Why? That does not make any sense to me.
----- Original Message ----- 
From: "Federico Vanni" 
To: 
Sent: Sunday, December 21, 2008 2:57 PM
Subject: [Csnd] Re: Re: Re: Re: dynamic range


> ok Alan, thanks...
> so why we don't change the 'ampdb' opcode using
> a maximum dB value of 96???
> it should be more accurate teorically...
> best
> fv
>
>
>
>
>
> Il giorno 21/dic/08, alle ore 15:02, Alan Peter Fitch ha scritto:
>
>> jpff@cs.bath.ac.uk wrote:
>>>> ...so why in many books is wrote that the dynamic range
>>>> of 16 bit systems is 96dB and not 90 dB?
>>>> see curtis roads and many others.
>>>> fv
>>>>
>>>
>>> I cannot speak for Cutis Roads, but 16bits translates to a ratio  of 
>>> 96dB.
>>> That is true but misleading.  In audio we hace to handle + and -
>>> displacement from a norm, and so what we call 16bits is really 15  bits 
>>> and
>>> a sign.  Hence the dynamic range of "16bit" audio is 90dB.
>>>
>>> Does it really matter?
>>>
>>> ==John ff
>>>
>>>
>>
>> The 96db figure is the dynamic range of maximum signal to quantization
>> noise, assuming quantization noise can be approximated as white
>> gaussian, and has a maximum value of +/- half an LSB.
>>
>> In other words the range of a signal from maximum 16 bits to the  minimum
>> that would be below the quantization noise level.
>>
>> The other figure you are talking about is expressing an amplitude  value
>> in dB. dB are always relative to something. Normally in audio, dB (as
>> Richard Dobson has repeated many times!) are relative to full  scale, the
>> maximum value that the signal can take.
>>
>> So a maximum amplitude sinewave would be 0dBFS (dB full scale).
>>
>> There is another point of confusion here: with 2's complement
>> arithmetic, the possible range of values of a signal is -2^15 to  2^15 -1
>> i.e. -32768 to +32767.
>>
>> However a full amplitude sinewave centred on zero would have to be
>> symmetrical, i.e. -32767 to +32767. Of course as quantization is to
>> +/-0.5 LSB you could argue that the maximum is
>>
>> -32767.5 to +32767.5
>>
>> if you wanted to.
>>
>> If you want to express that in dB then the amplitude is +32767.5 - but
>> relative to what? The minimum representable sinewave would be +/-0.5
>> lsb, so if you express the maximum amplitude relative to the  minimum you
>> get
>>
>>   20log10(32767.5 / 0.5) = 96.32dB
>>
>> To summarise
>>
>> 1) the often quoted 96dB is the ratio of the power in a full amplitude
>> sinewave to the power in the quantization noise, assuming quantization
>> noise can be approximated as white guassian noise.
>>
>> 2) the amplitude of a sinewave expressed in dB *must* be expressed
>> relative to a reference. If the reference is 0.5LSB, then the  maximum is
>> 96dB.
>>
>> 3) Most audio engineers express dbFS, the maximum amplitude is 0dBFS,
>> for a 16 bit system the minimum amplitude would be -96.32dBFS
>>
>> I hope this helps,
>>
>> regards
>> Alan
>>
>>
>> -- 
>> Alan Fitch
>>
>>
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>
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And one cannot change existing opcodes as it runs the danger of breaking
existing music.

> Why? That does not make any sense to me.
> ----- Original Message -----
> From: "Federico Vanni" 
> To: 
> Sent: Sunday, December 21, 2008 2:57 PM
> Subject: [Csnd] Re: Re: Re: Re: dynamic range
>
>
>> ok Alan, thanks...
>> so why we don't change the 'ampdb' opcode using
>> a maximum dB value of 96???
>> it should be more accurate teorically...
>> best
>> fv