Is an upsampled Maximum Length Sequence also an MLS?

Hello--

Suppose that I am to take a Maximum Length Sequence (MLS) that has been 
generated using a linear feedback shift register, and I am to upsample 
the MLS to a higher sampling frequency.

Is the upsampled MLS signal also an MLS? Does it have the same 
properties as the original MLS?

The reason why I ask this is because I would like to excite a linear 
system with an MLS signal, and sample the output of the linear system at 
a higher sampling rate than the sampling rate of the original source MLS 
signal.

Then by convolution of the output of the system with the input, I would 
like to find the linear system's impulse response.

I have a hunch that it is possible to determine the impulse response of 
the linear system in this fashion, but this is nothing more than a 
guess, and I am looking for a more theoretically-sound understanding.

On Aug 24, 9:47&#4294967295;pm, Nicholas Kinar <n.ki...@usask.ca> wrote:
> Hello--
>
> Suppose that I am to take a Maximum Length Sequence (MLS) that has been
> generated using a linear feedback shift register, and I am to upsample
> the MLS to a higher sampling frequency.
>
> Is the upsampled MLS signal also an MLS? Does it have the same
> properties as the original MLS?
>
> The reason why I ask this is because I would like to excite a linear
> system with an MLS signal, and sample the output of the linear system at
> a higher sampling rate than the sampling rate of the original source MLS
> signal.
>
> Then by convolution of the output of the system with the input, I would
> like to find the linear system's impulse response.
>
> I have a hunch that it is possible to determine the impulse response of
> the linear system in this fashion, but this is nothing more than a
> guess, and I am looking for a more theoretically-sound understanding.

i have a little MLS tutorial at

 http://www.dspguru.com/info/tutor/mls2.htm

as best as i can tell, upsampling will get you nothing except the
original impulse response convolved with a sinc().  i dunno.  the
"upsampled MLS" will have a flat, white-like spectrum up to the
*original* Nyquist frequency, not the upsampled Nyquist.

why not generate the MLS at the higher sampling frequency?  you'll
have to generate a longer MLS, but it's just bits.

r b-j

robert bristow-johnson <rbj@audioimagination.com> writes:
> [...]
> it's just bits.

Did you hear the one about the husband who was eating that
new breakfast cereal "Nut N'Bits" when his wife sleepily
walked in and asked, "Whatcha' eatin', honey?"? 
-- 
Randy Yates                      % "She tells me that she likes me very much,
Digital Signal Labs              %     but when I try to touch, she makes it
mailto://yates@ieee.org          %                            all too clear."
http://www.digitalsignallabs.com %        'Yours Truly, 2095', *Time*, ELO  

On Tue, 25 Aug 2009 06:30:38 -0400, Randy Yates <yates@ieee.org>
wrote:

>robert bristow-johnson <rbj@audioimagination.com> writes:
>> [...]
>> it's just bits.
>
>Did you hear the one about the husband who was eating that
>new breakfast cereal "Nut N'Bits" when his wife sleepily
>walked in and asked, "Whatcha' eatin', honey?"? 

Hi Randy,
   Ha ha.  I'm ashamed to say, but it took me a 
while to "figure out" that joke.

Husband-wife jokes are among the most "fun" category 
of jokes.  Here's an ol' one from Henny Youngman:

Wife: "I'm bored.  I wanna go somewhere on vacation."

Husband: "Where do you want to go?"

Wife: Someplace where I've never been before."

Husband: "Have you tried the kitchen?"

[-Rick-]

Hi Robert--

Thank you for your response!

> 
> i have a little MLS tutorial at
> 
>  http://www.dspguru.com/info/tutor/mls2.htm
> 
> as best as i can tell, upsampling will get you nothing except the
> original impulse response convolved with a sinc().  i dunno.  the
> "upsampled MLS" will have a flat, white-like spectrum up to the
> *original* Nyquist frequency, not the upsampled Nyquist.

I agree, it wouldn't really change the spectrum of the original sequence 
at all.

> 
> why not generate the MLS at the higher sampling frequency?  you'll
> have to generate a longer MLS, but it's just bits.
> 
> r b-j

This would be very feasible for systems which are not bandlimited.

My main research application area is acoustics.  A loudspeaker can't 
adequately produce frequencies greater than 20 kHz.  If I sample the 
source signal at a higher frequency, the loudspeaker can't adequately 
produce the higher frequencies.

If I sample the output of the acoustic system under test at the same 
sampling rate as the original MLS, then I may have difficulty adequately 
applying DSP filters, since I would require a higher sampling rate to be 
able to do this.

Randy Yates wrote:
> robert bristow-johnson <rbj@audioimagination.com> writes:
>> [...]
>> it's just bits.
> 
> Did you hear the one about the husband who was eating that
> new breakfast cereal "Nut N'Bits" when his wife sleepily
> walked in and asked, "Whatcha' eatin', honey?"? 

I would suppose that he would also have milk with the cereal.  Bits are 
too crunchy when eaten alone.

> 
> Husband: "Have you tried the kitchen?"
> 

...and the wife is another engineer, and figures out how to re-design 
the kitchen.

The answer is no as there is a trivial counterexample:

If you have two bits of state, an MLS is 1 1 0.

If you upsample this by two, you have the sequence 1 1 1 1 0 0.

This sequence is length six, requires three bits of state
to geneate, yet is not length seven and so is not maximal
length.

Is this a trick question?

Steve

On Aug 25, 10:35&#4294967295;am, Nicholas Kinar <n.ki...@usask.ca> wrote:
>
> Thank you for your response!
>

yer welcome.


> > why not generate the MLS at the higher sampling frequency? &#4294967295;you'll
> > have to generate a longer MLS, but it's just bits.
>
>
> This would be very feasible for systems which are not bandlimited.

i don't get it.  MLS *is* for bandlimited systems.  (unlike linear
swept frequency measurements a.k.a. Time-Delay Spectrometry) the
theory of MLS is about a discrete-time sequence from the start.

if your system is bandlimited to much less than the driving test
signal, what problem is in that?  so you see some big sinc-like lobes
in your impulse response.  it's still correct.

> My main research application area is acoustics. &#4294967295;A loudspeaker can't
> adequately produce frequencies greater than 20 kHz. &#4294967295;If I sample the
> source signal at a higher frequency, the loudspeaker can't adequately
> produce the higher frequencies.

and your test system will measure that fact.  big deal.

the problem is in the other direction.  if you have a device under
test that *does* have interesting behavioral artifacts at high
frequencies, you have a problem if your test signal does not excite
the device at those frequencies.  there is no problem with a test
signal that even greatly exceeds the device under test in frequency
response.

> If I sample the output of the acoustic system under test at the same
> sampling rate as the original MLS, then I may have difficulty adequately
> applying DSP filters, since I would require a higher sampling rate to be
> able to do this.

you mean you can generate an MLS at a higher sampling frequency than
you can run a digital filter at?  that's a curiousity.  what hardware
(or DSP card) are you using for either?

BTW, as i point out in that tutorial, MLS has some truly bizarre
behavior with non-linearities in your device under test.  and
loudspeakers are not known for being the most linear of transducers.
you might want to consider linearly swept frequency measurements.

r b-j

Steve Pope wrote:
> The answer is no as there is a trivial counterexample:
> 
> If you have two bits of state, an MLS is 1 1 0.
> 
> If you upsample this by two, you have the sequence 1 1 1 1 0 0.
> 
> This sequence is length six, requires three bits of state
> to geneate, yet is not length seven and so is not maximal
> length.
> 
> Is this a trick question?
> 
> Steve

No, not a trick question at all.  It's just that I might have to sample 
the output of the system at a higher rate to be able to apply a digital 
filter.

But then how would I apply something such as the Fast Hadamard Transform 
to be able to determine the impulse response?  Both the input sequence 
and the output sequence of the LTI system would have to be the same length.