To determine the impulse response of a room, a Maximum Length Sequence (MLS) is produced by a loudspeaker. The room is considered to be a LTI system. A microphone is used to capture the output of this linear system. A cross-correlation (or in some texts, a "convolution operation") is then used to determine the impulse response of the room, given that we know the original MLS. In most of the acoustics papers that I have read, the initial state (or seed) of the LFSR is simply a series of ones {1, 1, 1,...}. However, in cryptography, the initial state of the LFSR could be selected as a random number. Are there any signal processing benefits of choosing a random number as the initial state of the LFSR? What if I was to take multiple measurements with the same seed used in the LFSR, and the linear system under test would have some sort of biased frequency response for that particular seed value. Wouldn't it be better, from a signal processing perspective, to change the seed value of the LFSR for each measurement? Or does this really matter?
Are there any DSP benefits of choosing a random seed for an MLS?
Started by ●August 25, 2009
Reply by ●August 25, 20092009-08-25
Nicholas Kinar wrote:> To determine the impulse response of a room, a Maximum Length Sequence > (MLS) is produced by a loudspeaker. The room is considered to be a LTI > system. > > A microphone is used to capture the output of this linear system. A > cross-correlation (or in some texts, a "convolution operation") is then > used to determine the impulse response of the room, given that we know > the original MLS. > > In most of the acoustics papers that I have read, the initial state (or > seed) of the LFSR is simply a series of ones {1, 1, 1,...}. > > However, in cryptography, the initial state of the LFSR could be > selected as a random number. > > Are there any signal processing benefits of choosing a random number as > the initial state of the LFSR? > > What if I was to take multiple measurements with the same seed used in > the LFSR, and the linear system under test would have some sort of > biased frequency response for that particular seed value. Wouldn't it > be better, from a signal processing perspective, to change the seed > value of the LFSR for each measurement? > > Or does this really matter?It matters for cryptography. It matters for acoustic tests it you want to keep the results secret from a poacher with his own microphone. Otherwise, no. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●August 25, 20092009-08-25
> > It matters for cryptography. It matters for acoustic tests it you want > to keep the results secret from a poacher with his own microphone. > > Otherwise, no. > > JerryThanks for your response Jerry. This makes sense to me. Essentially an MLS is an MLS, no matter what the seed, and a random seed isn't going to change the properties of the source signal constructed from the MLS sequence. Have to watch out for these poachers. Dangerous things can lurk in the jungles of DSP. :-) Now what if I have two devices that both generate an MLS at the same time. I would like for each measurement of the impulse response made by one device to be independent of the measurement made by another device at the same time. Would this justify the use of a random seed for each MLS used to generate the source signals?
Reply by ●August 25, 20092009-08-25
On 25 Aug., 18:07, Nicholas Kinar <n.ki...@usask.ca> wrote:> > It matters for cryptography. It matters for acoustic tests it you want > > to keep the results secret from a poacher with his own microphone. > > > Otherwise, no. > > > Jerry > > Thanks for your response Jerry. �This makes sense to me. �Essentially an > MLS is an MLS, no matter what the seed, and a random seed isn't going to > change the properties of the source signal constructed from the MLS > sequence. > > Have to watch out for these poachers. �Dangerous things can lurk in the > jungles of DSP. > > :-) > > Now what if I have two devices that both generate an MLS at the same > time. �I would like for each measurement of the impulse response made by > one device to be independent of the measurement made by another device > at the same time. > > Would this justify the use of a random seed for each MLS used to > generate the source signals?you would want the two measument sequences to have as little correlation as possible to make them independent, if the sequence is long enough I guess you could pick two seeds that makes them non over lapping gold codes maybe? -Lasse
Reply by ●August 25, 20092009-08-25
Nicholas Kinar wrote:> >> >> It matters for cryptography. It matters for acoustic tests it you want >> to keep the results secret from a poacher with his own microphone. >> >> Otherwise, no. >> >> Jerry > > > Thanks for your response Jerry. This makes sense to me. Essentially an > MLS is an MLS, no matter what the seed, and a random seed isn't going to > change the properties of the source signal constructed from the MLS > sequence. > > Have to watch out for these poachers. Dangerous things can lurk in the > jungles of DSP. > > :-) > > > Now what if I have two devices that both generate an MLS at the same > time. I would like for each measurement of the impulse response made by > one device to be independent of the measurement made by another device > at the same time. > > Would this justify the use of a random seed for each MLS used to > generate the source signals?An MLS is cyclic. The seed just determines where in the cycle it starts. Two identical MLSs with different seeds are simply delayed or advanced versions of one another. Besides, even if you use different generators, I don't see how you could isolate their effects. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●August 25, 20092009-08-25
> > gold codes maybe? >Thanks for your response, Lasse. Yes, I agree that Gold codes have very little overlap, but I don't know if they could be used in lieu of an MLS. More research would be required, I guess.
Reply by ●August 25, 20092009-08-25
> > An MLS is cyclic. The seed just determines where in the cycle it starts. > Two identical MLSs with different seeds are simply delayed or advanced > versions of one another. Besides, even if you use different generators, > I don't see how you could isolate their effects. >Probably it is not possible to isolate the effects of each MLS sequence. Thanks, Jerry.
Reply by ●August 25, 20092009-08-25
Nicholas Kinar wrote:> >> >> gold codes maybe? >> > > Thanks for your response, Lasse. Yes, I agree that Gold codes have very > little overlap, but I don't know if they could be used in lieu of an > MLS. More research would be required, I guess.Since Gold codes are generated from two (2^N - 1) length Maximum Length Sequences, then can the Fast Hadamard Transform be applied to the linear system response? The Fast Hadamard Transform operates on a 2^N sequence, but I believe that the Gold code has a length of (2^N + 1) Does the Gold code have similar properties to the FHT, in that the SNR is high? How would I process a Gold code to obtain the frequency response of the system?
Reply by ●August 25, 20092009-08-25
> > Does the Gold code have similar properties to the FHT, in that the SNR > is high? How would I process a Gold code to obtain the frequency > response of the system?Or the impulse response. The frequency response is trivial to obtain from the impulse response.
Reply by ●August 25, 20092009-08-25
On Aug 25, 12:20�pm, Jerry Avins <j...@ieee.org> wrote:> Nicholas Kinar wrote: > > >> It matters for cryptography. It matters for acoustic tests it you want > >> to keep the results secret from a poacher with his own microphone. > > >> Otherwise, no. > > >> Jerry > > > Thanks for your response Jerry. �This makes sense to me. �Essentially an > > MLS is an MLS, no matter what the seed, and a random seed isn't going to > > change the properties of the source signal constructed from the MLS > > sequence. > > > Have to watch out for these poachers. �Dangerous things can lurk in the > > jungles of DSP. > > > :-) > > > Now what if I have two devices that both generate an MLS at the same > > time. �I would like for each measurement of the impulse response made by > > one device to be independent of the measurement made by another device > > at the same time. > > > Would this justify the use of a random seed for each MLS used to > > generate the source signals? > > An MLS is cyclic. The seed just determines where in the cycle it starts. > Two identical MLSs with different seeds are simply delayed or advanced > versions of one another.that is the main kernel to answer the OP. however,> Besides, even if you use different generators, > I don't see how you could isolate their effects.MLS is fine if your device-under-test (DUT) is perfectly LTI. it turns out that non-linearities in the DUT cause the apparent impulse response to have spurious spikes that are at fixed locations in the impulse response (which means you can rerun the test average until the cows come home and those spurious spikes ain't going away). i discuss this briefly at the end of http://www.dspguru.com/info/tutor/mls2.htm . different MLS's generated by different primitive polynomials will put those spikes at different places in the impulse response. you can pick out 3 (or a bigger odd number) different primitive polynomials, run your MLS test 3 different times with the 3 different polynomials, line up your 3 different impulse responses on top of each other and, point-by-point, pick out the median for each sample. it's unlikely, for the same nonlinearity, that the 3 different tests will spike at exactly the same place. this idea comes from or is motivated by a paper from an interesting person, Paul Kovitz, whom i haven't heard much from for a decade. r b-j