Hello, I have some questions pertaining to the frequency domain plots and complex exponential values. Can someone pls clarify. 1) This is regarding creating waveform plots in frequency domain (DTFT) - I have seen waveform plots after transform which show real, imaginary, magnitude and phase - I have also seen waveform plots that show only one plot after the transform (DTFT) Is this because the value is e is expressed in terms of complex exponential? Also, when a complex exponential is expressed as e power (i*angle) = cos(angle) + isin(angle) Does i above indicate that sin part is associated with the imaginary part and does not have any specific value associated to it? Thanks
frequency domain plot etc.
Started by ●July 27, 2011
Reply by ●July 27, 20112011-07-27
On Jul 27, 8:45�am, "manishp" <manishp.p18@n_o_s_p_a_m.gmail.com> wrote:> Hello, > > I have some questions pertaining to the frequency domain plots and complex > exponential values. Can someone pls clarify. > > 1) This is regarding creating waveform plots in frequency domain (DTFT) > > � - I have seen waveform plots after transform which show real, imaginary, > magnitude and phase > � - I have also seen waveform plots that show only one plot after the > transform (DTFT)Not seeing the plots you have in mind, I can only guess, and probably inaccurately. Real and imaginary suffices to specify spectrum. (I wouldn't call that a waveform plot. Waveforms exist in time. Spectra are frequency descriptions of the same information.) Magnitude and phase is another way to describe a spectrum. Both plots together are likelt presented only to illustrate their relationship. They are polar and rectangular representations.> Is this because the value is e is expressed in terms of complex > exponential?What do you mean? 'e' is approximately 2.718281828459045235360287471352662497757.... It is defined as the limit of (1+x)^(1/x) as x->0. It is a dimensionless constant.> Also, when a complex exponential is expressed as e power (i*angle) = > cos(angle) + isin(angle) > Does i above indicate that sin part is associated with the imaginary partThat's what i (in electrical engineering, j) means. i*i = -1> and does not have any specific value associated to it?Specific value associated with what, i, or i*sin(angle)?> ThanksYou're welcome. Jerry -- Engineering is the art of making what you want from things you can get.
Reply by ●July 27, 20112011-07-27
Hello Jerry, Thanks a lot ... my response and questions below ...>> I have some questions pertaining to the frequency domain plots andcomple=>x >> exponential values. Can someone pls clarify. >> >> 1) This is regarding creating waveform plots in frequency domain (DTFT) >> >> =A0 - I have seen waveform plots after transform which show real,imagina=>ry, >> magnitude and phase >> =A0 - I have also seen waveform plots that show only one plot after the >> transform (DTFT) > >Not seeing the plots you have in mind, I can only guess, and probably >inaccurately. Real and imaginary suffices to specify spectrum. (I >wouldn't call that a waveform plot. Waveforms exist in time. Spectra >are frequency descriptions of the same information.) Magnitude and >phase is another way to describe a spectrum. Both plots together are >likelt presented only to illustrate their relationship. They are polar >and rectangular representations.ok thanks ... i get an idea now.>> Is this because the value is e is expressed in terms of complex >> exponential? > >What do you mean? 'e' is approximately >2.718281828459045235360287471352662497757.... It is defined as the >limit of (1+x)^(1/x) as x->0. It is a dimensionless constant.my question was the need to represent the frequency domain using multiple plots (real, imaginary, magnitude, phase) Is it related to the fact that the values are expressed using e (power) ((-j2*pi/2)*k)>> Also, when a complex exponential is expressed as e power (i*angle) =3D >> cos(angle) + isin(angle) >> Does i above indicate that sin part is associated with the imaginarypart> >That's what i (in electrical engineering, j) means. i*i =3D -1 > >> and does not have any specific value associated to it? > >Specific value associated with what, i, or i*sin(angle)?what is the significance of i (not i*sin(angle))? I am assuming it only indicates that the there is real part and an imaginary part. And the imaginary part is associated with i component... PS: apologies for asking fundamental questions. I have just started learning ...
Reply by ●July 27, 20112011-07-27
On Jul 27, 8:45�am, "manishp" <manishp.p18@n_o_s_p_a_m.gmail.com> wrote:> Hello, > > I have some questions pertaining to the frequency domain plots and complex > exponential values. Can someone pls clarify. > > 1) This is regarding creating waveform plots in frequency domain (DTFT) > > � - I have seen waveform plots after transform which show real, imaginary, > magnitude and phase > � - I have also seen waveform plots that show only one plot after the > transform (DTFT) > > Is this because the value is e is expressed in terms of complex > exponential? > > Also, when a complex exponential is expressed as e power (i*angle) = > cos(angle) + isin(angle) > Does i above indicate that sin part is associated with the imaginary part > and does not have any specific value associated to it? > > ThanksConsider looking over my website: www.fourier-series.com it contains info on the fourier series, complex numbers and the DFT. It goes shows how the real and imaginary parts of the DFT come together. brent
Reply by ●July 27, 20112011-07-27
On Wed, 27 Jul 2011 07:45:03 -0500, manishp wrote:> Hello, > > I have some questions pertaining to the frequency domain plots and > complex exponential values. Can someone pls clarify. > > 1) This is regarding creating waveform plots in frequency domain (DTFT) > > - I have seen waveform plots after transform which show real, > imaginary, > magnitude and phase > - I have also seen waveform plots that show only one plot after the > transform (DTFT) > > Is this because the value is e is expressed in terms of complex > exponential? > > Also, when a complex exponential is expressed as e power (i*angle) = > cos(angle) + isin(angle) > Does i above indicate that sin part is associated with the imaginary > part and does not have any specific value associated to it?What is your educational background? You're asking all sorts of questions that are answered in a course of study in signal processing, are answered in a consistent and rational way, and are answered in an ordering such that later questions build upon earlier answers. Right now you're trying to build a house by putting up a wall here, an unconnected section of foundation there, a bit of shingle (oh! need to get some sheathing under that!) over there, etc. I'm not sure of a good book for signal processing self-study, but if there is one you need to get it and go through it. Perhaps a copy of the ARRL Handbook and my book on control theory -- but I'm not sure if either one will answer your questions about the DFT. -- www.wescottdesign.com
Reply by ●July 27, 20112011-07-27
On Jul 27, 12:15�pm, Tim Wescott <t...@seemywebsite.com> wrote:> On Wed, 27 Jul 2011 07:45:03 -0500, manishp wrote: > > Hello, > > > I have some questions pertaining to the frequency domain plots and > > complex exponential values. Can someone pls clarify. > > > 1) This is regarding creating waveform plots in frequency domain (DTFT) > > > � - I have seen waveform plots after transform which show real, > > � imaginary, > > magnitude and phase > > � - I have also seen waveform plots that show only one plot after the > > transform (DTFT) > > > Is this because the value is e is expressed in terms of complex > > exponential? > > > Also, when a complex exponential is expressed as e power (i*angle) = > > cos(angle) + isin(angle) > > Does i above indicate that sin part is associated with the imaginary > > part and does not have any specific value associated to it? > > What is your educational background? �You're asking all sorts of > questions that are answered in a course of study in signal processing, > are answered in a consistent and rational way, and are answered in an > ordering such that later questions build upon earlier answers. > > Right now you're trying to build a house by putting up a wall here, an > unconnected section of foundation there, a bit of shingle (oh! �need to > get some sheathing under that!) over there, etc. > > I'm not sure of a good book for signal processing self-study, but if > there is one you need to get it and go through it. �Perhaps a copy of the > ARRL Handbook and my book on control theory -- but I'm not sure if either > one will answer your questions about the DFT.A text used in EE101 seems appropriate. Something like basic AC theory. (I got me early self-study information from Audel's Electrician's Guide, published around 1920. It's not out of date yet. Jerry -- Engineering is the art of making what you want from things you can get.
Reply by ●July 27, 20112011-07-27
On Jul 27, 11:18�am, "manishp" <manishp.p18@n_o_s_p_a_m.gmail.com> wrote:> Hello Jerry, > > Thanks a lot ... my response and questions below ... > > > > > > > > > > > > >> I have some questions pertaining to the frequency domain plots and > comple= > >x > >> exponential values. Can someone pls clarify. > > >> 1) This is regarding creating waveform plots in frequency domain (DTFT) > > >> =A0 - I have seen waveform plots after transform which show real, > imagina= > >ry, > >> magnitude and phase > >> =A0 - I have also seen waveform plots that show only one plot after the > >> transform (DTFT) > > >Not seeing the plots you have in mind, I can only guess, and probably > >inaccurately. Real and imaginary suffices to specify spectrum. (I > >wouldn't call that a waveform plot. Waveforms exist in time. Spectra > >are frequency descriptions of the same information.) Magnitude and > >phase is another way to describe a spectrum. Both plots together are > >likelt presented only to illustrate their relationship. They are polar > >and rectangular representations. > > ok thanks ... i get an idea now. > > >> Is this because the value is e is expressed in terms of complex > >> exponential? > > >What do you mean? 'e' is approximately > >2.718281828459045235360287471352662497757.... It is defined as the > >limit of (1+x)^(1/x) as x->0. It is a dimensionless constant. > > my question was the need to represent the frequency domain using multiple > plots (real, imaginary, magnitude, phase)Real and imaginary can ve derived from phase and magnitude. I can direct you to the same place by telling you that it is 5 miles away on a heading of 53.13 degrees north of due east (polar; magnitude & angle) or telling you that the spot is 4 miles north of you and 3 miles east (rectangular; real & imaginary). They are different expressions of the same fact.> Is it related to the fact that the values are expressed using e (power) > ((-j2*pi/2)*k)That's an odd expression. 2*pi/2 is more simply written "pi". e^ix cos(x) + i*sin(x); Euler's identity. In particular, e^i*pi = -1 so e^((-j2*pi/2)*k) (or e^(k*pi)) = -1^k = 1,-1,1,-1,... as k increases from 0.> >> Also, when a complex exponential is expressed as e power (i*angle) =3D > >> cos(angle) + isin(angle) > >> Does i above indicate that sin part is associated with the imaginary > partYes.> >That's what i (in electrical engineering, j) means. i*i =3D -1 > > >> and does not have any specific value associated to it? > > >Specific value associated with what, i, or i*sin(angle)? > > what is the significance of i (not i*sin(angle))? > I am assuming it only indicates that the there is real part and an > imaginary part. And the imaginary part is associated with i componenti identifies the imaginary part. It is called a rotation operator. Real numbers are plotted left and right. Imaginary numbers are plotted up and down. The compass directions East, North, West, and South correspond to the numeric directions +, +i, -, and -i. Complex number coordinates are exact analogs of Cartesian coordinates x and y. There is no mystery here, only (quite understandable) confusion.> PS: apologies for asking fundamental questions. I have just started > learning ...You should read up on complex numbers and basic AC theory. Jerry -- Engineering is the art of making what you want from things you can get.
Reply by ●July 28, 20112011-07-28
On Jul 27, 2:45�pm, "manishp" <manishp.p18@n_o_s_p_a_m.gmail.com> wrote:> Hello, > > I have some questions pertaining to the frequency domain plots and complex > exponential values. Can someone pls clarify. > > 1) This is regarding creating waveform plots in frequency domain (DTFT) > > � - I have seen waveform plots after transform which show real, imaginary, > magnitude and phase > � - I have also seen waveform plots that show only one plot after the > transform (DTFT) > > Is this because the value is e is expressed in terms of complex > exponential?No. It is because the FT is expressed as a complex *number*. Complex numbers can be visualized on either carthesian or polar form. Use the one that better suits the purpose.> Also, when a complex exponential is expressed as e power (i*angle) = > cos(angle) + isin(angle) > Does i above indicate that sin part is associated with the imaginary part > and does not have any specific value associated to it?This is rather trivial complex arithmetics. Do you know complex numbers at all? If not, you might want to take a math class. Rune
Reply by ●July 28, 20112011-07-28
On Jul 27, 11:18�am, "manishp" <manishp.p18@n_o_s_p_a_m.gmail.com> wrote: ...> what is the significance of i (not i*sin(angle))? > I am assuming it only indicates that the there is real part and an > imaginary part. And the imaginary part is associated with i component... > > PS: apologies for asking fundamental questions. I have just started > learning ...started learning specifically *what*? it appears to me, from the questions you're asking, that you are starting in the concepts of what is now often called "Signals and Systems", or LTI system theory. well, it's okay to be just starting. but, to not waste people's time (as if we're so worried about wasting our time, we never spend any on comp.dsp) you should be clear about what you have really learned (or what college math level you have attained). what courses or equivalent level have you under your belt?: college algebra trigonometry calculus (basic) differential equations (basic) complex variables LTI system theory requires some concept from and ability in all of these math subject areas. are you comfortable in all of them? electrical engineering subjects like circuit analysis helps with context, but is not necessary. LTI system theory is an applied mathematics topic, normally taught to electrical engineering students in electrical engineering courses. but it really is a broader mathematical topic with application inside and outside of the EE discipline. r b-j
Reply by ●July 28, 20112011-07-28
On Jul 27, 5:45 am, "manishp" <manishp.p18@n_o_s_p_a_m.gmail.com> wrote:> Hello, > > I have some questions pertaining to the frequency domain plots and complex > exponential values. Can someone pls clarify. > > 1) This is regarding creating waveform plots in frequency domain (DTFT) > > - I have seen waveform plots after transform which show real, imaginary, > magnitude and phase > - I have also seen waveform plots that show only one plot after the > transform (DTFT) > > Is this because the value is e is expressed in terms of complex > exponential?No, the complex exponent is just a convenient way of determining the results, it's an abstraction. Basically, a DTFT converts a sampled time funtion x(n) into a sum of sinusoids, of the form A1 cos(wn+phase1) + A2 cos(2wn + phase2) + ...... AN cos(Nwn + phaseN) So how would express that result? One was is just to plot A1, A2 up to AN, that is called magnitude plot, sometimes you just don' t care about the phase so it's not plotted. Other times you need the phase too, so you plot that. Other times you want it expressed into another form like A1 cos(wn+phase1) = B + i C this is called the imagery form, but their is nothing imagery about it A = sqrt(B^2 + C^2) phase1 = arctan(C/B)> > Also, when a complex exponential is expressed as e power (i*angle) = > cos(angle) + isin(angle) > Does i above indicate that sin part is associated with the imaginary part > and does not have any specific value associated to it? >Yes.> Thanks
