Some sort of sloping?

[mx]

Apologies if this is a dumb question. Is there some sort of sloping applied with this spectrum analyzer? Or is it an inherent property of the Constant Q Transform? Or perhaps I'm just holding it wrong, as it were?

To test the analyzer, I ran a white noise source through it. I saw a pretty distinct dB slope downwards from the highest octave to the lowest octave. I found that pretty puzzling, because white noise ought to have a constant magnitude over time rather than a slope. I confirmed that the noise source was white using two other spectrum analyzers (just FFT based, not CQT). I looked through the source code and couldn't find at first glance anything that would be responsible for this sloping. Am I just "holding it wrong" as they say, possibly not understanding the full properties of the CQT? Or is this an issue with cqt-analyzer?

[mx]

Looking at it with spaced sine waves, everything looks appropriately constant. The low frequencies do take much longer to appear and be stable/constant in the analyzer though. I wonder if it has something to do with the time resolution at the lower frequencies.

[jmerkt]

Hello and thanks for the input!

The slope with white noise you are observing, to my knowledge, is a property of the Constant Q Transform (CQT).
Looking at the CQT as a collection of logarithmic spaced band-passes, the bandwidth of the these filters increases with frequency. Hence, with rising frequency, they integrate over a bigger absolute frequency range, creating the observed slope.
With sine tones, it behaves differently, because these only contain one distinct frequency and don't sum with increasing bandwidth.

The FFT has a constant bandwidth across all frequency bins and therefore doesn't show the slope.

Future versions of the plugin could contain a parameter to actually apply a slope and observe equal power for white noise, but then its a trade-off observing single sine tones with equal magnitude independent of frequency. Maybe there is a clever way to handle this, but I have to think about it.

As you already guessed, the time resolution at low frequencies is lower, because we need a higher frequency resolution there and sadly can't have both at the same time.