Forums

LFSR flat frequency

Started by thomas_lpc January 21, 2005
Hello,

LFSR (linear feedback shift register) generate flat spectrum
and I prosssed the output of LFSR for DFT to see flat spectrum and it
does generate.

Somebody suggests mathamatical model to prove LFSR generate flat
spectrum. I would appriciate if somebody pass hints.

Regards,

Thomas




Hi Tomas!

Try:

FFT(Autocorrelation function(LFSR sequence))

It is important to calculate ACF on the whole sequence L=(2 exp n) -1.

Best wishes,
Predrag

----- Original Message -----
From: "thomas_lpc" <>
To: <>
Sent: Friday, January 21, 2005 5:32 PM
Subject: [matlab] LFSR flat frequency >
> Hello,
>
> LFSR (linear feedback shift register) generate flat spectrum
> and I prosssed the output of LFSR for DFT to see flat spectrum and it
> does generate.
>
> Somebody suggests mathamatical model to prove LFSR generate flat
> spectrum. I would appriciate if somebody pass hints.
>
> Regards,
>
> Thomas >
>





Hi Thomas
As Predrag says, the LFSR sequence(which is also called as pseudorandom
binary sequence) has almost delta-correlation. i.e. its autocorrelation
function is a symmetric, narrow triangular waveform with width equal to
two times the bit-width. Further, the peak of the function is 2^N-1 and
the remaining values of the function lie at (+ or -1). This can be
proved. Though the this function is (almost) like a delta function, it
is indeed not because this function repeats every 2^N-1 samples. That is
why it is called as "pseudo-random".
Because the waveform has an impulse like auto-correlation function, its
spectrum will be flat and hence white.
Ideally white-noise should not be predictable at any time period, (i.e.
ACF is a pure delta function) but since the sequence is predictable also
it is called as pseudo-random.

Hope this helps.

Regards
arun -----Original Message-----
From: Valozic [mailto:]
Sent: Monday, January 24, 2005 4:34 PM
To: ; thomas_lpc
Subject: Re: [matlab] LFSR flat frequency
Hi Tomas!

Try:

FFT(Autocorrelation function(LFSR sequence))

It is important to calculate ACF on the whole sequence L=(2 exp n) -1.

Best wishes,
Predrag

----- Original Message -----
From: "thomas_lpc" <>
To: <>
Sent: Friday, January 21, 2005 5:32 PM
Subject: [matlab] LFSR flat frequency >
> Hello,
>
> LFSR (linear feedback shift register) generate flat spectrum
> and I prosssed the output of LFSR for DFT to see flat spectrum and it
> does generate.
>
> Somebody suggests mathamatical model to prove LFSR generate flat
> spectrum. I would appriciate if somebody pass hints.
>
> Regards,
>
> Thomas >
>



   Hello Arun & Valozic,
 
                      Thanks guys, your hints helped me to come up with a mathematical model to prove LFSR generate flat spectrum.
 
    cheers,
 
    Thomas  

a...@wipro.com wrote:

Hi Thomas
As Predrag says, the LFSR sequence(which is also called as pseudorandom
binary sequence) has almost delta-correlation. i.e. its autocorrelation
function is a symmetric, narrow triangular waveform with width equal to
two times the bit-width. Further, the peak of the function is 2^N-1 and
the remaining values of the function lie at (+ or -1). This can be
proved. Though the this function is (almost) like a delta function, it
is indeed not because this function repeats every 2^N-1 samples. That is
why it is called as "pseudo-random".
Because the waveform has an impulse like auto-correlation function, its
spectrum will be flat and hence white.
Ideally white-noise should not be predictable at any time period, (i.e.
ACF is a pure delta function) but since the sequence is predictable also
it is called as pseudo-random.

Hope this helps.

Regards
arun-----Original Message-----
From: Valozic [mailto:p...@vtszg.hr]
Sent: Monday, January 24, 2005 4:34 PM
To: m...@yahoogroups.com; thomas_lpc
Subject: Re: [matlab] LFSR flat frequency
Hi Tomas!

Try:

FFT(Autocorrelation function(LFSR sequence))

It is important to calculate ACF on the whole sequence L=(2 exp n) -1.

Best wishes,
Predrag

----- Original Message -----
From: "thomas_lpc"
To:
Sent: Friday, January 21, 2005 5:32 PM
Subject: [matlab] LFSR flat frequency>
> Hello,
>
> LFSR (linear feedback shift register) generate flat spectrum
> and I prosssed the output of LFSR for DFT to see flat spectrum and it
> does generate.
>
> Somebody suggests mathamatical model to prove LFSR generate flat
> spectrum. I would appriciate if somebody pass hints.
>
> Regards,
>
> Thomas<*> To visit your group on the web, go to:
http://groups.yahoo.com/group/matlab/

<*> To unsubscribe from this group, send an email to:
m...@yahoogroups.com

<*Confidentiality Notice
The information contained in this electronic
message and any attachments to this message are
intended for the exclusive use of the addressee(s)
and may contain confidential or privileged information.
If you are not the intended recipient, please notify
the sender at Wipro or M...@wipro.com immediately
and destroy all copies of this message and any attachments.



Thomas,

Further, the “white” applies in the range of (+/- Fs/2).

Whereas, a true white-noise is flat in [-infinity, infinity].

Regards

arun

-----Original Message-----
From: Thomas Patrick [mailto:t...@yahoo.com]
Sent:
Tuesday, January 25, 2005 3:57 PM
To: arun d naik (WT01 - EMBEDDED & PRODUCT ENGINEERING SOLUTIONS)
Cc: m...@yahoogroups.com
Subject: RE: [matlab] LFSR flat frequency

 

   Hello Arun & Valozic,

 

                      Thanks guys, your hints helped me to come up with a mathematical model to prove LFSR generate flat spectrum.

 

    cheers,

 

    Thomas  

a...@wipro.com wrote:


Hi Thomas
As Predrag says, the LFSR sequence(which is also called as pseudorandom
binary sequence) has almost delta-correlation. i.e. its autocorrelation
function is a symmetric, narrow triangular waveform with width equal to
two times the bit-width. Further, the peak of the function is 2^N-1 and
the remaining values of the function lie at (+ or -1). This can be
proved. Though the this function is (almost) like a delta function, it
is indeed not because this function repeats every 2^N-1 samples. That is
why it is called as "pseudo-random".
Because the waveform has an impulse like auto-correlation function, its
spectrum will be flat and hence white.
Ideally white-noise should not be predictable at any time period, (i.e.
ACF is a pure delta function) but since the sequence is predictable also
it is called as pseudo-random.

Hope t his helps.

Regards
arun -----Original Message-----
From: Valozic [mailto:p...@vtszg.hr]
Sent: Monday, January 24, 2005 4:34 PM
To: m...@yahoogroups.com; thomas_lpc
Subject: Re: [matlab] LFSR flat frequency
Hi Tomas!

Try:

FFT(Autocorrelation function(LFSR sequence))

It is important to calculate ACF on the whole sequence L=(2 exp n) -1.

Best wishes,
Predrag

----- Original Message -----
From: "thomas_lpc"
To:
Sent: Friday, January 21, 2005 5:32 PM
Subject: [matlab] LFSR flat frequency >
> Hello,
>
> LFSR (linear feedback shift register) generate flat spectrum
> and I prosssed the output of LFSR for DFT to see flat spectrum and it
> does generate.
>
> Somebody suggests mathamatical model to prove LFSR generate flat
> spectrum. I would appriciate if somebody pass hints.
>
> Regards,
>
> Thomas >
>
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<*> To visit your group on the web, go to:
http://groups.yahoo.com/group/matlab/

<*> To unsubscribe from this group, send an email to:
m...@yahoogroups.com

<* Confidentiality Notice
The information contained in this electronic
message and any attachments to this message are
intended for the exclusive use of the addressee(s)
and may contain confidential or privileged information.
If you are not the intended recipient, please notify
the sender at Wipro or M...@wipro.com immediately
and destroy all copies of this message and any attachments.