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understanding measured and viewable changes after resampling

I'm using Adobe Audition 3  to analyze a single channel of audio (e.g., just the Center channel of a 5.1 track).  Audition offers an 'Amplitude Statistics' function, as well as a 'Frequency Analysis' FFT view. 

When I resample a 96kHz/24 bit track to 48kHz  (using the foobar2k SoX plugin, though others give the same result)  the min/max sample values increase, and the minimum RMS power (in dB) decreases.  Peak amplitude rises a few hundredths of a dB (not consistently, depends on what track I measure, sometimes I see no change),  and max , average,and total RMS power ( in dB) stay  the same.

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Center from multi 96khz/32bit

Mono
Min Sample Value: -18289.15
Max Sample Value: 27042.06
Peak Amplitude: -1.67 dB
Possibly Clipped: 0
DC Offset: 0
Minimum RMS Power: -132.63 dB
Maximum RMS Power: -15.05 dB
Average RMS Power: -31.55 dB
Total RMS Power: -28.07 dB
Actual Bit Depth: 24 Bits

Using RMS Window of 50 ms

Center from sox resampled multi 48kHz/32bit:
Mono
Min Sample Value: -17149.08
Max Sample Value: 27218.93
Peak Amplitude: -1.61 dB
Possibly Clipped: 0
DC Offset: 0
Minimum RMS Power: -inf dB
Maximum RMS Power: -15.05 dB
Average RMS Power: -31.55 dB
Total RMS Power: -28.07 dB
Actual Bit Depth: 24 Bits

Using RMS Window of 50 ms


But in  a Frequency Analysis of the two (FFT size 65536, Blackmann-Harris)  the 48kHz curve is 3dB lower than the 96kHz curve ;  there are some differences in curve shape at either end of the spectrum, but otherwise the two curves are parallel. (attached  pic)

Can someone explain why I'm seeing this (the 3dB difference in visual comparison) when the amplitude stats do not indicate an overall 3dB change?  Is it a function of FFT analysis? 


 

 

Re: understanding measured and viewable changes after resampling

Reply #1
But in  a Frequency Analysis of the two (FFT size 65536, Blackmann-Harris)  the 48kHz curve is 3dB lower than the 96kHz curve ;  there are some differences in curve shape at either end of the spectrum, but otherwise the two curves are parallel. (attached  pic)

Can someone explain why I'm seeing this (the 3dB difference in visual comparison) when the amplitude stats do not indicate an overall 3dB change?  Is it a function of FFT analysis?  

If you use the same FFT size for both, but one has double the sampling rate, each bin is half as wide, and thus has 3dB less energy. 

This is why spectrum analyzers often report in units of dB/sqrt(Hz).  It makes the amplitude independent of the bin width, whereas if you just look at total energy the amplitude depends on the width of each FFT sample. 

Re: understanding measured and viewable changes after resampling

Reply #2
the minimum RMS power (in dB) decreases.
In this example, the minimum power is effectively silence. If the background noise was equally distributed (white) in the source, then after downsampling it would decrease by 3dB for each halving of the bandwidth. You can hear this comparing 8-bit recordings of different sampling rates. The decrease would be greater if the noise was shaped toward high frequencies, as would be the case coming from a delta-sigma converter.

You might be working on 24-bit resolution files padded to 32, which limit the smallest number than can be reported to ca. -146 dB. I looked at statistics function in CoolEdit (ancestor of Audition), and it shows me either 'float' or integer greater than 24 in the actual bit depth.

Peak amplitude always changes during resampling, depending on where on the reconstructed wave the new sampling points fall, and the phase relationship of the frequencies that were filtered in the process, which is why you need to leave a sufficient margin when normalizing. The biggest change is during high frequency sections, such as sibilant sounds.

Re: understanding measured and viewable changes after resampling

Reply #3
Thank you both for the explanation! 

It sound like for apples-to-apples Frequency Analysis here , I should make the sample rates the same.

Re: understanding measured and viewable changes after resampling

Reply #4
Thank you both for the explanation! 

It sound like for apples-to-apples Frequency Analysis here , I should make the sample rates the same.


Or adjust the FFT size so that the length of the portion of data you are analyzing is constant in time.  E.g. if you double the sampling rate (each sample half as long) take twice as many samples so that you span the same duration.

Re: understanding measured and viewable changes after resampling

Reply #5

Or adjust the FFT size so that the length of the portion of data you are analyzing is constant in time.  E.g. if you double the sampling rate (each sample half as long) take twice as many samples so that you span the same duration.
 

Sorry, yes indeed, that's the other way, but in Audition it's not possible to layer two analyses on top of each other when you change the FFT size.  So it's quicker for me just to resample one of the tracks (using a simple Audition menu option) and use the same FFT size for both. 

 
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