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Phase in FIR

Started by Edison May 21, 2007
On 21 May, 18:12, "Edison" <e...@senscient.com> wrote:
> >Linear phase means constant time delay. In other words, the filter > >delays all frequencies in time equally. Phase distortion happens when > >different frequencies pass through with different time delays. > > Sorry to go round the point but I need to get this straight in my head. > > If the filter adds the same time delay to all frequencies then the > relative phase of a higher harmonic will shift upwards.
Yes.
> This will then > change the realtive phase of the harmonic to the fundamental will it not?
No. In a linear-phase system the funcamental will have changed phase, too. The net effect of adding a linear phase shift is to shift the signal in time. FT{x(t)} = integral x(t) exp(jwt) dt FT{x(t-T)} = integral x(t-T) exp(jwt)dt t-T = p => t = p+T, dp/dt = 1 => dt = dp FT{x(t-T)} = integral x(p) exp(jw(p+T)) dp (p = t) = exp(jwT) integral x(t)exp(jwt) dt = exp(jwT)FT{x(t)} and as you can see, the phase term wT is linear with frequency. Rune
Rune Allnor wrote:

   ...

> In a linear-phase system the fundamental will have > changed phase, too. The net effect of adding a linear > phase shift is to shift the signal in time.
That might be a confusing way to put it. What we call a linear-phase filter changes the phase of each component an ampunt proportional to its frequency. That is precisely equivalent to a time delay that is independent of frequency. Viewed in time, the signal is merely "moved over". The same thing happens when a signal propagates in a medium at a finite speed. The relative phases of the components of an FM broadcast don't depend on the distance between transmitter and receiver. ... Jerry -- Engineering is the art of making what you want from things you can get. &macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;
On 21 Mai, 22:29, Tim Wescott <t...@seemywebsite.com> wrote:
> On Mon, 21 May 2007 09:59:23 -0700, Andor wrote: > > Edison wrote: > >> Hi, > > >> I'm trying to specify a DSP system to measure a two sine waves around > >> 100kHz and their resulting harmonics down to the 5th. > > >> The phase information is important as well as the magnitude of the > >> harmonics. > > >> In order to avoaid any aliasing and phase problems with an analog filt=
er I
> >> 'm intending to oversample at 4MSPS. > > > Aliasing is your friend :-). If you know the (lowest) frequency of > > your periodic signal (having several harmonics this signal won't be a > > sine wave), you can sample at almost any frequency you like, and still > > extract the full information of the periodic signal. Best is some > > sampling frequency that is irrational with the frequencies of your > > periodic signals. > > > You can easily calculate the amplitude and the phase of the harmonics > > of your periodic test signals (given that you know their period) from > > the aliases. I would suggest Goertzel algorithm to exctract the 5 > > amplitude/phase pairs. Remember that every alias-wrap-around > > introduces a 180=B0 phase shift. > > > Regards, > > Andor > > This undersampling trick is cool, but only applies if you can be sure that > the signal shape doesn't change quickly over time -- if you're looking for > harmonic distortion with a known input in the lab it's great. If you're > out in the field and there's transients -- it's not so great.
Well, the trick only applies to measurement of periodic signals (in the lab or in the field, doesn't matter). All we need to know is the period and the number of harmonics present in the signal (an upper bound could be guaranteed by a continuous-time lowpass filter prior to sampling). The amplitudes / phases of the harmonics can be extracted by a linear set of equations (which is simpler than Goertzel which I suggested in the previous post). In the presence of measurement noise, the linear set of equations can easily be updated with additional measurements and solved in, for example, the least-squares sense. I think this trick could really be used in practice. Regards, Andor
On 21 May, 23:23, Jerry Avins <j...@ieee.org> wrote:
> Rune Allnor wrote: > > ... > > > In a linear-phase system the fundamental will have > > changed phase, too. The net effect of adding a linear > > phase shift is to shift the signal in time. > > That might be a confusing way to put it.
Is it? Why? The question was clear enough, paraphrased as I interpreted it: Does the different added phase terms between frequency components distort the signal. I don't think my answer above is wrong? Maybe if we include the DC component, but I don't want to get into one of those "what is the phase of DC" wars... Rune
"kl31n" <kl31n(get rid of this to write me back)@hotmail.com> writes:
> [...] > I'm saying this without any sort of arrogance, but unfortunately > people tend to think that DSP is some sort of magic that happens > beyond the rule of physics and that's why weird questions are usually > originated.
That's like saying "differential equations is some sort of magic that happens beyond the rule of physics." Well, it does happen beyond the rule of physics, in that domain called "mathematics." It just so happens that many physical things are modeled by differential equations, but that doesn't make them physical. Same with DSP.
> The term "time delay" is ambiguous
Assuming that the independent variable is time and we know the sample rate [1], time delay is absolutely precise and well-defined when discussing a linear phase digital filter, and all that is required to answer the OP's question. --Randy [1] Otherwise we would need to use the term "sample delay." -- % Randy Yates % "Bird, on the wing, %% Fuquay-Varina, NC % goes floating by %%% 919-577-9882 % but there's a teardrop in his eye..." %%%% <yates@ieee.org> % 'One Summer Dream', *Face The Music*, ELO http://home.earthlink.net/~yatescr
Andor wrote:
> On 21 Mai, 22:29, Tim Wescott <t...@seemywebsite.com> wrote: >> On Mon, 21 May 2007 09:59:23 -0700, Andor wrote: >>> Edison wrote: >>>> Hi, >>>> I'm trying to specify a DSP system to measure a two sine waves around >>>> 100kHz and their resulting harmonics down to the 5th. >>>> The phase information is important as well as the magnitude of the >>>> harmonics. >>>> In order to avoaid any aliasing and phase problems with an analog filter I >>>> 'm intending to oversample at 4MSPS. >>> Aliasing is your friend :-). If you know the (lowest) frequency of >>> your periodic signal (having several harmonics this signal won't be a >>> sine wave), you can sample at almost any frequency you like, and still >>> extract the full information of the periodic signal. Best is some >>> sampling frequency that is irrational with the frequencies of your >>> periodic signals. >>> You can easily calculate the amplitude and the phase of the harmonics >>> of your periodic test signals (given that you know their period) from >>> the aliases. I would suggest Goertzel algorithm to exctract the 5 >>> amplitude/phase pairs. Remember that every alias-wrap-around >>> introduces a 180&#65533; phase shift. >>> Regards, >>> Andor >> This undersampling trick is cool, but only applies if you can be sure that >> the signal shape doesn't change quickly over time -- if you're looking for >> harmonic distortion with a known input in the lab it's great. If you're >> out in the field and there's transients -- it's not so great. > > Well, the trick only applies to measurement of periodic signals (in > the lab or in the field, doesn't matter). > > All we need to know is the period and the number of harmonics present > in the signal (an upper bound could be guaranteed by a continuous-time > lowpass filter prior to sampling). > > The amplitudes / phases of the harmonics can be extracted by a linear > set of equations (which is simpler than Goertzel which I suggested in > the previous post). In the presence of measurement noise, the linear > set of equations can easily be updated with additional measurements > and solved in, for example, the least-squares sense. I think this > trick could really be used in practice.
If the period is known, then reducing all measurement times modulo(period) Eliminates almost all other computation. Consider a sampling scope. (Juan Amodei dreamed that up around 1960.) Jerry -- Engineering is the art of making what you want from things you can get. &macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;
Rune Allnor wrote:
> On 21 May, 23:23, Jerry Avins <j...@ieee.org> wrote: >> Rune Allnor wrote: >> >> ... >> >>> In a linear-phase system the fundamental will have >>> changed phase, too. The net effect of adding a linear >>> phase shift is to shift the signal in time. >> That might be a confusing way to put it. > > Is it? Why? The question was clear enough, paraphrased > as I interpreted it: Does the different added phase > terms between frequency components distort the signal. > > I don't think my answer above is wrong? Maybe if we > include the DC component, but I don't want to get into > one of those "what is the phase of DC" wars...
What you wrote isn't wrong. I think it might be open to more than one interpretation. If I'm wrong, what's the harm? Jerry -- Engineering is the art of making what you want from things you can get. &macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;
"Randy Yates" <yates@ieee.org> wrote in message 
news:m3fy5piz3z.fsf@ieee.org...
> "kl31n" <kl31n(get rid of this to write me back)@hotmail.com> writes: >> [...] >> I'm saying this without any sort of arrogance, but unfortunately >> people tend to think that DSP is some sort of magic that happens >> beyond the rule of physics and that's why weird questions are usually >> originated.
> That's like saying "differential equations is some sort of magic that > happens beyond the rule of physics." Well, it does happen beyond the > rule of physics, in that domain called "mathematics." It just so > happens that many physical things are modeled by differential > equations, but that doesn't make them physical. Same with DSP.
I get your point, but that's not quite what I meant. My intention is simply to underline that when the model tries to describe something physical - and DSP does - it's often useful to discern the correctness of the results that one can get out of the model crosschecking them against their physical meaning.
>> The term "time delay" is ambiguous > > Assuming that the independent variable is time and we know the sample > rate [1], time delay is absolutely precise and well-defined when > discussing a linear phase digital filter, and all that is required to > answer the OP's question.
What's the definition of something ambiguous? Something that needs assumptions to be interpreted. :) Given the OP's message to which I answered, it was my understanding that he was confused just about how the constant group delay influenced the phase delay and that's where I came in. It wasn't my intention to criticize the expression "time delay", which, as you say, is legitimate, but to move the OP's attention on the phase delay with respect to the group delay. Best regards, kl31n
glen herrmannsfeldt wrote:
> Randy Yates wrote: > (snip) > >> Assuming that the independent variable is time and we know the sample >> rate [1], time delay is absolutely precise and well-defined when >> discussing a linear phase digital filter, and all that is required to >> answer the OP's question. > > Since you already put physics into the discussion, remember that > time delay is reference frame dependent.
:-) I suppose it is safe to assume that input and output ports have zero relative velocity. Jerry -- Engineering is the art of making what you want from things you can get. &macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;
Randy Yates wrote:
(snip)

> Assuming that the independent variable is time and we know the sample > rate [1], time delay is absolutely precise and well-defined when > discussing a linear phase digital filter, and all that is required to > answer the OP's question.
Since you already put physics into the discussion, remember that time delay is reference frame dependent. -- glen