[sdiy] Vote for your favorite noise source

[Magnus Danielson]

From: Tim Ressel <madhun2001 at yahoo.com>
Subject: Re: [sdiy] Vote for your favorite noise source
Date: Mon, 13 May 2002 11:22:37 -0700 (PDT)

Tim,

> Wow,
> 
> Thanks for all the responses. I knew if I asked, I'd
> get alot of noise back...

That's the topic, ain't it? ;O)

> Something about the shift-register method you may not
> know: they don't produce all frequencies! Instead, you
> get a picket-fench effect.

Correctomundo!

If you have a PRBS consisting of N stages and of propper Maximum
Length Sequence (MLS) type, you have a sequence of the length

     N
L = 2 - 1

If you clock this thingie with the clock frequency fclk, then the loop
time tloop becomes:

                N
         L     2  - 1
t     = ---- = ------
 loop   f       f
         clk     clk

Which makes the fundamental frequency of the output waveform (it is a
repeting static waveform) of the frequency ffund:

                f       f
          1      clk     clk
f     = ----- = ---- = ------
 fund   t        L      N
         loop          2  - 1

Since it is a repeating waveform of that frequency, all it's overtones
will be distanced with the same frequency as the fundamental has.

Now, in the above equations several things is obvious:

* Increasing N increases loop-time

* Increasing N decreases overtone distance (i.e. makes noise "denser")

* Increasing fclk makes loop-time shorter

* Increasing fclk makes overtone distance larger (i.e. makes noise
  "sparser")

Also, not as obvious, but quite clear anyhow:

* Increasing fclk makes upper noise frequency higher

So, given this at hand, having a fairly high fclk and a sufficiently
high N should make a good noise-core.

> One day I was playing
> around with a new RF spectrum analyzer we just
> released. I wanted an interesting source, so I built
> an 8-stage shift register noise source. Much to my
> surprise instead of the flat line I expected
> (ageraging and peak hold turned on), I saw a picket
> fence. I got 255 frequency lines between 0hz and the
> clock frequency. Of course, with a large chain like 32
> registers, the lines are so close together, ya ain't
> gonna notice it. 

Right. Another thing to remember, besides the short looptime (tic tic
tic) having a sparse noise-frequency set makes narrow Q peaks SOUND
quite different from that of having real noise or just a very dense
noise-spectrum.

> One nice thing about the shift register method is: its
> easy to get low freqency noise. Just slow down the
> clock. The problem with filtering wideband noise is
> you are selecting a small band by filtering, and
> therefore getting a small portion of the energy ergo
> low amplitude. 

Right. Slowing down the clock has other problems too.

> One topic I'm surprised didn't come up was
> distribution. When evaluating noise sources for signal
> processing, the distribution is important. It can be
> seen like this: picture doing a histogram of the
> amplitudes of the noise. That histrgram shows the
> distribution. Uniform distribution will have a
> histogram that ramps linearly to zero. Gaussian
> distribution will have what else? a Gaussian curve. 

Right.

> I saw flash by a notion of of using resistor banks on
> the shift register output to for an FIR filter.
> Interesting idea. Has anyone done an inverse-FFT of
> the pink curve yet?

Haven't dug out Octave yeat...

> This will yield the weights of the
> FIR filter. Query: the -3dB slope of the pinking
> filter, is that per octave of per decade?

Per octave, and you should notice that it is actually 20log(1/sqrt2))
per octave.... roughtly -3.0103 dB/Oct. That "-3 dB" is just the
approximation... worth recalling actually, even if it doesn't make
much of a difference in this case.

> And does
> -3dB refer to voltage or power? I assume voltage.

-3 dB is -3 dB! Bel as such is a power-ratio scale (originally that
is) and whenever you encounter voltage or currents you square them in
order to convert them into power... that squaring gets ripped into the
scaling after the log has been taken

                             2
L = 10*log(P/Pref) = 10*log(V /Zref/Pref) = 20*log(V/Vref)

Since V is the volume of your room, you know at which level L you have
in reference to the reference volume Vref. Volume is given in l³ as
you all know. The level is shifted by one depending on if the building
is located in the USA or in Europe. There reference litre is an well
archived Congac stored in a safe in Paris (at BIPM). I have yeat to go
there to have some, which would definitly change the volume of the
whole world... ah well ;O)

Cheers,
Magnus - anyone can point out where I stopped being ultraserious?