🚀 go-pugleaf

Sasha Lanning wrote:
 
 > I am looking for the autocorrelation function for a specific kind of
 > square wave.    I need the autocorrelation function for a square wave 
 > with a variable duty cycle and a random phase shift along the period 
 > with amplitude -1 to 1.

The autocorrelation function you want can be obtained very easily by
integrating the product of the lagged waveform over one period.  For an
arbitrary square wave, the value of this product must be -1, 0 or +1 at
each point, so the integration task is simply one of determining the
boundaries of the interval(s) within which the integrand adopts each of
its three values.  Sketches help a lot here.

The problem you describe is a particularly simple example of
autocorrelation analysis, so I would urge you to invest some effort in
mastering it both conceptually and mathematically.

  Charles Metz

On Fri, 25 Aug 2000 14:59:58 -0700, Sasha Lanning
<sdlannin@newton.berkeley.edu> wrote:


Hello Sasha,

>I am looking for the autocorrelation function for a specific kind of
>square wave.    

I wonder what exactly do you mean by "function".  The 
word function means different things in different 
situations.  I think of a function as a mathematical 
relationship.  For example, the area of a circle is a 
function of the circle's radius.

Also, traditionally, the phrase squarewave means a bi-level 
signal (or waveform) with exactly a 50% duty cycle.
If it doesn't have a 50% duty cycle, then it's not 
a squarewave.  Perhaps it would be better to call 
your waveform a "rectangular pulsed" signal, or 
a "pulsed waveform".

I'm nit-picking here because terminology is so darned 
important when we have no diagrams to look at.

>I need the autocorrelation function for a square wave with a
>variable duty cycle and a random phase shift along the period with
>amplitude -1 to 1.
>
>The autocorrelation function for a square wave with .5 duty cycle is a
>triangle wave varying between 0 and .5, repeating every period.

Humm, ... the triangular part sounds reasonable.

>Numerically, I have been able to find the autcorrelation function for a
>square wave with greater than and less than .5 duty cycles.

Does that mean you're modeling autocorrelation on a 
computer, or working with paper and pencil?

>The functions
>look similar to a triangle wave, except that they have flat portions
>instead
>of peaks on the low part of the graph.

I have no idea what you mean by "peaks on the low part of 
the graph", but it seems to me that that the autocorrelation 
of a rectangular waveform (regardless of duty cycle) 
will be triangles, with the spacing between the triangles 
being inversely proprtional to the duty cycle of the pulses.

>Any help or information will be greatly appreciated!

In an attempt to keep his stress at a sufficiently high 
level, I recommend that you contact an EE grad student 
there at UC Berkeley who has strong math skills.  
His name is Julius Kasuma, and I'll bet he can stand 
at the whiteboard and solve darned near any technical 
problem you have.

Good Luck,
[-Rick-]