Spectrogram 🔒

License Required: The Spectrogram window requires a valid LinFIR license.

The Spectrogram visualises the time-frequency energy distribution of the impulse response as a 2-D colour map, making it easy to spot resonances, ringing, and temporal smearing that are difficult to see in a standard frequency response plot.

• Loudspeaker Design mode — shows the predicted sum impulse response for the currently selected angle (on-axis by default); when a non-zero angle is selected in the angle selector the spectrogram updates to reflect that off-axis response, and the window title shows the active angle (e.g. Spectrogram — Predicted Sum — +15°H +0°V)
• Room Calibration mode — shows the averaged measurement impulse response

Accessing the Spectrogram

Menu: View → Spectrogram
Keyboard shortcut: W

Layout

The window is divided into two panels:

• Main plot — the colour-mapped spectrogram
• Colorbar (right edge) — dB scale matching the current colormap range

A control bar above the plot exposes all parameters.

Controls

Transform Algorithm

Two algorithms are available, selectable via the CQT (Morlet) / STFT (Fourier) toggle buttons:

CQT — Constant-Q Transform (default)

Implemented as a frequency-domain Morlet (analytic Gaussian) filter bank:

1. The IR is forward-FFT’d once into an analytic spectrum.
2. For each log-spaced frequency f₀, the spectrum is multiplied by a Gaussian window of relative bandwidth 1/Q and inverse-FFT’d.
3. The magnitude of the result is the instantaneous amplitude (envelope) at f₀.

This gives constant relative bandwidth — better frequency resolution at low frequencies and better time resolution at high frequencies — which matches the logarithmic frequency axis used throughout LinFIR.

STFT — Short-Time Fourier Transform

A Gaussian-windowed STFT (75% overlap) with linear frequency bins interpolated onto the log display grid. Provides uniform frequency resolution across the spectrum; the window size controls the time/frequency trade-off. The Gaussian window (σ = 0.4 · N/2) offers very low spectral sidelobes, reducing frequency leakage.

Resolution Preset

A ComboBox selects the resolution preset for the active algorithm:

The time–frequency trade-off

Any time-frequency transform faces a fundamental constraint: you cannot simultaneously have perfect time resolution and perfect frequency resolution. Improving one always degrades the other. This is the acoustic equivalent of the Heisenberg uncertainty principle.

CQT Q factor

The Q factor defines the ratio of centre frequency to bandwidth for each analysis band:

$$Q = \frac{f_0}{\Delta f}$$

A band centred at \(f_0=1000, \text{Hz}\) with \(Q = 10\) has a bandwidth of \(\Delta f = 100,\text{Hz}\). The corresponding time resolution (temporal smear) is approximately:

$$\Delta t \approx \frac{Q}{f_0} = \frac{1}{\Delta f}$$

Because the CQT uses a constant relative bandwidth, low frequencies always have more time smear than high frequencies — this is physically correct and matches how we perceive sound.

STFT window size

The STFT divides the IR into short overlapping frames of fixed length N (in samples). Within each frame, the spectrum is computed with a uniform frequency resolution of \(\Delta f = f_s / N\):

$$\Delta t = \frac{N}{f_s}, \quad \Delta f = \frac{f_s}{N}$$

Unlike the CQT, the STFT resolution is the same at all frequencies — which can make low-frequency detail easier to read at the cost of poor high-frequency time resolution.

Colormap Range

Narrowing the range highlights low-level detail (resonances, room modes, late decay). Widening it shows the full dynamic range at a glance.

Normalize (per-band)

The Normalize toggle scales each frequency band independently so that its peak amplitude equals 0 dB.

Without normalization, the colormap is referenced to the global maximum of the entire spectrogram — bands with inherently lower energy (e.g. very low or very high frequencies) may appear entirely blue even if they contain meaningful decay structure.

With normalization enabled:

• Every frequency band fills the full colormap range from its own peak (0 dB) down to the configured minimum.
• Decay tails, resonances, and room modes become visible across the entire frequency range regardless of the relative SPL of each band.
• The colormap controls (Min dB / Max dB) still apply — they define the dynamic range displayed within each normalized band.

Note: Normalize is a purely visual operation. It does not affect the underlying computation or the impulse response data.

Axis Swap

The Freq × Time / Time × Freq button swaps the horizontal and vertical axes:

• Time × Freq (default) — time on X (ms), frequency on Y (Hz, log)
• Freq × Time — frequency on X (Hz, log), time on Y (ms)

Swapping the axes resets the zoom to fit the new layout.

Plot Interaction

Interpreting the Spectrogram

The colour follows a rainbow-like gradient:

What to look for:

• Narrow bright and straight red band — clean, impulse-like response; energy decays quickly at all frequencies
• Horizontal smearing at low frequencies — expected due to the longer wavelengths; the CQT’s time-smear is proportional to 1/f
• Persistent bright regions after t = 0 — cabinet resonances, port resonances, or room reflections; the frequency and decay time are directly readable from the plot
• Vertical stripes of colour in the axis-swapped view — resonant modes (a single frequency ringing for an extended time)

Pre-roll: The spectrogram always shows 200 ms before t = 0 (pre-padded with zeros). This prevents the CQT/STFT pre-ringing from being cropped and ensures the t = 0 onset is clearly visible.

Related Documentation

• Graph Interaction — zoom, pan, and detached windows
• Directivity Analysis — directivity sonogram and overlay plot
• License — license features and activation