On 6/17/2009 12:37:31 PM, jmG wrote:
>You have too many good points
>Philip,
>
>I don't understand the idea of
>not getting first the spectrum
>and deal with db after. The
>portion that you plug in
>Fourier is the "Fourier
>period", the spectrum comes
>out indexed, what is the
>purpose of plotting the
>spectrum indexes on log scale
>? Further, the signal is a
>pure function with some degree
>of noise (user). But in
>reality there is little noise
>or negligible noise because
>all the converting devices
>between the very primary
>sensitive (capturing) device
>that converts the physics into
>signal ... the transmission,
>the readout before the A/D.
>
>jmG
Hi Jean,
You have picked up on a couple of the right points, but are possibley looking from the wrong side of the 'solution'. As you rightly say, it would be great if we could get the sample period to be an exact multiple of the signal periods, and if the analog to digital conversion had negligible noise. Unfortunately, Luc and others (and me sometimes) are stuck at the other end without the option of the exact period or 'perfect' (infinite precision) A/D converter.
So Luc's sheet shows what happens when we don't get our sample right. The main effects are actually the 'bad sampling' - I have just had to do one for an internal report showing that Fourier has the same 'problems' as Wavelets in respect of imperfect sampling.
The A/D noise will be low unless we change the number of bits to a low number e.g. 3, 5, 6, 7 etc. Even then the Fourier transform will still be pretty good (which is amazing really(*). The base noise can't get above +/-1/2 lsb peak so as an rms it is low.
The use of dB and a log scale are just because they are so common in electrical engineering. I'm sure part of the point of the simulation is to flag up a warning to other users of spectrum analysers as to the 'funny effects' that can be seen. [I tend to stick with lin-lin plots in mcd, so I can see what mcd sees]
Philip Oakley
(*) that ability to 'pull' the signal out of the very bad noise is similar to watching a snowy TV! [the things that digital USA will miss...]
Random noise of amplitude rms = 1/2lsb will average out to linear to better than a further 8 bits (i.e the mean level, after digitisation, will average to the true value to better than 1/256th of the digitisation bit)