spectrum

Setting ranges for Spectrum Analyzer

Aim: reproduce analysis of Monty Montgomery's proof that 16-bits can capture signals below 96dB using analysis of these files:

- Sample 1: 1kHz tone at 0 dB (16 bit / 48kHz WAV)

- Sample 2: 1kHz tone at -105 dB (16 bit / 48kHz WAV)

Above: Spectral analysis of a -105dB tone encoded as 16 bit / 48kHz PCM. 16 bit PCM is clearly deeper than 96dB, else a -105dB tone could not be represented, nor would it be audible

Firstly, I found the -105dB file entirely inaudible, so one has to rely on spectrum analysis to see that any low sound was captured.

The dB range for the Spectrum Analyzer is not under Preferences > Spectrograms. Here are the defaults (see also http://manual.audacityteam.org/man/Spectrograms_Preferences):

It is instead under Preferences > Interface > Meter/Waveform dB range (see also http://manual.audacityteam.org/man/Interface_Preferences#Display):

I found that one could reset the dB range and simply replot without closing the Spectrum Analyzer.

However, for the max frequency range, I found that one had to close the Spectrum Analyzer and reopen it to catch the change. The highest frequency plotted by the Spectrum Analyzer will not always be exactly the same as the max frequency, it may be much higher.

I was able with the Rectangular option to reproduce the original spectrum quite well:

Visit also: http://manual.audacityteam.org/man/Audacity_Waveform#dB

Spectrum Analysis of high frequencies

I wanted to analyse this high frequency intermodulation test file from Monty Montgomery:

30kHz tone + 33kHz tone (24 bit / 96kHz) [5 second WAV]

Note firstly that on opening a WAV file in Audacity you have the option to copy the original file or work on the file inplace (and I tried both, the result in this case was the same).

One has to be very careful about the "default" project sample rate and the "active" project sample rate. On my first attempt, even though it showed 96kHz in the top-left near the waveform, I knew something was wrong, because when I tried to set the highest frequency of the spectrum analyzer window to 48kHz it would not go higher than 22 kHz. From http://manual.audacityteam.org/man/Spectrograms_Preferences:

'Maximum Frequency: This value corresponds to the top of the vertical scale. The value can be set to 100 Hz or any higher value. Irrespective of the entered value, the top of the scale will never exceed half the current sample rate of the track (for example, 22050 Hz if the track rate is 44100 Hz) because any given sample rate can only carry frequencies up to half that rate. '

It in fact showed only 44.1kHz in the lower left as the project sample rate, I had to switch that also to 96kHz:

To be extra careful, I then set the default sample rate for projects to 96 kHz (see http://manual.audacityteam.org/man/Quality_Preferences) and then reopened the project, this time permitting copying of the original WAV file. I could then generate a spectrum with up to 48kHz, but it was still empty:

But as you can see from the waveform (noting that one can't hear 30kHz and 33kHz) the frequencies are clearly present and at decent amplitude !

But from http://wiki.audacityteam.org/wiki/Suggested_Frequency_Analysis_Capabilit...

'Currently there is a hard upper limit of 100KHz for the maximum visible frequency in the spectrogram view. Most users will have audio files with a sample rate of 192KHz or less, and that a 100KHz limit is a reasonable default computationally and memory wise, however a warning might be more appropriate than a hard limit.'

And from: Are Your High Resolution Recordings Really High Resolution? by Teresa Goodwin:

' Setting up Audacity to Confirm Frequency Response of Downloaded Files

Open the Audacity program, click Audacity and select Preferences in the drop-down menu click Tracks, under Display - Default view mode choose Spectrogram click OK. Next click File and select Open in the drop-down menu, click Media and then Music and then pick the music file you want to test, then click Open. The music file will open as a playable spectrogram, ..

Here is a spectrogram of a 24/88.2 music file with authentic ultrasonic frequencies.'

The article above claims that Analyze > Plot Spectrum should also work:

'Next you can make a plot spectrum of about two minutes of the music from the spectrogram, highlight a section with the most high frequency energy, click Analyze and select Plot Spectrum in the drop-down menu.

Here is a plot spectrum of a 24/88.2 music file with authentic ultrasonic frequencies.'

But I tried it and again could see nothing. Until I tried the Hanning Window instead of the Rectangular window and it worked !

Visit also: Quick Tips: Audio Frequency Analysis using Audacity