Complex Input
in [DSP]
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From: Eric Jacobsen on 13 Nov 2009 21:36 On 11/13/2009 4:53 PM, Jerry Avins wrote: > kadirerturk wrote: >> On 5 Kasım, 20:15, Jerry Avins <j...(a)ieee.org> wrote: >>> jasonkee111 wrote: >>>> Hi. i read a lot of article focusing on real input. In physical world, >>>> does the input in complex form? If exist, where it comes from and >>>> what is >>>> the application? Or actually it is just theory only? >>> Whatever you can measure is real. Complex arithmetic is a simplified way >>> to deal with complicated mathematics. It isn't "only theory". It deals >>> with actual things. >>> >>> Jerry >>> -- >>> Engineering is the art of making what you want from things you can get. >>> ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ >> >> Actually all events ( I mean data) has two part. One is real which we >> can measure and other is imaginary which we can not measure. The >> imaginary side always exist and it can be easily prove by simple >> mathematics. You can obtain imaginary side of any data using by >> Hilbert Transform of real side of that data. >> >> Kadir > > How much does it weigh? > > Jerry Depends on whether it's the Heaviside or not. -- Eric Jacobsen Minister of Algorithms Abineau Communications http://www.abineau.com
From: Phil O. Sopher on 14 Nov 2009 06:06 "jasonkee111" <jasonkee111(a)gmail.com> wrote in message news:g_WdnUsR7unJjG7XnZ2dnUVZ_gOdnZ2d(a)giganews.com... > Hi. i read a lot of article focusing on real input. In physical world, > does the input in complex form? If exist, where it comes from and what is > the application? Or actually it is just theory only? We use Complex Numbers to represent sinusoids (should that be "cisoids"?) that have both a magnitude and also a phase relationship. Why do we do this? Well, we don't have to, because we can do everything with sin(wt+a) and cos(wt+a), but when we differentiate, we change from sin to cos and sometimes the sign changes (cos to sin) and sometimes it doesn't (sin to cos). What a mess of rules to remember and be inherently error-prone. However, if you wish, you can work in those terms with what I assume you will consider to be real input. If we could represent everything by an exponential, e^wt, then the differential is always w.e^wt which is easier to deal with. It all stems from e^jwt = cos(wt) + j.sin(wt). You need to have a grounding in that, but I ain't prepared to give you one off the cuff. So, it is up to you as to whether you consider complex form as a proper (carefully not using the word, "real") representation or just a theoretical one. Like a lot of mathematics, you have to advance a little bit in your theory to find that, with it under your belt, life is suddenly so much easier. (Just like vectors being easier to deal with than 3-dimensional geometry)
From: John Monro on 14 Nov 2009 07:34 jasonkee111 wrote: > Hi. i read a lot of article focusing on real input. In physical world, > does the input in complex form? If exist, where it comes from and what is > the application? Or actually it is just theory only? > > Thanks > > Hi Jasonkee111, Actual, physical signals in complex form do exist and are commonly available at the back of high-class communications receivers. These receivers have two actual BNC connectors marked I (in-phase) and Q (quadrature phase). For each sinusoidal component in the I signal there is a corresponding equal-amplitude sinusoidal component present in the Q signal, but offset in phase by 90 degrees. Having a complex signal available makes subsequent analog or digital signal processing simpler by suppressing the negative-frequency component. With on negative frequencies present signal can be shifted up or down in frequency without the complication of having a 'image' signal being produced. It is an interesting contradiction that the signals with the simplest spectrum(positive frequencies or negative frequencies only) require two signal wires (I and Q) while more complicated signals with mirror-image positive and negative-frequency components require only one signal wire (plus earth in all cases). Regards, John actual,
From: Jerry Avins on 14 Nov 2009 08:43 Phil O. Sopher wrote: > "jasonkee111" <jasonkee111(a)gmail.com> wrote in message > news:g_WdnUsR7unJjG7XnZ2dnUVZ_gOdnZ2d(a)giganews.com... >> Hi. i read a lot of article focusing on real input. In physical world, >> does the input in complex form? If exist, where it comes from and what is >> the application? Or actually it is just theory only? > > We use Complex Numbers to represent sinusoids (should that be > "cisoids"?) that have both a magnitude and also a phase relationship. > > Why do we do this? > > Well, we don't have to, because we can do everything with sin(wt+a) > and cos(wt+a), but when we differentiate, we change from sin to cos > and sometimes the sign changes (cos to sin) and sometimes it > doesn't (sin to cos). What a mess of rules to remember and be > inherently error-prone. > > However, if you wish, you can work in those terms with what > I assume you will consider to be real input. > > If we could represent everything by an exponential, e^wt, then the > differential is always w.e^wt which is easier to deal with. > > It all stems from e^jwt = cos(wt) + j.sin(wt). > > You need to have a grounding in that, but I ain't prepared to > give you one off the cuff. > > So, it is up to you as to whether you consider complex form as a > proper (carefully not using the word, "real") representation or just > a theoretical one. > > Like a lot of mathematics, you have to advance a little bit in your > theory to find that, with it under your belt, life is suddenly > so much easier. (Just like vectors being easier to deal with than > 3-dimensional geometry) Excellently put! The use of exponentials introduces the need for negative frequency, but that's a small price to pay. Unfortunate intellectual baggage comes from developing the mindset that rather than a small price, negative frequency is a fundamental part of the structure of the universe. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
From: Jerry Avins on 14 Nov 2009 08:50
John Monro wrote: > jasonkee111 wrote: >> Hi. i read a lot of article focusing on real input. In physical world, >> does the input in complex form? If exist, where it comes from and >> what is >> the application? Or actually it is just theory only? >> >> Thanks >> >> > > Hi Jasonkee111, > > Actual, physical signals in complex form do exist and are commonly > available at the back of high-class communications receivers. No. What is available there are two real signals, one representing I, the other Q. > These receivers have two actual BNC connectors marked I (in-phase) and Q > (quadrature phase). For each sinusoidal component in the I signal there > is a corresponding equal-amplitude sinusoidal component present in the Q > signal, but offset in phase by 90 degrees. > > Having a complex signal available makes subsequent analog or digital > signal processing simpler by suppressing the negative-frequency component. > > With on negative frequencies present signal can be shifted up or down in > frequency without the complication of having a 'image' signal being > produced. > > It is an interesting contradiction that the signals with the simplest > spectrum(positive frequencies or negative frequencies only) require two > signal wires (I and Q) while more complicated signals with mirror-image > positive and negative-frequency components require only one signal wire > (plus earth in all cases). This is an excellent example of mathematical simplicity masking reality. Tell me, John, Which leg of a two-phase 220VAC power line gives imaginary shocks? Jerry -- Engineering is the art of making what you want from things you can get. ����������������������������������������������������������������������� |