Page 6 of this text: http://cmclab.rice.edu/433/notes/Fitz_BandpassNotes.pdf Gives one equation defining a signal's fourier transform, and another equation defining that signal's energy spectrum. I thought that the fourier transform IS the energy spectrum.. please forgive my noobishness, can someone tell me what the conceptual difference is between a signal's fourier transform and its energy spectrum? Thanks, any help would be much appreciated
What's the difference between a signal's fourier transform, and its energy spectrum
Started by ●December 19, 2007
Reply by ●December 19, 20072007-12-19
maxplanck wrote:> Page 6 of this text: > http://cmclab.rice.edu/433/notes/Fitz_BandpassNotes.pdf > > Gives one equation defining a signal's fourier transform, and another > equation defining that signal's energy spectrum. > > I thought that the fourier transform IS the energy spectrum.. please > forgive my noobishness, can someone tell me what the conceptual difference > is between a signal's fourier transform and its energy spectrum? > > Thanks, any help would be much appreciatedEnergy is [proportional to] the square of voltage. The energy spectrum has no phase information. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●December 19, 20072007-12-19
>maxplanck wrote: >> Page 6 of this text: >> http://cmclab.rice.edu/433/notes/Fitz_BandpassNotes.pdf >> >> Gives one equation defining a signal's fourier transform, and another >> equation defining that signal's energy spectrum. >> >> I thought that the fourier transform IS the energy spectrum.. please >> forgive my noobishness, can someone tell me what the conceptualdifference>> is between a signal's fourier transform and its energy spectrum? >> >> Thanks, any help would be much appreciated > >Energy is [proportional to] the square of voltage. The energy spectrum >has no phase information. > >Jerry >-- >Engineering is the art of making what you want from things you can get. >�����������������������������������������������������������������������aha, thanks a lot!
Reply by ●December 19, 20072007-12-19
Signals fourier transform and signal's energy density spectrum are related to each other by the following relation: Energy_density_spectrum=[Fourier_transform]x[Fourier_transform_conjugate]; Energy density spectrum is sometimes a convenient way of obtaining the power dissipation numbers of periodic signals embedded in noise. Finite duration signals are all energy signals. Example: impulse response of a FIR filter is an energy signal. Impulse (of strength unity) is an energy signal whose energy is 1. Energy density spectrum is also useful in computing signal to noise ratio (SNR). SNR is a measure which tells the purity of a signal. Regards Bharat Pathak Founder and CEO Arithos Designs www.arithos.com : dsp design consultancy and training company.>Page 6 of this text: >http://cmclab.rice.edu/433/notes/Fitz_BandpassNotes.pdf > >Gives one equation defining a signal's fourier transform, and another >equation defining that signal's energy spectrum. > >I thought that the fourier transform IS the energy spectrum.. please >forgive my noobishness, can someone tell me what the conceptualdifference>is between a signal's fourier transform and its energy spectrum? > >Thanks, any help would be much appreciated >
Reply by ●December 19, 20072007-12-19
On Dec 19, 6:05 pm, "maxplanck" <erik.bo...@comcast.net> wrote:> >maxplanck wrote: > >> Page 6 of this text: > >>http://cmclab.rice.edu/433/notes/Fitz_BandpassNotes.pdf > > >> Gives one equation defining a signal's fourier transform, and another > >> equation defining that signal's energy spectrum. > > >> I thought that the fourier transform IS the energy spectrum.. please > >> forgive my noobishness, can someone tell me what the conceptual difference > >> is between a signal's fourier transform and its energy spectrum? > > >Energy is [proportional to] the square of voltage.i thought it was power that is proportional to the square of voltage (or signal value). for energy, you gotta toss in an additional time factor.> >The energy spectrum has no phase information. > > aha, thanks a lot!actually, the topic ain't closed without considering what Bharat pointed out: On Dec 19, 9:28 pm, "bharat pathak" <bha...@arithos.com> wrote:> Signals fourier transform and signal's energy density spectrum are > related > to each other by the following relation: > > Energy_density_spectrum=[Fourier_transform]x[Fourier_transform_conjugate];an equivalent expression is Energy_density_spectrum = (abs{Fourier_transform})^2 which indicates that we're chucking the phase information.> Energy density spectrum is sometimes a convenient way of obtaining > the power dissipation numbers of periodic signals embedded in noise.i guess, if you make assumptions about the noise. reasonable assumptions, like that the noise does not, itself, spike at these discrete frequencies.> Finite duration signals are all energy signals. Example: impulse response > of a FIR filter is an energy signal. Impulse (of strength unity) is an > energy signal whose energy is 1.any fully stable IIR filter has for its impulse response, a finite energy signal.> Energy density spectrum is also useful in computing signal to noise ratio > (SNR). SNR is a measure which tells the purity of a signal.but, again, you have to decide who, in the spectrum, is the signal who is the noise. (sometimes, as in watermarking, the roles of the two get reversed.) r b-j hey Bharat, i took a look at your website. good luck there in Bangalore.
Reply by ●December 20, 20072007-12-20
>hey Bharat, i took a look at your website. good luck there in >Bangalore.thanks. good that your pointed that any stable IIR's impulse response will be of finite duration and thus will be considered as energy signal. i just wanted to avoid it for sometime as the reader might get more confused and hence wanted to illustrate with simple examples.
Reply by ●December 20, 20072007-12-20
robert bristow-johnson wrote: ...> > Finite duration signals are all energy signals. Example: impulse response > > of a FIR filter is an energy signal. Impulse (of strength unity) is an > > energy signal whose energy is 1. > > any fully stable IIR filter has for its impulse response, a finite > energy signal.Yeah, but only for discrete time because only in discrete time can you derive the implication BIBO stable => finite energy. Exercise for the reader: give an example of a continuous time IIR filter that is BIBO stable but does not have finite energy :-). Regards, Andor
Reply by ●December 20, 20072007-12-20
>robert bristow-johnson wrote: >... >> > Finite duration signals are all energy signals. Example: impulseresponse>> > of a FIR filter is an energy signal. Impulse (of strength unity) isan>> > energy signal whose energy is 1. >> >> any fully stable IIR filter has for its impulse response, a finite >> energy signal. > >Yeah, but only for discrete time because only in discrete time can you >derive the implication > >BIBO stable => finite energy. > >Exercise for the reader: give an example of a continuous time IIR >filter that is BIBO stable but does not have finite energy :-). > >Regards, >AndorAndor, Is the answer PLL, by any chance?? I am doing a guess work here. Regards Bharat>
Reply by ●December 20, 20072007-12-20
On 20 Des, 04:53, robert bristow-johnson <r...@audioimagination.com> wrote:> On Dec 19, 6:05 pm, "maxplanck" <erik.bo...@comcast.net> wrote: > > > >maxplanck wrote: > > >> Page 6 of this text: > > >>http://cmclab.rice.edu/433/notes/Fitz_BandpassNotes.pdf > > > >> Gives one equation defining a signal's fourier transform, and another > > >> equation defining that signal's energy spectrum. > > > >> I thought that the fourier transform IS the energy spectrum.. please > > >> forgive my noobishness, can someone tell me what the conceptual difference > > >> is between a signal's fourier transform and its energy spectrum? > > > >Energy is [proportional to] the square of voltage. > > i thought it was power that is proportional to the square of voltage > (or signal value). for energy, you gotta toss in an additional time > factor.Assuming that "Fourier Transform" means the DTFT (valid for signals of infinite duration), it is the other way around: The energy is proportional to the squared integral (view with fixed-width font) inf E ~ integral |X(w)|^2 dw < inf w = -inf while the power spectrum needs the additional time factor T P ~ lim integral 1/2T |X(w)|^2 dw < inf T-> inf w = -T Rune
Reply by ●December 20, 20072007-12-20
On 20 Des, 13:21, Rune Allnor <all...@tele.ntnu.no> wrote:> On 20 Des, 04:53, robert bristow-johnson <r...@audioimagination.com> > wrote: > > > > > > > On Dec 19, 6:05 pm, "maxplanck" <erik.bo...@comcast.net> wrote: > > > > >maxplanck wrote: > > > >> Page 6 of this text: > > > >>http://cmclab.rice.edu/433/notes/Fitz_BandpassNotes.pdf > > > > >> Gives one equation defining a signal's fourier transform, and another > > > >> equation defining that signal's energy spectrum. > > > > >> I thought that the fourier transform IS the energy spectrum.. please > > > >> forgive my noobishness, can someone tell me what the conceptual difference > > > >> is between a signal's fourier transform and its energy spectrum? > > > > >Energy is [proportional to] the square of voltage. > > > i thought it was power that is proportional to the square of voltage > > (or signal value). for energy, you gotta toss in an additional time > > factor. > > Assuming that "Fourier Transform" means the DTFT (valid for > signals of infinite duration), it is the other way around: > The energy is proportional to the squared integral (view > with fixed-width font) > > inf > E ~ integral |X(w)|^2 dw < inf > w = -inf > > while the power spectrum needs the additional time factor > > T > P ~ lim integral 1/2T |X(w)|^2 dw < inf > T-> inf w = -T > > Rune- Skjul sitert tekst - > > - Vis sitert tekst -Those formulas should, of course, be in time domain: inf E ~ sum |x[n]|^2 < inf n=-inf N P ~ lim sum 1/(2N+1)T |x[n]|^2 < inf N->inf n=-N Rune
