## Spectrogram Graph

This graph shows a spectrogram plot over the region from 10Hz to the end of the measurement sweep. The spectrogram is like a waterfall viewed from above, with the level indicated by colour. The scale showing how colour relates to level is displayed to the right of the plot. The vertical axis of the plot shows time, increasing towards the top of the plot. The time starts before the peak of the impulse so that the onset of the response can be seen. The areas where the response is decaying more slowly show up as streaks rising up towards the top of the graph. The dashed line shows the peak level in the plot at each frequency.

The spectrogram plot is generated in the same way as the Spectral Decay plot, shifting the impulse response window to the right by a proportion of the time range to generate each succeeding slice. The window types may be selected via the Spectral Decay entries in the Analysis Preferences. The plot uses logarithmically spaced data at 96 points per octave with 1/48th octave smoothing applied.

To produce the spectrogram plot click the Generate in the bottom left corner of the graph area (shortcut Alt+G). The legend panel shows the plot value at the intersection of the vertical and horizontal cursor lines.

An ideal Spectrogram decays very rapidly off the bottom of the scale range. Here is an example of a plot produced from a soundcard loopback measurement in Fourier mode.

### Spectrogram Controls

Mode selects the type of spectrogram plot that will be produced, which can be either Fourier or Wavelet. In Fourier mode the plot uses fixed width windows, which mean the plot has the same time resolution at all frequencies. If the plot spans a wide range of frequencies this usually means the time resolution is either too low at high frequencies or too high at low frequencies. A 100 ms window, for example, gives 10 Hz frequency resolution. At low frequencies that is a big octave fraction (1/1.4 octaves at 20 Hz), at high frequencies a very, very small octave fraction (1/1386 octaves at 20 kHz). For a time-frequency plot it would be more useful if the tradeoff between time and frequency resolution varied with frequency, using a constant octave fraction for frequency resolution rather than a constant number of Hz and so giving higher time resolution at high frequencies and lower at low frequencies. A wavelet transform can achieve that, specifically a constant Q Continuous Wavelet Transform (CWT). A constant Q wavelet transform is mathematically equivalent to using a frequency-dependent window to produce the spectrogram, which is what REW does. This method is faster than typical CWT calculations, but may produce some artefacts in parts of the response that extend to frequencies close to half the sample rate - using a higher sample rate shifts these beyond the usual range of interest.

Here is a 1/6 octave Wavelet spectrogram of the same soundcard loopback measurement shown above. It becomes narrower as frequency increases, reflecting the increasing time resolution of the wavelet plot.

Here is the same measurement from the first image above as a 1/12 octave Wavelet spectrogram.

The difference between the Fourier and Wavelet spectrograms can be more easily seen when looking at responses with reflections. Here are two plots of a response which has a series of reflections at 1 ms intervals after the peak. In the Fourier spectrogram, using a 10 ms window and a 10 ms span, the effect on the frequency response and decay are clearly visible, with peaks at 1 kHz intervals. However, the reflections themselves cannot be distinguished.

The wavelet plot also shows the frequency response and decay effects, but thanks to its greater time resolution at high frequencies the reflections themselves become visible as horizontal bars.

In Wavelet mode the Freq. Resolution control allows resolutions between 1 octave and 1/24th octave to be selected.

Match time scale to window and range adjusts the time axis range so that it starts at the Window width before zero (e.g. -300 ms for a 300 ms Window setting) and ends at the Time Range (e.g. 1000 ms for a 1000 ms Time Range) so that the plot shows all the generated data.

Match top of scale to peak adjusts the Scale Top value so that it corresponds to the highest level found in the data.

Normalise to peak at each frequency scales (boosts) the plot at each frequency so that it has the same peak value. This can be useful when examining energy decay or the time alignment between drive units as it removes the level differences. Note that using 3D enhancement with normalisation may result in artefacts along the frequency axis.

Select Plot the peak energy curve to overlay a line showing where the highest SPL occurs at each frequency, this can highlight variations in peak energy arrival time versus frequency - an ideal peak energy curve would be a straight line with the same time value for all frequencies.

If Show modal frequencies is selected the theoretical modal frequencies for the room dimensions entered in the Modal Analysis section of the EQ Window are plotted at the bottom of the graph.

3D enhancement gives the plot a more three-dimensional appearance.

Draw contours adds contour lines at the dB interval set in the adjacent spinner.

The Colour Scheme for the plot can be changed, the plots above use the "Rainbow" scheme, here is a plot using the "Flame" colour scheme.

This plot uses the "Copper" colour scheme with 3D enhancement active.

Scale Gamma adjusts the way colours are distributed along the scale, gamma values below one emphasis variations at the top of the scale, values above one emphasise variations at the bottom of the scale. A gamma value of 0.5 was used for the copper colour scheme image above.

The Scale Top, Scale Bottom and Scale Range controls adjust how the plot colours correspond to the values in the Spectrogram data. Any values higher than the Scale Top are drawn in the colour at the top of the scale, any values lower than the Scale Bottom are drawn in the colour at the bottom. If the Scale Top setting is changed the Scale Bottom will be adjusted to keep the same Scale Range. If the Scale Bottom is changed the Scale range will be adjusted to keep the same Scale Top. If the Scale Range is changed the Scale Bottom will be adjusted, keeping the same Scale Top.

The Time Range control determines how much spectrogram data will be generated after the time = zero point. The width of the window that is moved along the impulse response to generate the spectrogram is set by the Window control. The corresponding frequency resolution is shown next to the window setting.

The control settings are remembered for the next time REW runs. The Apply Default Settings button restores the controls to their default values.

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