Hello All, The classical modulation scheme is defined as, x(n)*cos(w_0*n) <-> 0.5*[X(w+w_0) + X(w-w_0)] - eq(1) Similarly, text books also define frequency shifting as, x(n)*exp(j*w_0*n) <-> X(w-w_0) - eq(2) It appears to me that scheme in eq(2) is much cleaner way of modulating a signal than scheme in eq(1). Second scheme requires complex multiplication in time while first scheme requires some additional manipulation. So, I am wondering why eq(1) is normally defined as a standard modulation method. _____________________________ Posted through www.DSPRelated.com
modulation scheme
Started by ●July 26, 2014
Reply by ●July 26, 20142014-07-26
In your eq.(1), the result of the modulation is
a real-valued signal while eq.(2) gives a
complex-valued signal. The identity
cos(theta) = 0.5*[ e^{j theta} + e^{-j theta} ]
relates the two notions.
Reply by ●July 26, 20142014-07-26
On Sat, 26 Jul 2014 01:44:47 -0500, SBR123 wrote:> Hello All, > > The classical modulation scheme is defined as, > > x(n)*cos(w_0*n) <-> 0.5*[X(w+w_0) + X(w-w_0)] - eq(1)That is double sideband modulation, which is neither classical nor very good. Perhaps you are thinking of amplitude modulation, which would be (1 + x(n)) * cos(w_0 * n) assuming that x(n) is restricted to the interval (-1, +1)?> > Similarly, text books also define frequency shifting as, > > x(n)*exp(j*w_0*n) <-> X(w-w_0) - eq(2) > > > It appears to me that scheme in eq(2) is much cleaner way of modulating > a signal than scheme in eq(1).Well, it certainly would be if only we could figure out how to get those damned imaginary numbers to actually make an antenna do something. Usually, by the time you translate things to voltages on a wire you _really_ want to have everything real.> Second scheme requires complex > multiplication in time while first scheme requires some additional > manipulation. > > So, I am wondering why eq(1) is normally defined as a standard > modulation method.(a), it isn't, (b), if you're thinking AM, it is no longer a very common modulation method, and (c), AM was conceived and executed because it's an EASY modulation method with 1920's technology. You can make a decent AM transmitter with three to five vacuum tubes (MOPA RF section using two tubes, plus a two-tube audio preamp/final amp stage in class A, or a three-tube audio preamp/final amp stage in class B or AB). You can make a workable AM receiver with just one tube, or with a diode and a really good set of earphones -- a table-top set in the 1920's that would be considered "nice" may have had just three or four tubes, and with two tubes in the receiver you could hear shortwave AM from around the world. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com
Reply by ●July 27, 20142014-07-27
Thank you very much, Mr. Dvsarvate & Mr. Wescott, I think I get an idea but still not yet fluent with modulation, transmission etc. When I get there, I will come back on this question _____________________________ Posted through www.DSPRelated.com
Reply by ●July 28, 20142014-07-28
On Sat, 26 Jul 2014 22:24:44 -0500, "SBR123" <100967@dsprelated> wrote:>Thank you very much, Mr. Dvsarvate & Mr. Wescott, > >I think I get an idea but still not yet fluent with modulation, >transmission etc. >When I get there, I will come back on this questionHello Mr. SBR123, You might have a look at: http://www.cypress.com/?docID=41217 [-Rick-]> >_____________________________ >Posted through www.DSPRelated.com
Reply by ●July 28, 20142014-07-28
On Sat, 26 Jul 2014 18:03:39 -0500, Tim Wescott <tim@seemywebsite.really> wrote:>On Sat, 26 Jul 2014 01:44:47 -0500, SBR123 wrote: > >> Hello All, >> >> The classical modulation scheme is defined as, >> >> x(n)*cos(w_0*n) <-> 0.5*[X(w+w_0) + X(w-w_0)] - eq(1) > >That is double sideband modulation, which is neither classical nor very >good. > >Perhaps you are thinking of amplitude modulation, which would be > >(1 + x(n)) * cos(w_0 * n) > >assuming that x(n) is restricted to the interval (-1, +1)? > >> >> Similarly, text books also define frequency shifting as, >> >> x(n)*exp(j*w_0*n) <-> X(w-w_0) - eq(2) >> >> >> It appears to me that scheme in eq(2) is much cleaner way of modulating >> a signal than scheme in eq(1). > >Well, it certainly would be if only we could figure out how to get those >damned imaginary numbers to actually make an antenna do something. >Usually, by the time you translate things to voltages on a wire you >_really_ want to have everything real.Hi Tim, Cute. But actually, you've touched upon a critically important topic here. Now and then I teach a DSP class and one part of my class covers the basics of quadrature (I/Q) processing with signal samples having both real and imaginary parts. For example, an analog complex down-conversion followed by two analog lowpass filters driving two A/D converters. I show some sort of block diagram on the screen and then show some algebraic equations that describe the mathematical relationships of various signals in the block diagram. The equations always contain the 'j-operator' signifying a complex signal somewhere in the block diagram. I then go through my standard spiel suggesting that the students do NOT think of the 'j' symbol as a number, but rather think of it as a "operation" performed on a number to generate a new number. Invariably, a thoughtful student asks, "How do we implement the j-operator in hardware?" Tim, ...that question is not at all silly! And it's a question whose answer is not given enough attention in the standard college DSP textbooks.>> Second scheme requires complex >> multiplication in time while first scheme requires some additional >> manipulation. >> >> So, I am wondering why eq(1) is normally defined as a standard >> modulation method. > >(a), it isn't, (b), if you're thinking AM, it is no longer a very common >modulation method,Whoa. Wait. I'm listenin' to AM radio right now in my office!>and (c), AM was conceived and executed because it's an >EASY modulation method with 1920's technology.Standard broadcast AM radio has some important shortcomings. Its RF bandwidth is twice that of the information signal's bandwidth, AM broadcasts are quite susceptable to RF noise between the transmitter and the AM receiver, and (if I recall correctly) only one quarter of the transmitter's power goes toward radiating a single sideband of the transmitted RF. Given all that, broadcast AM radio has one overwhelming quality. The AM receivers were simple and affordable! [-Rick-]
Reply by ●July 28, 20142014-07-28
Rick Lyons <R.Lyons@_bogus_ieee.org> wrote: (snip, someone wrote)>>Well, it certainly would be if only we could figure out how to get those >>damned imaginary numbers to actually make an antenna do something. >>Usually, by the time you translate things to voltages on a wire you >>_really_ want to have everything real.(snip)>> (a), it isn't, (b), if you're thinking AM, it is no longer a >> very common modulation method,> Whoa. Wait. I'm listenin' to AM radio right now in my > office!I most often listen to AM for sports and traffic reports. There is some music there, but FM stations have more. Maybe, though, when far away from big cities, AM stations also reach out farther.>>and (c), AM was conceived and executed because it's an >>EASY modulation method with 1920's technology.> Standard broadcast AM radio has some important shortcomings. > Its RF bandwidth is twice that of the information signal's > bandwidth, AM broadcasts are quite susceptable to > RF noise between the transmitter and the AM receiver, and > (if I recall correctly) only one quarter of the transmitter's > power goes toward radiating a single sideband of the > transmitted RF.OK, but there are two sidebands, so half the power is in the sidebands, assuming the usual demodulator. Reminds me that for vistigial sideband (analog TV), since one sideband has reduced bandwidth, and both sidebands go into the demodulator, the receiver has to correct for the frequency response of the sum. Higher frequencies have half the amplitude of the lower ones.> Given all that, broadcast AM radio has one overwhelming > quality. The AM receivers were simple and affordable!But now FM radios, using modern analog ICs, are pretty simple and affordable, too. And if not, go to a thrift store and buy a used one. Seems to me the main advantage now is that the lower AM frequencies can reach farther, especially at night. We now have HD radio, with digital subcarriers on top of the usual AM and FM stations, though I don't know anyone with a receiver for them. -- glen
