Hi Guys, First please excuse my ignorance, I am just starting in DSP as a bit of a hobby. I Have Richard Lyons "understanding dsp" here and am working my way through the "Sampling Bandpass Signals" chapter. I understand the idea of Aliases and aliasing in the sampled signal spectrum but in the diagrams for the continuous signal spectrum there is always an inverse of the signal. So say there is an amplitude of 1 and 2MHz then there is also have an amplitude of 1 at -2MHz. This doesn't seem to be explained, probably as it is something basic that I should already know. Could someone direct me to some information that would explain this to me. Thanks for any help. Andy

# Absolute Beginner - inverted signal?

Started by ●June 9, 2008

Reply by ●June 9, 20082008-06-09

"BobTheDog" <andrew.capon@zen.co.uk> writes:> Hi Guys, > > First please excuse my ignorance, I am just starting in DSP as a bit of a > hobby. > > I Have Richard Lyons "understanding dsp" here and am working my way > through the "Sampling Bandpass Signals" chapter. I understand the idea of > Aliases and aliasing in the sampled signal spectrum but in the diagrams for > the continuous signal spectrum there is always an inverse of the signal. So > say there is an amplitude of 1 and 2MHz then there is also have an > amplitude of 1 at -2MHz. > > This doesn't seem to be explained, probably as it is something basic that > I should already know. > > Could someone direct me to some information that would explain this to > me. > > Thanks for any help. > > AndyHi Andy, Yes, it is something basic. A real (as opposed to complex) signal will always have a symmetric spectrum. If you pick up a book on linear system theory (I like [signalsandsystems]) and read about the properties Fourier transforms, you will find out why. --Randy @BOOK{signalsandsystems, title = "{Signals and Systems}", author = "{Alan~V.~Oppenheim, Alan~S.~Willsky, with Ian~T.~Young}", publisher = "Prentice Hall", year = "1983"} -- % Randy Yates % "My Shangri-la has gone away, fading like %% Fuquay-Varina, NC % the Beatles on 'Hey Jude'" %%% 919-577-9882 % %%%% <yates@ieee.org> % 'Shangri-La', *A New World Record*, ELO http://www.digitalsignallabs.com

Reply by ●June 9, 20082008-06-09

Reply by ●June 9, 20082008-06-09

Reply by ●June 10, 20082008-06-10

SteveSmith wrote:> http://www.dspguide.com/ch10/3.htmPretty good description. It is sometimes described as periodic boundary conditions, especially when used for the solutions of differential equations. Still, I find the part where modifications to the spectrum (FFT of the time domain signal) to "spill over from one period into the adjacent period" to be a little strange. It really can't do that because there are no frequency components in the transform that can do that. The problem, as I see it, is in ones belief in the modifications to the transform (most obvious in the case of circular convolution). That is, the modified spectrum is not the desired spectrum. But I can also see it in terms of spilling over. Now, why does the audio spectrum in ch10/5.htm not have a negative part? -- glen

Reply by ●June 10, 20082008-06-10

>Now, why does the audio spectrum in ch10/5.htm not have >a negative part? > >-- glen >Hi Glen, It would certainly be useful to show the negative frequencies in this figure. Thanks for the suggestion-- I'll add it to my list for the next edition. Steve

Reply by ●June 11, 20082008-06-11

On Jun 10, 12:12�pm, "SteveSmith" <Steve.Smi...@SpectrumSDI.com> wrote:> >Now, why does the audio spectrum in ch10/5.htm not have > >a negative part? > > >-- glen > > Hi Glen, > It would certainly be useful to show the negative frequencies in this > figure. �Thanks for the suggestion-- I'll add it to my list for the next > edition. > Steveus old analog guys have learned that perspective using old fashioned heterodyne spectrum analyzers. If you tune below the zero, you can actually see the negative frequencies, mirror images of the positive ones...sure enough they are there... :-) Mark

Reply by ●June 12, 20082008-06-12

On Wed, 11 Jun 2008 08:58:47 -0700 (PDT), Mark <makolber@yahoo.com> wrote:>On Jun 10, 12:12�pm, "SteveSmith" <Steve.Smi...@SpectrumSDI.com> >wrote: >> >Now, why does the audio spectrum in ch10/5.htm not have >> >a negative part? >> >> >-- glen >> >> Hi Glen, >> It would certainly be useful to show the negative frequencies in this >> figure. �Thanks for the suggestion-- I'll add it to my list for the next >> edition. >> Steve > >us old analog guys have learned that perspective using old fashioned >heterodyne spectrum analyzers. If you tune below the zero, you can >actually see the negative frequencies, mirror images of the positive >ones...sure enough they are there... :-) > >MarkHi Mark, Neat. I think I tried that decades ago, but I forget what it was that I saw on the old fashioned spectrum analyzer. It seems like you've verified that Steve Smith was not just "making up" this whole notion of negative frequencies. [-Rick-]

Reply by ●June 12, 20082008-06-12

Rick Lyons wrote:> On Wed, 11 Jun 2008 08:58:47 -0700 (PDT), Mark <makolber@yahoo.com> > wrote: > >> On Jun 10, 12:12 pm, "SteveSmith" <Steve.Smi...@SpectrumSDI.com> >> wrote: >>>> Now, why does the audio spectrum in ch10/5.htm not have >>>> a negative part? >>>> -- glen >>> Hi Glen, >>> It would certainly be useful to show the negative frequencies in this >>> figure. Thanks for the suggestion-- I'll add it to my list for the next >>> edition. >>> Steve >> us old analog guys have learned that perspective using old fashioned >> heterodyne spectrum analyzers. If you tune below the zero, you can >> actually see the negative frequencies, mirror images of the positive >> ones...sure enough they are there... :-) >> >> Mark > > Hi Mark, > Neat. I think I tried that decades ago, but I forget > what it was that I saw on the old fashioned spectrum > analyzer. It seems like you've verified that Steve Smith > was not just "making up" this whole notion of negative > frequencies.There's no need to assume negative frequencies for explaining what one sees on the spectrum analyzer, but as with exponential forms for sine and cosine, it is a convenient thing to do. Elevating a convenient construct to an immutable reality can occasionally lead one far astray. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������

Reply by ●June 12, 20082008-06-12

On 12 Jun, 14:28, Rick Lyons <R.Lyons@_BOGUS_ieee.org> wrote:> On Wed, 11 Jun 2008 08:58:47 -0700 (PDT), Mark <makol...@yahoo.com> > wrote:> >us old analog guys have learned that perspective using old fashioned > >heterodyne spectrum analyzers. �If you tune below the zero, you can > >actually see the negative frequencies, mirror images of the positive > >ones...sure enough they are there... � :-) > > >Mark > > Hi Mark, > � Neat. �I think I tried that decades ago, but I forget > what it was that I saw on the old fashioned spectrum > analyzer. � It seems like you've verified that Steve Smith > was not just "making up" this whole notion of negative > frequencies.What about AM? What's the point of SSB AM without the concept of 'negative frequency'? No need to play tricks with the novices minds by 'tuning the spectrum analyzer to -5 Hz' when a trivial mixer will show the effect. Once you see the output of that analog mixer with an extra sideband below the carrier, you understand that something 'weird' is going on. Negative frequencies are there to help you explain what is happening and you avoid the hurdle of trying tho understand what it means to 'tune a reciever to negative frequency'. Rune