Spectrogram View
Bill 11Nov2014: Here is a start on detailed documentation of spectrogram view. I intend to continue with this, showing the log(f) view, then concluding with some sort of comparison that shows that different settings (window size, linear vs. log(f), min and max frequency) are better for different source material. I also need to demonstrate when the Frequency Gain setting can be useful.
What the Colors Mean
To demonstrate how the various settings affect the appearance of an audio track in spectrogram view, we will start with this artificially constructed test track. It consists of 5 segments of a sine wave tone at 2000 Hz, each 2 seconds long. The first segment is at a level of -10 dB, the second at -30 dB, and subsequent segments at -50 dB, -70 dB and -90 dB.
This is how the track appears in waveform view.
This is how the track appears in spectrogram view, using the default settings.
The default settings are:
- Window size: 256
- Window type: Hanning
- Minimum frequency (Hz): 0
- Maximum frequency (Hz): 8000
- Gain (dB): 20
- Range (dB): 80
- Frequency Gain (dB/dec): 0
What do these settings mean and how to they relate to what you see on the screen?
As you can clearly see, the minimum and maximum frequency settings determine the minimum and maximum frequencies displayed, as indicated in the track vertical scale.
Gain can be said to increase the "brightness" of the display. It does this by amplifying the signal by the indicated amount. With the default setting of 20 dB, any frequency band that originally had (before amplification) a level of -20 dB or greater (and now, after amplification has a level greater than 0 dB) will be displayed as white. Similarly the "lower" level bands will also "get brighter".
There are six color bands in spectrogram view: white, red, magenta, dark blue, light blue and grey. The Range setting determines the spacing between colors.
With the default settings of Gain = 20 dB and Range = 80 dB, the colors correspond to the following levels:
- anything above -20 dB is indistinguishably white (the tone at -10 dB in the image above is white)
- levels from -40 dB to -20 dB transition from red to white (the tone at -30 dB in the image above is light red)
- levels from -60 dB to -40 dB transition from magenta to red (the tone at -50 dB in the image above is magenta)
- levels from -80 dB to -60 dB transition from dark blue to magenta (the tone at -70 dB in the image above is bluish purple)
- levels from -100 dB to -80 dB transition from light blue to dark blue (the tone at -90 dB in the image above is light blue)
- anything below -100 dB is grey
Time Smearing and Frequency Smearing
If this is a pure tone, why does the spectrogram show energy at frequencies between 0 Hz and 5000 Hz?
Spectrogram view uses the fast fourier transform (FFT) to display the frequency information versus time. There is an inherent trade-off between frequency resolution and time resolution. When using the default window size of 256 the spectrogram is drawn quickly, but the frequency resolution is not so good.
The image below shows the time smearing at the start of the track.
Changing the Window Size to 2048 and displaying the entire track results in this view of the track.
We can see that the frequency resolution has increased. That is, there is much less "frequency smearing" with the larger window size. Note that the "spikes" every two seconds are the result of the discontinuities created when joining the segments of tone at different levels.
Looking at the first 0.04 seconds of the track, we can see the the "time smearing" has increased with a window size of 2048 compared to 256.
You can zoom in on the vertical (frequency) axis.
After zooming in, the vertical ruler changes to allow greater precision of the scale.
Effect of Different Window Types
In the case of this particular test track we can get even better frequency resolution by changing the Window Type to Blackman-Harris
Changing to a rectangular window causes the track to be redrawn faster at the expense of very bad frequency smearing. Note that this is still at a window size of 2048.
