pseudo-random noise test signal + crestfaktor

[ondra_zoltan]

hello,

i have a Labview problem. I need to do a generator of pseudo-random noise test signal with parameters according to standart ITU-T O.131. The main parameter is Crestfaktor which must be in range 10 dB to 11 dB.

Anyone have any idea? Thank you..

[mikeporter]

The first part of your answer lies in Paragraph 2 of the standard where it says you need a noise source, "...having a probability density distribution of amplitudes which is substantially near to a Gaussian distribution." LabVIEW has several signal generation VIs, one of which creates an output with a Gaussian distribution.

The standard also tells you the amplitude requirements for the signal.

Once you have a signal with the correct amplitude, you can send it to the DUT (device under test) using an appropriate analog output card. By the way the part of the document that talks about the signal bandwidth will tell you how fast you will need to update the output.

Also don't forget to use a **hardware** reconstruction filter on the output. A simple RC lowpass filter works fine in many cases. All analog outputs are step functions and regardless of how small the steps are, you need to remove the high frequency components resulting from the step edges.

Mike...

[Bob_Schor]

Wow!  It must be several decades since I've thought about PRBS's (Pseudo-Random Binary Sequences), a key element of the standard document you reference.

A PRBS is relatively easy to generate if you understand the principle.  To generate the 17-bit sequence of the Standard, where bits 3 and 17 become the new bit.  I coded this up, but it needs some explanation.

The key step is to create a 17-bit quantity, which I do by creating a Boolean Array of length 17.  A proper PRBS must be initialized with any non-zero 17-bit number -- I use a U32 value called "Seed" (but don't check if it is > 131071), along with a Flag that gets set the first time Seed is non-zero (to prevent re-initialization).  This is the code shown in the initial Case structure's False

limb, where the non-zero Seed is converted to a 32-bit Boolean Array, 15 bits are discarded, and we have an initialized 17-bit Binary Shift Register (which we store in a LabVIEW Shift Register).  The "already-initialized" True Case just passes the Shift Registers through.  The rest of the code implements the specified PRBS -- bits 3 and 17 (Array Indices 2 and 16) are XOred, and placed in Position 17 where they will be rotated into Position 1 to produce the next 17-bit PRBS value (after expressing the bit pattern as a new 17-bit integer).

Bob Schor

[ondra_zoltan]

Thank you Bob Schor for the PRBS. Do you know how to solve the Crestfaktor on the output of PRBS? I tried solve this problem, but i could not figure. Btw I have the LabVIEW 2014

Thank you.

[Bob_Schor]

Sure.  The Crest Factor is defined as the ratio of the peak value of a waveform to its RMS value.  A PRBS of order N is designed to produce all of the numbers from 1 to the (Nth power of 2 - 1) -- let's call this number P (for "PRBS Size").

I'm going to do this "mathematically" -- it should be an easy exercise to write LabVIEW code to generate a PRBS sequence of arbitrary size, find its peak, find its RMS, and take the ratio, but let's derive what it should be.

So what is the Peak Value of a sequence that takes on all values from 1 to P?  [Hint -- it is slightly larger than P-1].

A slightly harder question is what is the RMS value of the P numbers that constitute the PRBS sequence?  Well, let's first sort these numbers, and what do we have?  Why, the integers from 1 to P.  To get the RMS, we need to sum the squares of the integers, divide by the number of them, and take the square root.

The sum of the first P integers is P*(P+1)*(2P+1)/6.  Dividing by P give (P+1)*(2P+1)/6.  Now simply take the square root of this result.

If we say that P = 2^17 - 1, then the Crest Factor is 1.732.  Note that as P gets large, the Crest Factor will approach the square root of 3, which I remember from my high school days as 1.732 ...

Bob Schor 

[ondra_zoltan]

OK, I think I understand it. If the Crestfaktor on output should be in the range 10 dB to 11 dB. Crestfaktor = 20*log peak value/RMS value. How to do it?

Thank you again

[Bob_Schor]

The Crest Factor is a function of the signal.  If you are generating a PRBS, you need to understand the meaning of the word "Random" -- you don't "control" it, it is what it is.  For a PRBS of infinite duration (which we can model as a PRBS that completes a single cycle, namely, in your 17-stage case, 2^17-1 outputs), we can derive the Crest Factor, which is 1.732.  If you want to express this in dB, go right ahead.  However, don't try to "adjust" it -- if you want to do that, you'll have to come up with a different signal.

Bob Schor