Hi all, I have a signal a+jb generated inside DSP. Now, I want to feed the signal to a quadrature modulator, upconvert it to 100MHz and measure it with a spectrum analyzer or scope. My question is, the signal a+jb is complex, the quadrature upconversion is also complex, exp(j*2*pi*100e6). Will I see the complex signal, (a+jb)*exp(j*2*pi*100e6) on the spectrum? Also, for the complex signal generated from signal generator, GMSK, CDMA....etc. They have energy at both negative frequency and positive frequency, or only on one side? Many Thanks, cfy30

# confused about complex signal

Started by ●December 7, 2008

Reply by ●December 7, 20082008-12-07

cfy30 wrote:> Hi all, > > I have a signal a+jb generated inside DSP. Now, I want to feed the signal > to a quadrature modulator, upconvert it to 100MHz and measure it with a > spectrum analyzer or scope. > > My question is, the signal a+jb is complex, the quadrature upconversion is > also complex, exp(j*2*pi*100e6). Will I see the complex signal, > (a+jb)*exp(j*2*pi*100e6) on the spectrum?Probably not. IC quadrature modulators generally have only one output and this is 'real,' but if you had the need, you could construct a quadrature modulator to have a complex output. This modulator circuit would necessarily have two distinct output connections, one 'real' and one 'imaginary.' You could not view this complex signal on an analog spectrum analyser as they have only a single 'real' input. If you had a spectrum analyser that had a complex input (e.g. a FFT-based analyser) then it would be capable of displaying both positive-frequency components and negative- frequency components, with 0Hz in the middle. You would then see your complex signal appearing on one side or other of the 0Hz point.> > Also, for the complex signal generated from signal generator, GMSK, > CDMA....etc. They have energy at both negative frequency and positive > frequency, or only on one side? > > > Many Thanks, > cfy30Each of the in-phase (I) and quadrature-phase (Q) signals taken by itself has both positive-frequency and negative-frequency components. When these two signals are handled together as a complex IQ signal then either the positive-frequency components or the negative-frequency components cancel out, so you see energy only on one side of the 0Hz point. Regards, John

Reply by ●December 7, 20082008-12-07

On Dec 7, 6:46�pm, John Monro <johnmo...@optusnet.removethis.com.au> wrote:> You could not view this complex signal on an analog spectrum > analyser as they have only a single 'real' input. �If you > had a spectrum analyser that had a complex input (e.g. a > FFT-based analyser) then it would be capable of displaying > both positive-frequency components and negative- frequency > components, with 0Hz in the middle. �You would then see your > complex signal appearing on one side or other of the 0Hz point. >> Each of the in-phase (I) and quadrature-phase (Q) signals > taken by itself has both positive-frequency and > negative-frequency components. When these two signals are > handled together as a complex IQ signal then either the > positive-frequency components or the negative-frequency > components cancel out, so you see energy only on one side of > the 0Hz point.Is the cancellation guaranteed for all possible choices of a and b asked about by the OP or only for some choices of a and b. Put another way, given an arbitrary complex signal f(t), is it always true that either F(w) = 0 for w < 0, or F(w) = 0 for w > 0? Or is it just that for a complex signal, the conjugate symmetry constraint F(-w) = F*(w) does not hold at all frequencies w the way it should for real-valued signals?

Reply by ●December 7, 20082008-12-07

Hi John, I found something interesting. I thought the function of modulator is to do exp(j*2*pi*fc) but what I found from the data sheet is, the modulator simply take the I and Q data or real and imaginery data generated, multiply the I data with cos(2*pi*fc*t) and Q data with -sin(2*pi*fc*t), them sum them together at the output. If my understanding is correct, then signal at the modulator output is always real, i.e., there are energy at both negative and positive frequencies. Still trying to understand this more. Thanks, cfy30>cfy30 wrote: >> Hi all, >> >> I have a signal a+jb generated inside DSP. Now, I want to feed thesignal>> to a quadrature modulator, upconvert it to 100MHz and measure it witha>> spectrum analyzer or scope. >> >> My question is, the signal a+jb is complex, the quadrature upconversionis>> also complex, exp(j*2*pi*100e6). Will I see the complex signal, >> (a+jb)*exp(j*2*pi*100e6) on the spectrum? > >Probably not. IC quadrature modulators generally have only >one output and this is 'real,' but if you had the need, you >could construct a quadrature modulator to have a complex >output. This modulator circuit would necessarily have two >distinct output connections, one 'real' and one 'imaginary.' > >You could not view this complex signal on an analog spectrum >analyser as they have only a single 'real' input. If you >had a spectrum analyser that had a complex input (e.g. a >FFT-based analyser) then it would be capable of displaying >both positive-frequency components and negative- frequency >components, with 0Hz in the middle. You would then see your >complex signal appearing on one side or other of the 0Hz point. > > >> >> Also, for the complex signal generated from signal generator, GMSK, >> CDMA....etc. They have energy at both negative frequency and positive >> frequency, or only on one side? >> >> >> Many Thanks, >> cfy30 > >Each of the in-phase (I) and quadrature-phase (Q) signals >taken by itself has both positive-frequency and >negative-frequency components. When these two signals are >handled together as a complex IQ signal then either the >positive-frequency components or the negative-frequency >components cancel out, so you see energy only on one side of >the 0Hz point. > >Regards, >John >

Reply by ●December 13, 20082008-12-13

On Dec 8, 1:10�pm, "dvsarw...@yahoo.com" <dvsarw...@gmail.com> wrote:> On Dec 7, 6:46�pm, John Monro <johnmo...@optusnet.removethis.com.au> > wrote: > > > You could not view this complex signal on an analog spectrum > > analyser as they have only a single 'real' input. �If you > > had a spectrum analyser that had a complex input (e.g. a > > FFT-based analyser) then it would be capable of displaying > > both positive-frequency components and negative- frequency > > components, with 0Hz in the middle. �You would then see your > > complex signal appearing on one side or other of the 0Hz point. > > > Each of the in-phase (I) and quadrature-phase (Q) signals > > taken by itself has both positive-frequency and > > negative-frequency components. When these two signals are > > handled together as a complex IQ signal then either the > > positive-frequency components or the negative-frequency > > components cancel out, so you see energy only on one side of > > the 0Hz point. > > Is the cancellation guaranteed for all possible choices of a and b > asked about by the OP or only for some choices of a and b. > Put another way, given an arbitrary complex signal f(t), is it always > true that either F(w) = 0 for w < 0, or F(w) = 0 for w > 0? �Or > is it just that for a complex signal, the conjugate symmetry > constraint F(-w) = F*(w) does not hold at all frequencies w the > way it should for real-valued signals?Hi, The content of the 'a' and 'b' component effects the spectrum either side of 100MHz point in the up-converted signal, and has no effect on the cancellation that I mentioned. The OP was asking whether the converted signal had positive and negative frequency components. This will depend on the details of the design of the complex modulator that I referred to. If such a device were required I assumed it would be designed to deliver a pure analytic signal and as a result either the positive-frequency components or the negative-frequency components would be cancelled out. This cancellation is does not depend on the characteristics of signals 'a' and 'b' which may be components of an analytic signal or alternatively may be unrelated. Sorry for the delayed reply. My Internet Provider (OPTUS) has not been able to provide Newsgroups for the last few days. Regards, John

Reply by ●December 13, 20082008-12-13

On Dec 8, 2:44�pm, "cfy30" <cf...@yahoo.com> wrote:> Hi John, > > I found something interesting. I thought the function of modulator is to > do exp(j*2*pi*fc) but what I found from the data sheet is, the modulator > simply take the I and Q data or real and imaginery data generated, multiply > the I data with cos(2*pi*fc*t) and Q data with -sin(2*pi*fc*t), them sum > them together at the output. > > If my understanding is correct, then signal at the modulator output is > always real, i.e., there are energy at both negative and positive > frequencies. Still trying to understand this more. > > Thanks, > cfy30 > > > > >cfy30 wrote: > >> Hi all, > > >> I have a signal a+jb generated inside DSP. Now, I want to feed the > signal > >> to a quadrature modulator, upconvert it to 100MHz and measure it with > a > >> spectrum analyzer or scope. > > >> My question is, the signal a+jb is complex, the quadrature upconversion > is > >> also complex, exp(j*2*pi*100e6). Will I see the complex signal, > >> (a+jb)*exp(j*2*pi*100e6) on the spectrum? > > >Probably not. �IC quadrature modulators generally have only > >one output and this is 'real,' �but if you had the need, you > >could construct a quadrature modulator to have a complex > >output. �This modulator circuit would necessarily have two > >distinct output connections, one 'real' and one 'imaginary.' > > >You could not view this complex signal on an analog spectrum > >analyser as they have only a single 'real' input. �If you > >had a spectrum analyser that had a complex input (e.g. a > >FFT-based analyser) then it would be capable of displaying > >both positive-frequency components and negative- frequency > >components, with 0Hz in the middle. �You would then see your > >complex signal appearing on one side or other of the 0Hz point. > > >> Also, for the complex signal generated from signal generator, GMSK, > >> CDMA....etc. They have energy at both negative frequency and positive > >> frequency, or only on one side? > > >> Many Thanks, > >> cfy30 > > >Each of the in-phase (I) and quadrature-phase (Q) signals > >taken by itself has both positive-frequency and > >negative-frequency components. When these two signals are > >handled together as a complex IQ signal then either the > >positive-frequency components or the negative-frequency > >components cancel out, so you see energy only on one side of > >the 0Hz point. > > >Regards, > >JohnHi cfy30, This illustration may help: Take a complex signal containing only positive-frequency components. Physically this will have a wire ('I') with the in-phase components and a wire ('Q') with the quadrature components. The components on 'Q' is the same as the components on 'I' except that all components on Q have a phase of -90 degrees relative to I. Now take an otherwise identical complex signal with only negative- frequency components. It is similar to the above except that the components on its Q wire have a phase of +90 relative to the 'I' components. If we now sum the two 'I' signals and we separately sum the two 'Q' signals we find that the resulting I signal is twice the amplitude and the resulting Q signal is zero (because the phase difference between the two Q components is 180 degrees). What we have now is a 'real' signal which necessarily contains both positive and negative frequency components and yet exists on one single wire. Admittedly it does seem strange at first that while one wire is enough to carry both positive and negative frequencies, it requires two wires to carry either the positive or the negative frequencies alone. Sorry about the delayed reply, but my Internet Provider (OPTUS) is having trouble providing Newsgroups and it does not seem to be a high priority for them to fix the problem. On the other hand, I CAN download any number of ring-tones to my OPTUS phone so I suppose one takes the good with the bad (:=) Regards, John

Reply by ●December 14, 20082008-12-14

On Dec 13, 7:47�pm, johnmo...@optusnet.com.au wrote:> On Dec 8, 2:44�pm, "cfy30" <cf...@yahoo.com> wrote: > > > > > Hi John, > > > I found something interesting. I thought the function of modulator is to > > do exp(j*2*pi*fc) but what I found from the data sheet is, the modulator > > simply take the I and Q data or real and imaginery data generated, multiply > > the I data with cos(2*pi*fc*t) and Q data with -sin(2*pi*fc*t), them sum > > them together at the output. > > > If my understanding is correct, then signal at the modulator output is > > always real, i.e., there are energy at both negative and positive > > frequencies. Still trying to understand this more. > > > Thanks, > > cfy30 > > > >cfy30 wrote: > > >> Hi all, > > > >> I have a signal a+jb generated inside DSP. Now, I want to feed the > > signal > > >> to a quadrature modulator, upconvert it to 100MHz and measure it with > > a > > >> spectrum analyzer or scope. > > > >> My question is, the signal a+jb is complex, the quadrature upconversion > > is > > >> also complex, exp(j*2*pi*100e6). Will I see the complex signal, > > >> (a+jb)*exp(j*2*pi*100e6) on the spectrum? > > > >Probably not. �IC quadrature modulators generally have only > > >one output and this is 'real,' �but if you had the need, you > > >could construct a quadrature modulator to have a complex > > >output. �This modulator circuit would necessarily have two > > >distinct output connections, one 'real' and one 'imaginary.' > > > >You could not view this complex signal on an analog spectrum > > >analyser as they have only a single 'real' input. �If you > > >had a spectrum analyser that had a complex input (e.g. a > > >FFT-based analyser) then it would be capable of displaying > > >both positive-frequency components and negative- frequency > > >components, with 0Hz in the middle. �You would then see your > > >complex signal appearing on one side or other of the 0Hz point. > > > >> Also, for the complex signal generated from signal generator, GMSK, > > >> CDMA....etc. They have energy at both negative frequency and positive > > >> frequency, or only on one side? > > > >> Many Thanks, > > >> cfy30 > > > >Each of the in-phase (I) and quadrature-phase (Q) signals > > >taken by itself has both positive-frequency and > > >negative-frequency components. When these two signals are > > >handled together as a complex IQ signal then either the > > >positive-frequency components or the negative-frequency > > >components cancel out, so you see energy only on one side of > > >the 0Hz point. > > > >Regards, > > >John > > Hi cfy30, > > This illustration may help: > > Take a complex signal containing only positive-frequency components. > Physically this will have a wire ('I') �with the in-phase components > and a wire ('Q') with the quadrature components. �The components on > 'Q' is the same as the components on 'I' except that all components on > Q have a phase of -90 degrees relative to I. > > Now take an otherwise identical complex signal with only negative- > frequency components. �It is similar to the above except that the > components on its Q wire have a phase of +90 relative to the 'I' > components. > > If we now sum the two 'I' signals and we separately sum the two 'Q' > signals we find that the resulting I signal is twice the amplitude and > the resulting Q signal is zero (because the phase difference between > the two Q components is 180 degrees). �What we have now is a 'real' > signal which necessarily contains both positive and negative frequency > components and yet exists on one single wire. > > Admittedly it does seem strange at first that while one wire is enough > to carry both positive and negative frequencies, it requires two wires > to carry either the positive or the negative frequencies alone. > > Sorry about the delayed reply, but my Internet Provider (OPTUS) is > having trouble providing Newsgroups and it does not seem to be a high > priority for them to fix the problem. �On the other hand, �I CAN > download any number of ring-tones to my OPTUS phone so I suppose one > takes the good with the bad (:=) > > Regards, > JohnBUT do negative frequency means the orientation of the sinusoid (for e.g) right? Correct me if I'm wrong ... Also what is the practical significance of using an imaginary component when we are dealing with a quadrature composite signal. If I may also ask does 'j' represent orthonormal signals ?

Reply by ●December 14, 20082008-12-14

On Dec 14, 9:12�am, communications_engin...@yahoo.com wrote:> > BUT do negative frequency means the orientation of the sinusoid (for > e.g) right? Correct me if I'm wrong ... Also what is the practical > significance of using an imaginary component when we are dealing with > a quadrature composite signal. If I may also ask does 'j' represent > orthonormal signals ?- Hide quoted text - > > - Show quoted text -Negative frequency is really only relevent in the complex domain. A sinusoidal signal is comprised of two phasors: A negative frequency phasor, and a positive frequency phasor. Thes two complex exponentials add up to make a real sinusoid. I have built some flash programs that illustrate how phasors add up to make sinusoids: http://www.fourier-series.com/fourierseries2/complex_tutorial.html You want to work with complex numbers because you don;t really understand how sinusoidal motion (as a solution to a differential equation) makes sense, until you can see the complex exponentials.

Reply by ●December 14, 20082008-12-14

On Dec 15, 1:12�am, communications_engin...@yahoo.com wrote:> On Dec 13, 7:47�pm, johnmo...@optusnet.com.au wrote: > > > > > On Dec 8, 2:44�pm, "cfy30" <cf...@yahoo.com> wrote: > > > > Hi John, > > > > I found something interesting. I thought the function of modulator is to > > > do exp(j*2*pi*fc) but what I found from the data sheet is, the modulator > > > simply take the I and Q data or real and imaginery data generated, multiply > > > the I data with cos(2*pi*fc*t) and Q data with -sin(2*pi*fc*t), them sum > > > them together at the output. > > > > If my understanding is correct, then signal at the modulator output is > > > always real, i.e., there are energy at both negative and positive > > > frequencies. Still trying to understand this more. > > > > Thanks, > > > cfy30 > > > > >cfy30 wrote: > > > >> Hi all, > > > > >> I have a signal a+jb generated inside DSP. Now, I want to feed the > > > signal > > > >> to a quadrature modulator, upconvert it to 100MHz and measure it with > > > a > > > >> spectrum analyzer or scope. > > > > >> My question is, the signal a+jb is complex, the quadrature upconversion > > > is > > > >> also complex, exp(j*2*pi*100e6). Will I see the complex signal, > > > >> (a+jb)*exp(j*2*pi*100e6) on the spectrum? > > > > >Probably not. �IC quadrature modulators generally have only > > > >one output and this is 'real,' �but if you had the need, you > > > >could construct a quadrature modulator to have a complex > > > >output. �This modulator circuit would necessarily have two > > > >distinct output connections, one 'real' and one 'imaginary.' > > > > >You could not view this complex signal on an analog spectrum > > > >analyser as they have only a single 'real' input. �If you > > > >had a spectrum analyser that had a complex input (e.g. a > > > >FFT-based analyser) then it would be capable of displaying > > > >both positive-frequency components and negative- frequency > > > >components, with 0Hz in the middle. �You would then see your > > > >complex signal appearing on one side or other of the 0Hz point. > > > > >> Also, for the complex signal generated from signal generator, GMSK, > > > >> CDMA....etc. They have energy at both negative frequency and positive > > > >> frequency, or only on one side? > > > > >> Many Thanks, > > > >> cfy30 > > > > >Each of the in-phase (I) and quadrature-phase (Q) signals > > > >taken by itself has both positive-frequency and > > > >negative-frequency components. When these two signals are > > > >handled together as a complex IQ signal then either the > > > >positive-frequency components or the negative-frequency > > > >components cancel out, so you see energy only on one side of > > > >the 0Hz point. > > > > >Regards, > > > >John > > > Hi cfy30, > > > This illustration may help: > > > Take a complex signal containing only positive-frequency components. > > Physically this will have a wire ('I') �with the in-phase components > > and a wire ('Q') with the quadrature components. �The components on > > 'Q' is the same as the components on 'I' except that all components on > > Q have a phase of -90 degrees relative to I. > > > Now take an otherwise identical complex signal with only negative- > > frequency components. �It is similar to the above except that the > > components on its Q wire have a phase of +90 relative to the 'I' > > components. > > > If we now sum the two 'I' signals and we separately sum the two 'Q' > > signals we find that the resulting I signal is twice the amplitude and > > the resulting Q signal is zero (because the phase difference between > > the two Q components is 180 degrees). �What we have now is a 'real' > > signal which necessarily contains both positive and negative frequency > > components and yet exists on one single wire. > > > Admittedly it does seem strange at first that while one wire is enough > > to carry both positive and negative frequencies, it requires two wires > > to carry either the positive or the negative frequencies alone. > > > Sorry about the delayed reply, but my Internet Provider (OPTUS) is > > having trouble providing Newsgroups and it does not seem to be a high > > priority for them to fix the problem. �On the other hand, �I CAN > > download any number of ring-tones to my OPTUS phone so I suppose one > > takes the good with the bad (:=) > > > Regards, > > John > > BUT do negative frequency means the orientation of the sinusoid (for > e.g) right? Correct me if I'm wrong ...I'm not sure what you mean here. I take a negative frequency sinusoid to be one in which the imaginary (Q) has a phase of +90 degrees relative to the real (I) component. Also what is the practical significance of using an imaginary component when we are dealing with> a quadrature composite signal.It is useful to regard a real signal as containing equal positive and negative frequency components. The imaginary parts cancel out, hence the signal can exist on one wire. If you want either the negative frequency or the positive frequency component alone, then the imaginary component is non-zero and so you need two wires (I and Q) to contain the signal. If I may also ask does 'j' represent> orthonormal signals ?In this context the j operator is used to designate the imaginary component of a complex time-domain signal. It is also used to designate the imaginary component in the phasor representation of a signal.

Reply by ●December 15, 20082008-12-15

On Dec 15, 4:10�am, johnmo...@optusnet.com.au wrote:> On Dec 15, 1:12�am, communications_engin...@yahoo.com wrote: > > > > > On Dec 13, 7:47�pm, johnmo...@optusnet.com.au wrote: > > > > On Dec 8, 2:44�pm, "cfy30" <cf...@yahoo.com> wrote: > > > > > Hi John, > > > > > I found something interesting. I thought the function of modulator is to > > > > do exp(j*2*pi*fc) but what I found from the data sheet is, the modulator > > > > simply take the I and Q data or real and imaginery data generated, multiply > > > > the I data with cos(2*pi*fc*t) and Q data with -sin(2*pi*fc*t), them sum > > > > them together at the output. > > > > > If my understanding is correct, then signal at the modulator output is > > > > always real, i.e., there are energy at both negative and positive > > > > frequencies. Still trying to understand this more. > > > > > Thanks, > > > > cfy30 > > > > > >cfy30 wrote: > > > > >> Hi all, > > > > > >> I have a signal a+jb generated inside DSP. Now, I want to feed the > > > > signal > > > > >> to a quadrature modulator, upconvert it to 100MHz and measure it with > > > > a > > > > >> spectrum analyzer or scope. > > > > > >> My question is, the signal a+jb is complex, the quadrature upconversion > > > > is > > > > >> also complex, exp(j*2*pi*100e6). Will I see the complex signal, > > > > >> (a+jb)*exp(j*2*pi*100e6) on the spectrum? > > > > > >Probably not. �IC quadrature modulators generally have only > > > > >one output and this is 'real,' �but if you had the need, you > > > > >could construct a quadrature modulator to have a complex > > > > >output. �This modulator circuit would necessarily have two > > > > >distinct output connections, one 'real' and one 'imaginary.' > > > > > >You could not view this complex signal on an analog spectrum > > > > >analyser as they have only a single 'real' input. �If you > > > > >had a spectrum analyser that had a complex input (e.g. a > > > > >FFT-based analyser) then it would be capable of displaying > > > > >both positive-frequency components and negative- frequency > > > > >components, with 0Hz in the middle. �You would then see your > > > > >complex signal appearing on one side or other of the 0Hz point. > > > > > >> Also, for the complex signal generated from signal generator, GMSK, > > > > >> CDMA....etc. They have energy at both negative frequency and positive > > > > >> frequency, or only on one side? > > > > > >> Many Thanks, > > > > >> cfy30 > > > > > >Each of the in-phase (I) and quadrature-phase (Q) signals > > > > >taken by itself has both positive-frequency and > > > > >negative-frequency components. When these two signals are > > > > >handled together as a complex IQ signal then either the > > > > >positive-frequency components or the negative-frequency > > > > >components cancel out, so you see energy only on one side of > > > > >the 0Hz point. > > > > > >Regards, > > > > >John > > > > Hi cfy30, > > > > This illustration may help: > > > > Take a complex signal containing only positive-frequency components. > > > Physically this will have a wire ('I') �with the in-phase components > > > and a wire ('Q') with the quadrature components. �The components on > > > 'Q' is the same as the components on 'I' except that all components on > > > Q have a phase of -90 degrees relative to I. > > > > Now take an otherwise identical complex signal with only negative- > > > frequency components. �It is similar to the above except that the > > > components on its Q wire have a phase of +90 relative to the 'I' > > > components. > > > > If we now sum the two 'I' signals and we separately sum the two 'Q' > > > signals we find that the resulting I signal is twice the amplitude and > > > the resulting Q signal is zero (because the phase difference between > > > the two Q components is 180 degrees). �What we have now is a 'real' > > > signal which necessarily contains both positive and negative frequency > > > components and yet exists on one single wire. > > > > Admittedly it does seem strange at first that while one wire is enough > > > to carry both positive and negative frequencies, it requires two wires > > > to carry either the positive or the negative frequencies alone. > > > > Sorry about the delayed reply, but my Internet Provider (OPTUS) is > > > having trouble providing Newsgroups and it does not seem to be a high > > > priority for them to fix the problem. �On the other hand, �I CAN > > > download any number of ring-tones to my OPTUS phone so I suppose one > > > takes the good with the bad (:=) > > > > Regards, > > > John > > > BUT do negative frequency means the orientation of the sinusoid (for > > e.g) right? Correct me if I'm wrong ... > > I'm not sure what you mean here. > �I take a negative frequency sinusoid to be one in which the imaginary > (Q) has a phase of +90 degrees relative to the real (I) component. > > �Also what is the practical significance of using an imaginary > component when we are dealing with > > > a quadrature composite signal. > > It is useful to regard a real signal as containing equal positive and > negative frequency components. �The imaginary parts cancel out, hence > the signal can exist on one wire. > > If you want either the negative frequency or the positive frequency > component alone, then the imaginary component is non-zero and so you > need two wires (I and Q) to contain the signal. > > �If I may also ask does 'j' represent > > > orthonormal signals ? > > In this context the j operator is used to designate the imaginary > component of a complex time-domain signal. > It is also used to designate the imaginary component in the phasor > representation of a signal.Thanks.