Re: Amplitude Decibel conversion problem

On Oct 7, 11:07 pm, buleg...@xxxxxxxxxxxxxxx wrote:
On Oct 7, 2:52 pm, "jungledmnc" <jungled...@xxxxxxxxx> wrote:





Hi,
this question might be very trivial, but I haven't found good explanation
anywhere else.

I have an audio signal - some sine. Use a wavelabl to look at the
waveform, and its maximum is at about 0.6. When I change the display into
dB it shows about -5dB at that level.
But this does not make sense - the formula is 10*log10(amplitude). So it
should be -2.5dB. I have found, that this is because we use squares for
comparison :
10 * log10(amp1^2 / amp2^2) = 20 * log10(amp1 / amp2)

They say it is often used in electronics to compare voltages, but why is
it used in digital audio? Yeah I know that the digital values are
equivalent to resulting electrical power, but we are not comparing anything
to anything. So why should we square?

And if so, then when should we NOT square?

Thanks a lot.
dmnc

dB's always compare one power to another power by the formula that you
have written down.

In electronics we often do not directly measure power, but rather
voltage.  Most of our measuring equipment measures things in voltage.

So we are stuck in a position where we want to compare one power level
to another power level, but our measuring equipment measures voltages.

(Also in DSP most of the time the A/D converter is getting a voltage
equivelent input)

To properly compare one power level when we made the measurement in
voltage you have to first convert the measured voltage level into a
measured power level, and the reference voltage level into a reference
power level.

Here is where the shortcut comes in, but remember, dB's always compare
power levels.  It is the definition.

But when you are comparing voltage levels, it turns out you get to use
the trick of multiplying by 20*log(ratio) instead of 10*log(ratio),
becuase power proportional to the voltage squared.  so 10*log(V1^2/
V2^2) is the same as

20*log(V1/V2).  This is a shortcut or trick. Always go back to dB's
compare power per the definition formula 10*log(P1/P2).

The 20 log thing comes into play becuase in the real world you rarely
measure power directly.  You measure voltages directly, and then
apply the 20* trick to convert the voltages to power.- Hide quoted text -

- Show quoted text -


PS I have a website that describes some DSP stuff. One of the
programs that I wrote gives an overview of dB's as a precurser to
understanding windowing.

Look it over if you like. The dB stuff is on the first and especially
second page of the program.

http://www.fourier-series.com/fourierseries2/flash_programs/DFT_windows/index.html

.

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