[HAM] Vedr. Re: Vedr. Re: The New B-3

[Carl Mal]

Don't apologize, I appreciate the debate, not sure about this group tho, because this topic has been run ragged in most audio groups.

I'm still standing here with my arms folded tho, saying approximation.  The understanding of the sample error "leftovers", and the pattern/profile they take on allows further reconstruction of upper harmonics to a point, but again it's an algo.  This type of predictablility has allowed us to go beyond sampling, allowing modelling.

Here's what I'm trying to get at.  Zoom in on an audio signal on the ocsilloscope, zoom in on one in your wave editor.  They look different, because they are.

If you don't like my label of "approximation" and want me to call it something else, I will, I will even call it "exact" if we are dismissing the upper freq interactions of an anolog signal.

When I was talking filters, I meant on the DA side, sorry 'bout that back at you.

Carl

> Date: Fri, 1 Feb 2008 19:28:15 -0500
> From: b3jazz at gmail.com
> To: hammond at zeni.net
> Subject: Re: [HAM] Vedr. Re: Vedr. Re: The New B-3
>
> On Feb 1, 2008 5:56 PM, Carl Mal  wrote:
>> How can digital not be an approximation? Digital is discreet steps
>> -vs- analog's continuously varying voltage.
>
> First about sampling, then about quantization. From the
> Nyquist-Shannon sampling theorem:
> http://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem
>
> "Exact reconstruction of a continuous-time baseband signal from its
> samples is possible if the signal is bandlimited and the sampling
> frequency is greater than twice the signal bandwidth."
>
> This is a theorem that describes sampling, not quantizing. This could
> be achieved for example if one used a D/A converter with an infinite
> number of bits. Each sample would equal the actual voltage of the
> input signal at the sampling instant - not a quantized version of that
> voltage. This is not a realistic system.
>
>> By approximation, I mean the anti-aliasing filter that interpolates
>> between the steps is "approximating".
>
> The anti-aliasing filter does not interpolate between steps. Its
> purpose is to band limit the input signal so that aliasing does not
> occur. Any signal that is lower in frequency than its cutoff will be
> unaffected in amplitude, frequency and, if it is a proper filter,
> phase. In real systems which quantize the input signal, any signal
> within the Nyquist bandwidth (less than half the sampling frequency)
> will be sampled at the sampling instant and its value will be
> quantized or rounded to the nearest quantization level, dependent upon
> the resolution (number of bits) of the A/D converter. The result of
> this quantization is an error. The error is the difference between
> the actual level of the input signal and the level to which it is
> quantized. The result is that for each sample, the digitized signal
> is equal to the actual input value at the sample point plus the error
> value. The error shows up as a pattern-dependent noise component.
> This noise can be reduced to an arbitrarily low level by various
> techniques, for example increasing the number of bits in the converter
> (dynamic range is roughly 6 dB per bit). Also there are other
> techniques, dither, noise shaping, that can be used to make this noise
> inaudible in practice.
>
> Sorry for the pedantry. I'll go back to sleep now.
>
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