LFSR flat frequency

[Sridhar Gadda]

Hi,

Can anyone forward material related to proving Linear feeback
shift register generate flat frequency spectrum. I know one Idea is
perfoming DFT on smaples taken from LFSR. I am looking for
mathematical model.

any help can be appriciated.

With regards

Sridhar

 

[Rene Tschaggelar]

Sridhar Gadda wrote:

Hi,

Can anyone forward material related to proving Linear feeback
shift register generate flat frequency spectrum. I know one Idea is
perfoming DFT on smaples taken from LFSR. I am looking for
mathematical model.

They don't make a flat spectrum, sorry.
It is unevenly distributed between the clock and the
clock divided by the number of bits.
Plus som upper harmonics of course.

Rene
--
Ing.Buero R.Tschaggelar - http://www.ibrtses.com
& commercial newsgroups - http://www.talkto.net

 

[Allan Herriman]

On Thu, 18 Nov 2004 13:08:06 +0100, Rene Tschaggelar <none@none.net>
wrote:

Sridhar Gadda wrote:

Hi,

Can anyone forward material related to proving Linear feeback
shift register generate flat frequency spectrum. I know one Idea is
perfoming DFT on smaples taken from LFSR. I am looking for
mathematical model.

They don't make a flat spectrum, sorry.
It is unevenly distributed between the clock and the
clock divided by the number of bits.
Plus som upper harmonics of course.

The spectrum has a sin(x)/x envelope, due to the zero-order-hold
effect. The first null is at the clock frequency.

In theory, the spectrum is discrete, in that it consists of lines with
a spacing of the clock frequency divided by the number of LFSR states
(i.e. 2^number of bits - 1), but for practical register lengths and
clock frequencies, the line spacing will be much less than the
resolution bandwidth on any spectrum analyser.

Regards,
Allan

 

[john jardine]

"Rich Grise" <rich@example.net> wrote in message
newsan.2004.11.18.20.16.13.704491@example.net...

On Thu, 18 Nov 2004 23:45:55 +1100, Allan Herriman wrote:

On Thu, 18 Nov 2004 13:08:06 +0100, Rene Tschaggelar <none@none.net
wrote:

Sridhar Gadda wrote:

Hi,

Can anyone forward material related to proving Linear feeback
shift register generate flat frequency spectrum. I know one Idea is
perfoming DFT on smaples taken from LFSR. I am looking for
mathematical model.

They don't make a flat spectrum, sorry.
It is unevenly distributed between the clock and the
clock divided by the number of bits.
Plus som upper harmonics of course.

The spectrum has a sin(x)/x envelope, due to the zero-order-hold
effect. The first null is at the clock frequency.

In theory, the spectrum is discrete, in that it consists of lines with
a spacing of the clock frequency divided by the number of LFSR states
(i.e. 2^number of bits - 1), but for practical register lengths and
clock frequencies, the line spacing will be much less than the
resolution bandwidth on any spectrum analyser.

I'm wondering how you get from the LFSR output into the frequency
domain - just take the bit stream and act like it's an analog signal?
Maybe LPF it? What would happen if, each clock cycle, you latched the
register value into a DAC? What kind of difference might that make? Take
the DAC output for your signal, of course.

I've "listened" to a bit stream, and it definitely isn't pink
noise! It's kinda scraxxy, and (this was only about 16 bits)
clearly periodic. I don't remember if I tried it with a DAC,
but if I did, it must not have sounded much different or I'd have
remembered that I had and it did. ;-)

Thanks,
Rich

An 8 stage LFSR prog' I used for playing with, gives ...

128-64-32-16-8-4-2-129-192-96-48-24-12-6-131-65-1-60-80-40-20 ...
Just looks like a bunch of jagged steps. The patterning is obvious.
As you say, it probably sounds periodic as well.
regards
john

 

[Allan Herriman]

On Thu, 18 Nov 2004 21:06:29 GMT, Rich Grise <rich@example.net> wrote:

On Thu, 18 Nov 2004 23:45:55 +1100, Allan Herriman wrote:

On Thu, 18 Nov 2004 13:08:06 +0100, Rene Tschaggelar <none@none.net
wrote:

Sridhar Gadda wrote:

Hi,

Can anyone forward material related to proving Linear feeback
shift register generate flat frequency spectrum. I know one Idea is
perfoming DFT on smaples taken from LFSR. I am looking for
mathematical model.

They don't make a flat spectrum, sorry.
It is unevenly distributed between the clock and the
clock divided by the number of bits.
Plus som upper harmonics of course.

The spectrum has a sin(x)/x envelope, due to the zero-order-hold
effect. The first null is at the clock frequency.

In theory, the spectrum is discrete, in that it consists of lines with
a spacing of the clock frequency divided by the number of LFSR states
(i.e. 2^number of bits - 1), but for practical register lengths and
clock frequencies, the line spacing will be much less than the
resolution bandwidth on any spectrum analyser.

I'm wondering how you get from the LFSR output into the frequency
domain - just take the bit stream and act like it's an analog signal?

Exactly.

Maybe LPF it?

You could, but that would change the spectrum. Lowpass filtering

What would happen if, each clock cycle, you latched the
register value into a DAC?
What kind of difference might that make? Take
the DAC output for your signal, of course.

The register is a shift register, which makes each bit take the value
of the adjacent bit from the previous sample. You might wire it up so
the newest bit is either on the MSB or the LSB of the DAC. Either
way, this creates an FIR low pass filter. The difference (between the
bit ordering) determines the phase response of the filter, but that
won't matter for a noise signal.

Using a DAC this way is a waste of DAC. If you want to make
multi-level noise, make sure the individual bits have a low
correlation. The register value of an LFSR is notoriously bad as a
random number generator when used to make a parallel output.

Regards,
Allan

 

[Allan Herriman]

On Fri, 19 Nov 2004 15:57:30 +1100, Allan Herriman
<allan.herriman.hates.spam@ctam.com.au.invalid> wrote:

I'm wondering how you get from the LFSR output into the frequency
domain - just take the bit stream and act like it's an analog signal?

Exactly.

Maybe LPF it?

You could, but that would change the spectrum. Lowpass filtering

Sorry. ... Lowpass filtering may be useful to reduce the slew rate of
the signal if it is used in an audio application.

Regards,
Allan

 

[Rich Grise]

On Thu, 18 Nov 2004 23:45:55 +1100, Allan Herriman wrote:

On Thu, 18 Nov 2004 13:08:06 +0100, Rene Tschaggelar <none@none.net
wrote:

Sridhar Gadda wrote:

Hi,

Can anyone forward material related to proving Linear feeback
shift register generate flat frequency spectrum. I know one Idea is
perfoming DFT on smaples taken from LFSR. I am looking for
mathematical model.

They don't make a flat spectrum, sorry.
It is unevenly distributed between the clock and the
clock divided by the number of bits.
Plus som upper harmonics of course.

The spectrum has a sin(x)/x envelope, due to the zero-order-hold
effect. The first null is at the clock frequency.

In theory, the spectrum is discrete, in that it consists of lines with
a spacing of the clock frequency divided by the number of LFSR states
(i.e. 2^number of bits - 1), but for practical register lengths and
clock frequencies, the line spacing will be much less than the
resolution bandwidth on any spectrum analyser.

I'm wondering how you get from the LFSR output into the frequency

domain - just take the bit stream and act like it's an analog signal?
Maybe LPF it? What would happen if, each clock cycle, you latched the
register value into a DAC? What kind of difference might that make? Take
the DAC output for your signal, of course.

I've "listened" to a bit stream, and it definitely isn't pink
noise! It's kinda scraxxy, and (this was only about 16 bits)
clearly periodic. I don't remember if I tried it with a DAC,
but if I did, it must not have sounded much different or I'd have
remembered that I had and it did. ;-)

Thanks,
Rich

 

[Rich Grise]

On Fri, 19 Nov 2004 00:05:13 +0000, john jardine wrote:

"Rich Grise" <rich@example.net> wrote in message
newsan.2004.11.18.20.16.13.704491@example.net...
On Thu, 18 Nov 2004 23:45:55 +1100, Allan Herriman wrote:

On Thu, 18 Nov 2004 13:08:06 +0100, Rene Tschaggelar <none@none.net
wrote:

Sridhar Gadda wrote:

Hi,

Can anyone forward material related to proving Linear feeback
shift register generate flat frequency spectrum. I know one Idea is
perfoming DFT on smaples taken from LFSR. I am looking for
mathematical model.

They don't make a flat spectrum, sorry.
It is unevenly distributed between the clock and the
clock divided by the number of bits.
Plus som upper harmonics of course.

The spectrum has a sin(x)/x envelope, due to the zero-order-hold
effect. The first null is at the clock frequency.

In theory, the spectrum is discrete, in that it consists of lines with
a spacing of the clock frequency divided by the number of LFSR states
(i.e. 2^number of bits - 1), but for practical register lengths and
clock frequencies, the line spacing will be much less than the
resolution bandwidth on any spectrum analyser.

I'm wondering how you get from the LFSR output into the frequency
domain - just take the bit stream and act like it's an analog signal?
Maybe LPF it? What would happen if, each clock cycle, you latched the
register value into a DAC? What kind of difference might that make? Take
the DAC output for your signal, of course.

I've "listened" to a bit stream, and it definitely isn't pink
noise! It's kinda scraxxy, and (this was only about 16 bits)
clearly periodic. I don't remember if I tried it with a DAC,
but if I did, it must not have sounded much different or I'd have
remembered that I had and it did. ;-)

Thanks,
Rich

An 8 stage LFSR prog' I used for playing with, gives ...
128-64-32-16-8-4-2-129-192-96-48-24-12-6-131-65-1-60-80-40-20 ...
Just looks like a bunch of jagged steps. The patterning is obvious.
As you say, it probably sounds periodic as well.

Now that you mention it, the LED bank I had set up looked like
a marquee or something, but backwards and only one bit, and of course,
"random."

Which not only doesn't answer my other question, but makes for more!

Thanks,
Rich