keyboard shortcuts.

Note: THD is only available in Loudspeaker Design mode with Drivers display mode active, as harmonic distortion analysis is not applicable to in-room measurements.

Angle Selector (Loudspeaker Design mode only)

Purpose: Select which off-axis measurement angle to display when drivers have directivity data.

• Horizontal angles: Typically ±15°, ±30°, ±45°, ±60°, ±75°, ±90°
• Vertical angles: Same as horizontal
• Toggle H/V: Switch between horizontal and vertical axis selection

Only available when at least one driver has off-axis measurements. The selector is hidden in Room Calibration mode as directivity analysis is specific to anechoic/quasi-anechoic loudspeaker measurements.

See Directivity Analysis for complete details on polar measurements and analysis.

Visualization Options

Normalize

Purpose: Scale impulse and step responses to ±1 range for easier comparison.

When enabled:

• Impulse responses normalized to peak amplitude = 1
• Step responses normalized to maximum value = 1
• Useful for comparing relative timing and shape without amplitude differences

Sum Focus

Purpose: Emphasize the combined system response while dimming individual curves.

• Loudspeaker Design: Highlights the summed driver output at listening position
• Room Calibration: Highlights the averaged response across measurement positions
• Individual curves remain visible but with reduced opacity
• Useful for evaluating overall system performance

Unwrap Phase

Purpose: Display continuous phase response without ±180° wrapping discontinuities.

• Disabled: Phase wraps at ±180° (sawtooth pattern)
• Enabled: Phase continues beyond ±180° showing true accumulated phase shift
• Essential for analyzing linear phase filters and group delay
• Makes phase response easier to interpret across wide frequency ranges

Time-Centered Phase

Purpose: Remove linear phase component (constant group delay) from phase responses.

• Disabled: Phase includes linear delay component
• Enabled: Linear phase component subtracted via regression, flattening phase around 0°
• Highlights phase alignment issues without bulk delay obscuring differences
• See Time-Centered Phase section below for detailed algorithm and use cases

Smoothing

Purpose: Apply fractional-octave smoothing to magnitude, THD, directivity and group delay plots.

Smoothing options:

• None, 1/48, 1/24, 1/12, 1/6, 1/3 octave (higher = more smoothing)

Applies to:

• Magnitude (frequency response)
• Group delay
• THD (Total Harmonic Distortion)
• Directivity sonograms

Does not affect: Phase or time-domain plots (impulse, step response)

Note: Smoothing is cosmetic and does not affect filter calculations or exports. See Fractional Octave Smoothing section below for detailed behavior.

Mouse & Trackpad Controls

Zoom Controls

Zoom In - Multiple methods:

• Box zoom: Right-click and drag to select a region
• Trackpad pinch: Pinch gesture to zoom in/out
• Mouse wheel: Scroll to move the view within a graph

Zoom Out:

• Double-click anywhere on a graph to reset to auto-calculated bounds
• Double-click re-enables auto-bounds mode (graphs automatically adjust to data range)

Pan

Left-click and drag to move the view within a zoomed graph.

Legend Interaction

Click on color dots in the legend to show/hide individual curves:

• Hidden curves are grayed out in the legend
• Click again to show the curve
• Useful for isolating specific drivers or filters

Detach Graphs

Right-click on any graph to open it in a separate window:

• All graph types supported (Frequency, Phase, Group Delay, Impulse, Step, THD)
• Detached windows render in real-time following the active display mode
• Multiple graphs can be opened simultaneously for side-by-side comparison
• Ideal for multi-monitor setups and detailed analysis workflows
• Close detached windows: Cmd+W (macOS) / Ctrl+W (Windows)

Display Modes

Project Mode Impact

LinFIR supports two project modes that affect display terminology:

• Loudspeaker Design - Speaker design with drivers
• Room Calibration - Multi-position measurements for room correction

In Room Calibration mode:

• “Drivers” mode is renamed to “Measurements”
• Individual measurement curves are shown in Measurements mode
• Filter modes (FIR/IIR/FIR+IIR) display only global filters

In Loudspeaker Design mode:

• “Drivers” mode displays individual drivers
• Filter modes show both per-driver filters and global filters

Filters vs. Drivers/Measurements Mode

Filters Mode (Keyboard: F):

• Shows individual filter responses (FIR, IIR, or FIR+IIR combined)
• Press F multiple times to cycle through filter submodes:
  • FIR Filters - Shows only FIR filter responses
  • IIR Filters - Shows only IIR filter responses
  • FIR+IIR Filters - Shows combined FIR and IIR responses
• Loudspeaker Design: Per-driver crossover and correction filters displayed separately
• Room Calibration: Only global filters are shown
• Global filters shown as additional curves
• Useful for analyzing filter design and frequency response shaping

Drivers/Measurements Mode (Keyboard: D):

• Loudspeaker Design: Shows combined driver + filter responses (acoustic output)
  • Each curve represents the complete signal chain for that driver
  • Sum curve shows the total system response at listening position
• Room Calibration: Shows individual measurement positions and averaged response
  • Each curve represents a raw measurement location (no filters applied)
  • Sum curve shows the averaged response with global filters applied
• Useful for analyzing final acoustic performance

Graph Visibility Toggles

Show/hide individual graph types using keyboard shortcuts:

• M - Toggle Magnitude (Frequency Response) plot
• P - Toggle Phase Response plot
• G - Toggle Group Delay plot
• I - Toggle Impulse Response plot
• T - Toggle Step Response plot
• K - Toggle THD (Total Harmonic Distortion) plot

X-Axis Synchronization

Toggle: X key or toolbar button

When enabled, Sync X-axis synchronizes the horizontal axis across related plots:

Frequency Plots (Magnitude, Phase, Group Delay, Directivity Sonograms):

• All plots share the same frequency range
• Zooming any plot updates all frequency plots simultaneously
• Double-click resets all frequency plots to full range

Time Plots (Impulse, Step Response):

• All time-domain plots share the same time range
• Zooming any plot updates all time plots simultaneously
• Double-click resets all time plots to full range

Independent Y-Axes:

• Each plot maintains its own vertical scale
• Y-axis auto-bounds independently for each graph type

Use Cases:

• Compare magnitude and phase behavior at the same frequency
• Analyze impulse and step response in the same time window
• Maintain consistent zoom across multiple graph types

Impulse & Step Response Normalization

Toggle: N key or toolbar button

Normalizes impulse and step responses to peak amplitude = 1.0:

Purpose:

• Allows visual comparison between responses with different amplitudes
• Focuses on filter shape and time-domain characteristics
• Eliminates gain differences for easier visual analysis

Effect:

• All IR and SR curves are scaled to the same peak height
• Does not affect magnitude or phase plots
• Purely visual - does not modify underlying data

Use Cases:

• Compare filter shapes between drivers with different sensitivity
• Analyze time-domain behavior without gain differences obscuring details
• Identify pre-ringing or timing issues across multiple drivers

Sum Focus Mode

Toggle: S key or toolbar button (Drivers/Measurements mode only)

Synchronizes the time window of all temporal plots (Impulse & Step Response) to the Sum/Average curve boundaries:

How it Works:

1. Analyzes the Sum/Average impulse response to find its energy boundaries
2. Detects first and last samples above -60 dB threshold (1/1000th of peak)
3. Adds configurable margins before and after the detected energy region
4. Applies the same time window to all temporal plots (both Impulse and Step Response)
5. Enables auto-bounds for all time plots

Behavior:

• Requires at least 2 active curves to activate (otherwise ignored)
• Focuses all temporal plots on the main acoustic energy of the Sum/Average response
• Individual driver/measurement curves are zoomed to the same time window as the sum
• Easier to compare arrival times and transient behavior across all curves
• Works with adaptive display mode margins (configurable in Settings)

Use Cases:

• Loudspeaker Design: Quickly identify timing alignment issues across drivers
  • See if all drivers arrive within the sum’s main energy window
  • Detect delays or misalignment relative to system response
• Room Calibration: Focus on the averaged room response energy region
  • Compare individual measurement positions to the average response timing
  • Identify room reflections within the main energy window
• Eliminate clutter from pre-ringing or tail noise outside the main energy region

Only available in Drivers/Measurements Mode (not applicable to individual filters).

Note: Works in both Loudspeaker Design and Room Calibration project modes when display mode is set to Drivers/Measurements.

Phase Display Options

Unwrap Phase

Toggle: U key or toolbar button

Controls phase display format:

Wrapped Phase (default):

• Phase values constrained to ±180°
• Shows discontinuities (phase wraps) at ±180° boundaries
• Easier to read for simple filters
• Standard display format for most audio applications

Unwrapped Phase:

• Continuous phase values extending beyond ±180°
• Shows total accumulated phase shift
• Useful for analyzing group delay trends and overall phase shift

Note: Group delay is always computed from unwrapped phase internally. The Unwrap toggle only affects phase display, not group delay accuracy.

Time-Centered Phase

Toggle: C key or toolbar button (next to Unwrap Phase)

Removes the linear phase component (constant group delay) from phase responses:

Algorithm:

• Computes linear phase slope from IR peak position for all curves (drivers and filters)
• Subtracts the constant group delay (linear phase shift)
• Flattens phase around 0° while preserving relative phase differences
• Works with both wrapped and unwrapped phase display modes

In Loudspeaker Design Mode (Drivers):

When multiple speakers are active:

• Removes the linear delay of the Sum curve from all responses
• Centers all driver phases around 0° relative to the system response
• Highlights phase alignment issues between drivers
• Makes phase differences visible without bulk delay obscuring them

When single driver is active:

• Removes the linear component of that driver’s phase
• Flattens phase around 0° to show only non-linear phase shifts

In Room Calibration Mode (Measurements):

• Independent correction: Removes the linear phase component of each individual measurement independently
• No shared reference - each measurement position is treated separately
• Flattens each measurement’s phase around 0°
• Useful for comparing phase behavior across different room positions without timing offsets
• The averaged curve also has its own linear component removed

In Filters Mode (FIR, IIR, FIR+IIR):

• Per-filter correction: Removes the linear phase component of each individual filter
• Flattens each filter’s phase around 0°
• Reveals only non-linear phase rotations introduced by the filter
• Useful for analyzing filter phase behavior independent of bulk delay

Use Cases:

• Identify phase alignment issues between drivers without delay obscuring differences
• Visualize phase rotations introduced by filters (independent of linear delay)
• Compare filter phase characteristics across different designs
• Verify minimum-phase vs. linear-phase behavior

Fractional Octave Smoothing

Control: Dropdown menu in toolbar (1/48 oct to 1/3 oct, or “None”)

Apply smoothing to reduce measurement noise and reveal trends:

Smoothing Width:

• No smoothing - Show raw response (no averaging)
• 1/48 octave - Very fine smoothing (highest detail)
• 1/24 octave - Fine smoothing
• 1/12 octave - Moderate smoothing (default)
• 1/6 octave - Coarse smoothing
• 1/3 octave - Very coarse smoothing (lowest detail)

Effect:

• Wider smoothing = smoother curves, less detail
• Narrower smoothing = more detail, more noise visible

Applies to:

• Frequency response (magnitude), THD, Directivity Sonograms and group delay plots
• Does not affect phase, time-domain plots

Note: Smoothing is applied after all processing (filters, crossovers, correction). It affects display only, not exported data. It can also alter crossover slopes on the graphs.

Impulse Response Analysis

Automatic Pre-Ringing Detection

When hovering over impulse response curves, LinFIR displays additional analysis information:

Pre-ring Level (in dB relative to peak):

• Weighted RMS measurement of signal energy before the main peak
• Analysis stops at the last zero-crossing before peak (excludes rising edge)
• Uses Hilbert envelope to capture perceptible energy regardless of phase
• Perceptually weighted: energy closer to the peak is less penalized (temporal masking)
• Displayed as: Pre-ring: -50.0 dB (Likely masked)

Algorithm Details:

1. Find the impulse peak position and amplitude
2. Find the last zero-crossing before the peak (to exclude the rising edge)
3. Extract the pre-ringing region (from start to zero-crossing)
4. Calculate the Hilbert envelope of the pre-ringing region
5. Apply sigmoid weighting (closer to peak = less perceptual penalty)
   • Masking time at 50% penalty: 0.6 ms (default)
   • Weight floor: 0.2 (minimum weight for distant pre-ring)
   • Weight ceiling: 1.0 (maximum weight for near-peak pre-ring)
6. Calculate weighted RMS of the envelope
7. Convert to dB relative to peak amplitude

Weighting Rationale:

• Pre-ringing close to the peak is masked by the main transient (temporal masking)
• Pre-ringing far from the peak is more audible (less masking)
• Sigmoid function models gradual transition from masked to unmasked

Risk Assessment Labels

Pre-ringing levels are classified based on typical perceptual thresholds (indicative):

Important Notes:

• These are indicative estimates, not absolute rules
• Actual audibility depends on:
  • Program material (transient-rich vs. sustained tones)
  • Listening level
  • Individual hearing sensitivity
  • Room acoustics and background noise
• Use as a guideline for filter design, not strict limits
• Shorter FIR filters or increased causality reduce pre-ringing at the cost of magnitude and phase accuracy

Trade-offs:

• Longer FIR filters → More pre-ringing, better magnitude/phase accuracy
• Shorter FIR filters → Less pre-ringing, reduced correction capability
• Higher causality (e.g., minimum-phase) → Less pre-ringing, potential phase distortion
• Linear-phase (causality = 0) → Maximum pre-ringing, linear phase

Auto-Bounds Behavior

LinFIR automatically adjusts graph bounds to fit data:

Auto-Bounds Enabled (default):

• Graphs automatically scale to show all data
• Y-axis adjusts when switching between drivers or display modes
• X-axis adjusts based on data range (frequency or time)

Auto-Bounds Disabled (after user interaction):

• Manual zoom/pan disables auto-bounds for that axis
• Graph retains user-specified bounds
• Switching modes preserves manual bounds
• Double-click re-enables auto-bounds and resets to calculated range

Per-Axis Independence:

• X-axis and Y-axis auto-bounds are independent
• Dragging vertically disables Y auto-bounds, preserves X auto-bounds
• Dragging horizontally disables X auto-bounds, preserves Y auto-bounds
• Box zoom (right-click drag) disables both X and Y auto-bounds

Per-Graph Independence:

• Each graph type has independent auto-bounds state
• Zooming Frequency plot does not affect Impulse plot
• Switching between display modes preserves per-graph bounds

Keyboard Shortcuts Summary

Display Modes

• F - Switch to Filters display mode
• D - Switch to Drivers/Measurements display mode

Display Controls

• X - Toggle X-axis synchronization
• N - Toggle normalize impulse and step responses
• U - Toggle unwrap/wrap phase response
• C - Toggle time-centered phase
• S - Toggle focus on summed impulse response (Drivers/Measurements mode only)
• R - Toggle Directivity Sonogram window (Loudspeaker Design mode only, requires license)

Graph Visibility

• M - Toggle Magnitude Response plot
• P - Toggle Phase Response plot
• G - Toggle Group Delay plot
• I - Toggle Impulse Response plot
• T - Toggle Step Response plot
• K - Toggle THD (Klirr/Distortion) plot

Related Documentation

• Global Settings - Graph resolution, titles, colors
• Keyboard Shortcuts - Complete shortcut reference
• Driver Processing - Filters affecting graph display
• System Processing - Global filters and sum calculation