What is the relations hip between the instantaneous frequency of a signal and the group delay of that signal? If we think of a sinewave, it intuitive to think of the instantaneous frequency as just being the frequency of occilation however, in the case of a sine wave... to think of group delay for a signal with no 'group' isnt really intuitive. And in the case for a signal with some bandwith... lets say 3 sinewaves of diffrent frequencies added to together, sin(2pi*f1*t)+sin(2pi*f2+t)+sin(2Pi*f3*t) group delay seems to have a physicall meaning, but instantaneous frequency becomes abstract. Does Fourier Transform theory falls short when we want to analize instantaneous frequency? Does anyone have a link to some literature that may help. Thanx in advance.
Instantaneous freq vs Group Delay
Started by ●September 17, 2008
Reply by ●September 17, 20082008-09-17
On Sep 17, 10:52�am, "westocl" <cwest...@hotmail.com> wrote:> What is the relations hip between the instantaneous frequency of a signal > and the group delay of that signal? > > If we think of a sinewave, it intuitive to think of the instantaneous > frequency as just being the frequency of occilation however, in the case of > a sine wave... to think of group delay for a signal with no 'group' isnt > really intuitive. > > And in the case for a signal with some bandwith... lets say 3 sinewaves of > diffrent frequencies added to together, > sin(2pi*f1*t)+sin(2pi*f2+t)+sin(2Pi*f3*t) group delay seems to have a > physical meaning, but instantaneous frequency becomes abstract.just as in group delay (or phase delay), instantaneous frequency applies to each sinusoid individually. i haven't really thought about it much, but perhaps the duality property of the F.T. has something to say about this. instantaneous frequency applies to the phase in the time domain (of each individual sinusoid), and group delay is the same operation applied to the phase of the sinusoid in the frequency domain. but i suspect they don't have much to say about each other. r b-j
Reply by ●September 17, 20082008-09-17
On 17 Sep, 16:52, "westocl" <cwest...@hotmail.com> wrote:> What is the relations hip between the instantaneous frequency of a signal > and the group delay of that signal?I have no idea. Is there a relation?> If we think of a sinewave, it intuitive to think of the instantaneous > frequency as just being the frequency of occilation however,Correct. For a perfect sinudoidal the frequency never changes, so at any isntance the 'instantaneous frequency' equals the frequency of the sinusoidal.> in the case of > a sine wave... to think of group delay for a signal with no 'group' isnt > really intuitive.If you by this mean that it is hard to discuss the group delay of a perfect sinusoidal, you are correct. The group delay of a broad-band signal is given in terms of the differential of the phase, tau = - d arg(H(w))/dw If H(w) is 0 except for one w, what odes the differential look like?> And in the case for a signal with some bandwith... lets say 3 sinewaves of > diffrent frequencies added to together, > sin(2pi*f1*t)+sin(2pi*f2+t)+sin(2Pi*f3*t) group delay seems to have a > physicall meaning,I'm not sure about that, but we agree that the envlope moves.> but instantaneous frequency becomes abstract.Correct.> Does Fourier Transform theory falls short when we want to analize > instantaneous frequency?Yes, in the sense that 'isntantaneous frequency' is a not at all well-defined concept. The term makes some sense when one talks about FM modulation, but not necessarily in general. Rune
Reply by ●September 17, 20082008-09-17
>Does anyone have a link to some literature that may help.If you have access to a university library, you might find the following title helpful. It is a good reference on nonstationary signal analysis. Time Frequency Analysis: Theory and Applications by Leon Cohen. The Fourier transform magnitude bears no information about time variation of the frequency components. That is precisely why there are other tools to analyze nonstationary signals. Instantaneous frequency does not make much sense for multicomponent signals. It might give you some kind of average frequency over the components if that is what you want, though. As for group delay, I only find it intuitive concerning a filter. It then tells you how much each frequency component of the input signal will be relatively shifted. Linear phase filters have constant group delay for all frequencies, and hence are desirable in this sense. Hope this helps. Emre
Reply by ●September 17, 20082008-09-17
Rune Allnor wrote:> On 17 Sep, 16:52, "westocl" <cwest...@hotmail.com> wrote: > >>What is the relations hip between the instantaneous frequency of a signal >>and the group delay of that signal? > > I have no idea. Is there a relation?:-)>>Does Fourier Transform theory falls short when we want to analize >>instantaneous frequency?Eh? Eh?> Yes, in the sense that 'isntantaneous frequency' is a not at all > well-defined concept.For any signal X, let X* be a Hilbert transform of X: Instantaneous frequency = d(arctg(X*/X))/dt> The term makes some sense when one > talks about FM modulation, but not necessarily in general.The instantaneous frequency is fairly useless and meaningless parameter except for some special cases. Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com
Reply by ●September 17, 20082008-09-17
> > Does Fourier Transform theory falls short when we want to analize > instantaneous frequency? >Is it that the theory falls short or that you are just not computing the same thing? Dirk
Reply by ●September 17, 20082008-09-17
> > >Rune Allnor wrote: > >> On 17 Sep, 16:52, "westocl" <cwest...@hotmail.com> wrote: >> >>>What is the relations hip between the instantaneous frequency of asignal>>>and the group delay of that signal? >> >> I have no idea. Is there a relation? > >:-) > >>>Does Fourier Transform theory falls short when we want to analize >>>instantaneous frequency? > >Eh? Eh? > >> Yes, in the sense that 'isntantaneous frequency' is a not at all >> well-defined concept. > >For any signal X, let X* be a Hilbert transform of X: > >Instantaneous frequency = d(arctg(X*/X))/dt > >> The term makes some sense when one >> talks about FM modulation, but not necessarily in general. > >The instantaneous frequency is fairly useless and meaningless parameter >except for some special cases. > > >Vladimir Vassilevsky >DSP and Mixed Signal Design Consultant >http://www.abvolt.com>The instantaneous frequency is fairly useless and meaningless parameter >except for some special cases.Hmmm.. I ponered this too. But lets think pulse compression radar. in the case of linear FM transmit signals, on the receive side, you see 'dispersive delay lines'. Heres a 'special case', and a special signal in the since where the group dealy matches the instatneaous bandwith, and you can realize all type of processing gain, yada yada... This isnt by any mistake. just like you said, a 'special case'. so there must be a relationship. if group delay has any usefull meaning for signals with bandwith, instantaneus frquency must have some usefull meaning.
Reply by ●September 17, 20082008-09-17
Instantaneous frequency is a feature of a SIGNAL. Group Delay is a feature of a MEDIA. There is no fucking relation. VLV westocl wrote:>> >>Rune Allnor wrote: >> >> >>>On 17 Sep, 16:52, "westocl" <cwest...@hotmail.com> wrote: >>> >>> >>>>What is the relations hip between the instantaneous frequency of a > > signal > >>>>and the group delay of that signal? >>> >>>I have no idea. Is there a relation? >> >>:-) >> >> >>>>Does Fourier Transform theory falls short when we want to analize >>>>instantaneous frequency? >> >>Eh? Eh? >> >> >>>Yes, in the sense that 'isntantaneous frequency' is a not at all >>>well-defined concept. >> >>For any signal X, let X* be a Hilbert transform of X: >> >>Instantaneous frequency = d(arctg(X*/X))/dt >> >> >>>The term makes some sense when one >>>talks about FM modulation, but not necessarily in general. >> >>The instantaneous frequency is fairly useless and meaningless parameter >>except for some special cases. >> >> >>Vladimir Vassilevsky >>DSP and Mixed Signal Design Consultant >>http://www.abvolt.com > > >>The instantaneous frequency is fairly useless and meaningless parameter >>except for some special cases. > > > Hmmm.. I ponered this too. But lets think pulse compression radar. in > the case of linear FM transmit signals, on the receive side, you see > 'dispersive delay lines'. Heres a 'special case', and a special signal in > the since where the group dealy matches the instatneaous bandwith, and you > can realize all type of processing gain, yada yada... > > This isnt by any mistake. just like you said, a 'special case'. so there > must be a relationship. if group delay has any usefull meaning for signals > with bandwith, instantaneus frquency must have some usefull meaning. >
Reply by ●September 17, 20082008-09-17
> >Instantaneous frequency is a feature of a SIGNAL. >Group Delay is a feature of a MEDIA. >There is no fucking relation. > > >VLV > > > >westocl wrote: > >>> >>>Rune Allnor wrote: >>> >>> >>>>On 17 Sep, 16:52, "westocl" <cwest...@hotmail.com> wrote: >>>> >>>> >>>>>What is the relations hip between the instantaneous frequency of a >> >> signal >> >>>>>and the group delay of that signal? >>>> >>>>I have no idea. Is there a relation? >>> >>>:-) >>> >>> >>>>>Does Fourier Transform theory falls short when we want to analize >>>>>instantaneous frequency? >>> >>>Eh? Eh? >>> >>> >>>>Yes, in the sense that 'isntantaneous frequency' is a not at all >>>>well-defined concept. >>> >>>For any signal X, let X* be a Hilbert transform of X: >>> >>>Instantaneous frequency = d(arctg(X*/X))/dt >>> >>> >>>>The term makes some sense when one >>>>talks about FM modulation, but not necessarily in general. >>> >>>The instantaneous frequency is fairly useless and meaningless parameter>>>except for some special cases. >>> >>> >>>Vladimir Vassilevsky >>>DSP and Mixed Signal Design Consultant >>>http://www.abvolt.com >> >> >>>The instantaneous frequency is fairly useless and meaningless parameter>>>except for some special cases. >> >> >> Hmmm.. I ponered this too. But lets think pulse compression radar.in>> the case of linear FM transmit signals, on the receive side, you see >> 'dispersive delay lines'. Heres a 'special case', and a special signalin>> the since where the group dealy matches the instatneaous bandwith, andyou>> can realize all type of processing gain, yada yada... >> >> This isnt by any mistake. just like you said, a 'special case'. sothere>> must be a relationship. if group delay has any usefull meaning forsignals>> with bandwith, instantaneus frquency must have some usefull meaning. >>>Instantaneous frequency is a feature of a SIGNAL. >Group Delay is a feature of a MEDIA. >There is no fucking relation.hmph... if we characterized a MEDIA as a FIR response is not h(t) a signal? no reason to curse.
Reply by ●September 17, 20082008-09-17
emre <eguven@ece.neu.edu> wrote:>Instantaneous frequency does not make much sense for multicomponent >signals."Instantaneous frequency" doesn't make any sense for any signal. If the time axis is infintesimal then there is no frequency resolution and no spectrum. So I guess this phrase refers to the spectral peak of a very short signal, or a longer signal to which a short window is applied. Steve
