# LFSR flat frequency

Started by 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 ThomasAs Predrag says, the LFSR sequence(which is also called as pseudorandombinary sequence) has almost delta-correlation. i.e. its autocorrelationfunction is a symmetric, narrow triangular waveform with width equal totwo times the bit-width. Further, the peak of the function is 2^N-1 andthe remaining values of the function lie at (+ or -1). This can beproved. Though the this function is (almost) like a delta function, itis indeed not because this function repeats every 2^N-1 samples. That iswhy it is called as "pseudo-random".Because the waveform has an impulse like auto-correlation function, itsspectrum 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 alsoit is called as pseudo-random.Hope this helps.Regardsarun-----Original Message-----From: Valozic [mailto:p...@vtszg.hr]Sent: Monday, January 24, 2005 4:34 PMTo: m...@yahoogroups.com; thomas_lpcSubject: Re: [matlab] LFSR flat frequencyHi 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 PMSubject: [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 electronicmessage and any attachments to this message areintended for the exclusive use of the addressee(s)and may contain confidential or privileged information.If you are not the intended recipient, please notifythe sender at Wipro or M...@wipro.com immediatelyand 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 > > ------------------------ Yahoo! Groups Sponsor --------------------~--> In low income neighborhoods, 84% do not own computers. At Network for Good, help bridge the Digital Divide! http://us.click.yahoo.com/EA3HyD/3MnJAA/79vVAA/wHYolB/TM --------------------------------~- <*> 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.