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Re: A lot of people don't understand dither

"I checked the data sheet for the PCM1804, and the noise curves ... clearly show that ... the noise levels are close to -140dB apart from a few spikes (which ... lower the dynamic range to 112dB)"

No. The curves show the noise DENSITY, which is, by definition, the specific noise power measured over a unit bandwidth of 1 Hz.

In order to obtain the noise LEVEL (which is what you need for SNR and dynamic range calculations, and which is also what figures in the infamous SNR = 6 x NumberOfBits shortcut), you have to integrate the DENSITY over BANDWIDTH.

For a white noise spectrum with given noise density of Vn (dB) the resulting (RMS) noise level is then Vrms = Vn + 10*log(bandwidth), all in dB.

An ideal 16 bit system with 96 dB SNR over a bandwidth of 22kHz (CD) then has its density at -96-10*log(22000) = -139dBFS.

My PCM1804 with measured 108dB SNR over a bandwidth of 48kHz (running the recorder at 96kHz), has its density at -108-10*log(48000) = -155dBFS.

So if you measure -130dBFS for your system, then the equivalent RMS level (assuming 22kHz BW) is -87dBFS and that's 14.5 bits ;-)

But don't worry, chances are that if you were only looking at FFT-generated plots of the noise density floor your 'measurement' was wrong anyhow, as the plotted level depends on the size of the FFT itself. Try it. Take a white noise signal into Audition and take its spectrum with 1024, 4048, 32000 point FFT ...

The plots in the PCM1804 datasheet are made with 8192 point FFTs. The resulting levels don't show the true per-1-Hz noise density, but rather the density per frequency-bucket of Fsample/8192 Hz. So the floors in the plots are artificially high. That is OK, because to a skilled engineer the 'N=8192' tag in the plot says all.

Included link may help.



bring back dynamic range



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