On Tuesday, December 17, 2019 at 5:36:07 AM UTC-8, Richard (Rick) Lyons wro= te:> ... > ...an x(n) sequence has a period of N samples if and only if: >=20.> x[n+N] =3D x[n] for all n. .>=20 .> But that equality is ONLY true for infinite-length sequences, and infini= te-length sequences do not exist in reality. An infinite-length sequence is= an abstract idea, ...like a perfect circle or one of Euclid's lines having= infinite length and zero thickness. What this means is that, based on the = above periodicity definition, we will never encounter, nor ever be able to = generate, a periodic sequence in our real world. Hi Rick As George Box said: 'Essentially, all models are wrong, but some are useful'=20 You and I may never live long enough to see an infinite sequence, but there= may be sequences that meet the equation for all n that we have observed a= nd it is perfectly useful to take advantage of that periodicity condition w= here it is met. I started in with spectrum analysis when I was hired by a company called Sp= ectral Dynamics. One of their early systems analyzed machinery vibration of= machines that provided a once-per-rev tach signal. That signal was the ref= erence to a phased lock loop the could be used, along with choice of transf= orm size to guarantee that all rotational rates generated by a gear chain w= ould meet the periodicity condition as long as the loop was locked, even if= the base rotational frequency drifted or was intentionally varied. As digi= tal signal processing speeds increased, they went to sampling at a fixed ra= te, sampling the tach times and interpolating the data to synchronous sampl= ing times. So it can be perfectly reasonable for an analyst to treat local data as per= iodic if there is other knowledge to justify it. That other knowledge could= also be as simple as a comparison of the data values in the sequential dat= a blocks for compliance with the equation. Dale B. Dalrymple
mirroring a signal before FFT - why?
Started by ●December 14, 2019
Reply by ●December 18, 20192019-12-18
Reply by ●December 18, 20192019-12-18
dbd <d.dalrymple@sbcglobal.net> wrote:>As George Box said:>'Essentially, all models are wrong, but some are useful'I was wondering to whom to attribute this. I think it ought to be an official part of the scientific method. Steve
Reply by ●December 18, 20192019-12-18
On Tuesday, December 17, 2019 at 8:18:19 PM UTC-8, dbd wrote: Hi Dale. I interpret your words to mean: Some sequences have a strong periodic nature if: x[n+N] = x[n] for many values of n.
Reply by ●December 18, 20192019-12-18
On Wednesday, December 18, 2019 at 5:24:25 AM UTC-5, Richard (Rick) Lyons wrote:> On Tuesday, December 17, 2019 at 8:18:19 PM UTC-8, dbd wrote: > > Hi Dale. I interpret your words to mean: Some sequences have a strong periodic nature if: > > x[n+N] = x[n] for many values of n.this thread is an example of why I (still) read comp.dsp thanks Mark
Reply by ●December 18, 20192019-12-18
On 12/18/2019 05:24, Richard (Rick) Lyons wrote:> On Tuesday, December 17, 2019 at 8:18:19 PM UTC-8, dbd wrote: > > Hi Dale. I interpret your words to mean: Some sequences have a strong periodic nature if: > > x[n+N] = x[n] for many values of n. >Hi Rick, I assume you meant "for many values of N" or "for all N > some large number" -- Best wishes, --Phil pomartel At Comcast(ignore_this) dot net
Reply by ●December 18, 20192019-12-18
On Wednesday, December 18, 2019 at 8:39:42 AM UTC-8, Phil Martel wrote:> Hi Rick, I assume you meant "for many values of N" or "for all N > some > large number" > > -- > Best wishes, > --PhilHi Phil. No, I did mean "many values of n". The fixed variable N is the period (an integer measured in samples) of some sequence that appears to be periodic because it has repetitive equal-amplitude sample values separated by N samples. In my mind I've been formulating two different definitions of "periodicity" for finite-length sequences. But I'm not yet ready to advertise those definitions to you DSP guys for fear of looking like a knucklehead. Hey Phil, ... have you seen the following web page? https://www.dsprelated.com/showquiz/5 Regards, [-Rick-]
Reply by ●December 19, 20192019-12-19
On Wednesday, December 18, 2019 at 2:24:25 AM UTC-8, Richard (Rick) Lyons wrote:> On Tuesday, December 17, 2019 at 8:18:19 PM UTC-8, dbd wrote: >.> Hi Dale. I interpret your words to mean: Some sequences have a strong periodic nature if: .> .> x[n+N] = x[n] for many values of n. Rick, I would say that in any range of n where the equation is satisfied, our data is indistinguishable from samples from a periodic sequence despite the fact that our data sequence is always finite. That means an analyst can safely act as if the data were periodic. Real data may consist of samples of the sum of components of types like periodic-in-N, periodic-not-in-N, aperiodic and stocastic. Real DSP systems can't process infinite sequences, they don't need to to justify treating data as containing periodic components. As Jerry would post: "Engineering is the art of making what you want from things you can get." Dale B. Dalrymple
Reply by ●December 19, 20192019-12-19
On Thursday, December 19, 2019 at 1:32:09 AM UTC-8, dbd wrote:> > Rick, I would say that in any range of n where the equation is satisfied, our data is indistinguishable from samples from a periodic sequence despite the fact that our data sequence is always finite. That means an analyst can safely act as if the data were periodic. >> Dale B. DalrympleHi Dale. I agree with you. If we had a 10,000-sample sequence containing exactly 1,000 cycles of a cosine wave, we'd definitely say that sequence was "periodic" even though it does not satisfy the following textbook definition of periodicity: x[n+N] = x[n] for all n. [-Rick-]
Reply by ●December 19, 20192019-12-19
Richard (Rick) Lyons <r.lyons@ieee.org> wrote:>Hi Dale. I agree with you. If we had a 10,000-sample sequence containing >exactly 1,000 cycles of a cosine wave, we'd definitely say that sequence >was "periodic" even though it does not satisfy the following textbook >definition of periodicity: > > x[n+N] = x[n] for all n.The signal is short-term stationary and is also narrowband, and not noise-like. These may add up to it being "quasi-periodic", or some such. Steve
Reply by ●December 19, 20192019-12-19
On 12/18/2019 14:09, Richard (Rick) Lyons wrote:> On Wednesday, December 18, 2019 at 8:39:42 AM UTC-8, Phil Martel wrote: > >> Hi Rick, I assume you meant "for many values of N" or "for all N > some >> large number" >> >> -- >> Best wishes, >> --Phil > > Hi Phil. No, I did mean "many values of n". The fixed variable N is the period (an integer measured in samples) of some sequence that appears to be periodic because it has repetitive equal-amplitude sample values separated by N samples. > > In my mind I've been formulating two different definitions of "periodicity" for finite-length sequences. But I'm not yet ready to advertise those definitions to you DSP guys for fear of looking like a knucklehead. > > Hey Phil, ... have you seen the following web page? > > https://www.dsprelated.com/showquiz/5 > > Regards, > [-Rick-] >Thanks Rick, I understand what you were saying better now. I guess I was confused by the concept of sampling and processing blocks of N samples 0 <= n < N, N <= n < 2*N and so forth. I'll look over that quiz later. -- Best wishes, --Phil pomartel At Comcast(ignore_this) dot net
