Hi all, What is quadrature sampling?It says that sampling frequency be greater than signal BW.Does it not violate Nyquist criterion?What are its applications? Regards. Raghavendra

# What is quadrature sampling

Started by ●July 7, 2003

Reply by ●July 7, 20032003-07-07

"Raghavendra" <raghurash@rediffmail.com> wrote in message news:1776d39.0307070436.78b1ceeb@posting.google.com...> Hi all, > What is quadrature sampling?It says that sampling frequency be greaterAs I understand the term, it means that the sampling freq is exactly 4 times the IF frequency. Usually the BW of the signal is smaller than fs/2. By picking this sampling freq, it allows you to perform quadrature mixing to extract I,Q in a very easy fashion (multiply the signal with only a series of 1s, -1s and zeros). Cheers Bhaskar> than signal BW.Does it not violate Nyquist criterion?What are its > applications? > Regards. > Raghavendra

Reply by ●July 7, 20032003-07-07

In article <becb8p$3khtp$1@ID-82263.news.dfncis.de>, bhaskart@deja.com says...> "Raghavendra" <raghurash@rediffmail.com> wrote in message > news:1776d39.0307070436.78b1ceeb@posting.google.com... > > Hi all, > > What is quadrature sampling?It says that sampling frequency be greater > > As I understand the term, it means that the sampling freq is exactly 4 times > the IF frequency. Usually the BW of the signal is smaller than fs/2. > By picking this sampling freq, it allows you to perform quadrature mixing to > extract I,Q in a very easy fashion (multiply the signal with only a series > of 1s, -1s and zeros). > > Cheers > Bhaskar > > > than signal BW.Does it not violate Nyquist criterion?What are its > > applications? > > Regards. > > Raghavendra > > >heres an angle: quad sampling exploits the mathematical property that comparing a test signal (the information carrying signal) to a reference sin wave can be done independently to comparing it to a reference cosine wave. ie you can extract 2 bits of information from a single symbols width of signal by comparing it to 2 different reference points (sin and cos) at the receiving end. So for example, you quite literally extract symbols at (eg) 1200 baud, but you end up with a bit rate of 2400 bps. At the transmitting end, you start with a pair of bits (pull them out fo the incoming stream in pairs), apply one to the sin reference, apply one to the cos reference, then you add the two signals for transmission. What you end up with after this addition is just a single sinusoid. Its strange to imagine that 2 bits can be extracted from it. At the receiving end, to extract the I channel bit, the signal is compared to the cos reference wave, then to extract the Q channel bit, the same wave is compared to the sin reference wave. The curious part is that the 2 data bits can vary independently so that their combination for transmission will not affect extraction of the 'other' bit at the receiving end. Spiro -- http://www.mobilecomms.com.au http://www.nexiondata.com

Reply by ●July 7, 20032003-07-07

"Spiro" <HOUSTON_we_have_a_problem@127.0.0.1> wrote in message news:MPG.1974a224e288cf76989691@61.9.128.12...> In article <becb8p$3khtp$1@ID-82263.news.dfncis.de>, bhaskart@deja.com > says... > > "Raghavendra" <raghurash@rediffmail.com> wrote in message > > news:1776d39.0307070436.78b1ceeb@posting.google.com... > > > Hi all, > > > What is quadrature sampling?It says that sampling frequency be greater > > > > As I understand the term, it means that the sampling freq is exactly 4times> > the IF frequency. Usually the BW of the signal is smaller than fs/2. > > By picking this sampling freq, it allows you to perform quadraturemixing to> > extract I,Q in a very easy fashion (multiply the signal with only aseries> > of 1s, -1s and zeros).(snip)> heres an angle: > > quad sampling exploits the mathematical property that comparing a test > signal (the information carrying signal) to a reference sin wave can be > done independently to comparing it to a reference cosine wave. ie you > can extract 2 bits of information from a single symbols width of signal > by comparing it to 2 different reference points (sin and cos) at the > receiving end. So for example, you quite literally extract symbols at > (eg) 1200 baud, but you end up with a bit rate of 2400 bps. > > At the transmitting end, you start with a pair of bits (pull them out fo > the incoming stream in pairs), apply one to the sin reference, apply one > to the cos reference, then you add the two signals for transmission. > What you end up with after this addition is just a single sinusoid. Its > strange to imagine that 2 bits can be extracted from it. At the > receiving end, to extract the I channel bit, the signal is compared to > the cos reference wave, then to extract the Q channel bit, the same wave > is compared to the sin reference wave. The curious part is that the 2 > data bits can vary independently so that their combination for > transmission will not affect extraction of the 'other' bit at the > receiving end.It sounds pretty much the same as extracting both the signal and its derivative, which you can also do at half the Nyquist rate. As long as you extract the appropriate amount of information, Nyquist doesn't really care how you do it. -- glen

Reply by ●July 7, 20032003-07-07

On Tue, 08 Jul 2003 00:00:07 GMT, "Glen Herrmannsfeldt" <gah@ugcs.caltech.edu> wrote:> >"Spiro" <HOUSTON_we_have_a_problem@127.0.0.1> wrote in message >news:MPG.1974a224e288cf76989691@61.9.128.12... >> In article <becb8p$3khtp$1@ID-82263.news.dfncis.de>, bhaskart@deja.com >> says... >> > "Raghavendra" <raghurash@rediffmail.com> wrote in message >> > news:1776d39.0307070436.78b1ceeb@posting.google.com... >> > > Hi all, >> > > What is quadrature sampling?It says that sampling frequency be greater >> > >> > As I understand the term, it means that the sampling freq is exactly 4 >times >> > the IF frequency. Usually the BW of the signal is smaller than fs/2. >> > By picking this sampling freq, it allows you to perform quadrature >mixing to >> > extract I,Q in a very easy fashion (multiply the signal with only a >series >> > of 1s, -1s and zeros). > >(snip) > >> heres an angle: >> >> quad sampling exploits the mathematical property that comparing a test >> signal (the information carrying signal) to a reference sin wave can be >> done independently to comparing it to a reference cosine wave. ie you >> can extract 2 bits of information from a single symbols width of signal >> by comparing it to 2 different reference points (sin and cos) at the >> receiving end. So for example, you quite literally extract symbols at >> (eg) 1200 baud, but you end up with a bit rate of 2400 bps. >> >> At the transmitting end, you start with a pair of bits (pull them out fo >> the incoming stream in pairs), apply one to the sin reference, apply one >> to the cos reference, then you add the two signals for transmission. >> What you end up with after this addition is just a single sinusoid. Its >> strange to imagine that 2 bits can be extracted from it. At the >> receiving end, to extract the I channel bit, the signal is compared to >> the cos reference wave, then to extract the Q channel bit, the same wave >> is compared to the sin reference wave. The curious part is that the 2 >> data bits can vary independently so that their combination for >> transmission will not affect extraction of the 'other' bit at the >> receiving end. > >It sounds pretty much the same as extracting both the signal and its >derivative, which you can also do at half the Nyquist rate. As long as you >extract the appropriate amount of information, Nyquist doesn't really care >how you do it. > >-- glenYes, and lately I've seen Julius and a few folks use the term "innovation rate" in papers rather than sample rate to clarify this distinction (at least I think that's the intent). This touches on the real or complex sample debate that we have here occasionally as well... Eric Jacobsen Minister of Algorithms, Intel Corp. My opinions may not be Intel's opinions. http://www.ericjacobsen.org

Reply by ●July 7, 20032003-07-07

Raghavendra wrote:> > Hi all, > What is quadrature sampling?It says that sampling frequency be greater > than signal BW.Does it not violate Nyquist criterion?What are its > applications? > Regards. > RaghavendraHello Raghavendra, The Fourier transform of a real signal g(t) is a complex function of radian frequency, G(w) = Gr(w) + i*Gi(w). G(w) has the property that its real part is an even function, i.e., Gr(w) = Gr(-w), and that its imaginary part is an odd function, i.e., Gi(w) = -Gi(-w). This means that you can construct the entire signal from just one half of the bandwidth. For example, if g(t) had a bandwidth B, then, even though G(w) would have non-zero components from -2*pi*B to +2*pi*B, only half of that frequency range is unique. So why carry this redundant information around? In quadrature demodulation, you take the signal spectrum from 0 to 2*pi*B (or, more generally, from 2*pi*(fc - B/2) to 2*pi*(fc + B/2), i.e., some bandwidth around a carrier fc) and shift it down so that it is centered around 0 radians/second. This means that, since this new signal only extends to B/2 Hz, we can halve the sampling rate and not violate the Nyquist criterion. However, this also means that the resulting time-domain signal is no longer real (because the symmetry between positive and negative frequencies is no longer guaranteed). That's the entire idea behind quadrature modulation and demodulation. A quadrature demodulator takes a real signal and moves half of it down to baseband (i.e., around 0 Hz), making it a complex signal. A quadrature modulator does the inverse. -- % Randy Yates % "...the answer lies within your soul %% Fuquay-Varina, NC % 'cause no one knows which side %%% 919-577-9882 % the coin will fall." %%%% <yates@ieee.org> % 'Big Wheels', *Out of the Blue*, ELO http://home.earthlink.net/~yatescr

Reply by ●July 7, 20032003-07-07

A couple of extra points: Randy Yates wrote:> [...] > In quadrature demodulation, you take the signal spectrum from 0 to > 2*pi*B (or, more generally, from 2*pi*(fc - B/2) to 2*pi*(fc + B/2), > i.e., some bandwidth around a carrier fc) and shift it down so that it > is centered around 0 radians/second.I should also add that you throw away the signal spectrum from -2*pi*B to 0. I must inform you that you've been lied to all your life with this Nyquist criterion thing. It says that sampling at a rate of Fs provides a bandwidth of Fs/2. This is a lie! Sampling at a rate of Fs provides a bandwidth of Fs, that is, from -Fs/2 to +Fs/2! The problem is that real signals contain no useful information from -Fs/2 to 0, but that's not the sampling process's fault! It does indeed provide you with a bandwidth of Fs, and a quadrature demodulator is a device that allows you to make use of this full bandwidth. -- % Randy Yates % "...the answer lies within your soul %% Fuquay-Varina, NC % 'cause no one knows which side %%% 919-577-9882 % the coin will fall." %%%% <yates@ieee.org> % 'Big Wheels', *Out of the Blue*, ELO http://home.earthlink.net/~yatescr

Reply by ●July 7, 20032003-07-07

"Randy Yates" <yates@ieee.org> wrote in message news:3F0A2847.BA306D6C@ieee.org...> A couple of extra points: > > Randy Yates wrote: > > [...] > > In quadrature demodulation, you take the signal spectrum from 0 to > > 2*pi*B (or, more generally, from 2*pi*(fc - B/2) to 2*pi*(fc + B/2), > > i.e., some bandwidth around a carrier fc) and shift it down so that it > > is centered around 0 radians/second. > > I should also add that you throw away the signal spectrum from -2*pi*B to0.> > I must inform you that you've been lied to all your life with this > Nyquist criterion thing. It says that sampling at a rate of Fs provides > a bandwidth of Fs/2. This is a lie! Sampling at a rate of Fs provides > a bandwidth of Fs, that is, from -Fs/2 to +Fs/2! The problem is that > real signals contain no useful information from -Fs/2 to 0, but that's > not the sampling process's fault! It does indeed provide you with a > bandwidth of Fs, and a quadrature demodulator is a device that allows > you to make use of this full bandwidth.Well, you can do it that way. The way I like to think of it is that, for a signal of length T, there are T Fs unknows, and T Fs equations are needed to solve for them. Sampling the real signal at the appropriate number of points works, sampling the signal and its derivative at half that points works, and sampling the appropriate complex function at half the number of points works. The sample data must be linearly independent which restricts it a little bit. (Sampling the value, first, and second derivative at one third the number of points works, too, and doesn't have any connection to complex math.) -- glen

Reply by ●July 8, 20032003-07-08

"Glen Herrmannsfeldt" <gah@ugcs.caltech.edu> wrote in message news:<T5qOa.2362$N7.679@sccrnsc03>...> "Randy Yates" <yates@ieee.org> wrote in message > news:3F0A2847.BA306D6C@ieee.org... > > A couple of extra points: > > > > Randy Yates wrote: > > > [...] > > > In quadrature demodulation, you take the signal spectrum from 0 to > > > 2*pi*B (or, more generally, from 2*pi*(fc - B/2) to 2*pi*(fc + B/2), > > > i.e., some bandwidth around a carrier fc) and shift it down so that it > > > is centered around 0 radians/second. > > > > I should also add that you throw away the signal spectrum from -2*pi*B to > 0. > > > > I must inform you that you've been lied to all your life with this > > Nyquist criterion thing. It says that sampling at a rate of Fs provides > > a bandwidth of Fs/2. This is a lie! Sampling at a rate of Fs provides > > a bandwidth of Fs, that is, from -Fs/2 to +Fs/2! The problem is that > > real signals contain no useful information from -Fs/2 to 0, but that's > > not the sampling process's fault! It does indeed provide you with a > > bandwidth of Fs, and a quadrature demodulator is a device that allows > > you to make use of this full bandwidth. > > Well, you can do it that way. > > The way I like to think of it is that, for a signal of length T, there are T > Fs unknows, and T Fs equations are needed to solve for them. Sampling the > real signal at the appropriate number of points works, sampling the signal > and its derivative at half that points works, and sampling the appropriate > complex function at half the number of points works. The sample data must > be linearly independent which restricts it a little bit. > > (Sampling the value, first, and second derivative at one third the number > of points works, too, and doesn't have any connection to complex math.)Glen, I don't follow you. What are the T Fs equations? I also don't see how the number of equations required to solve for a certain number of unknowns has a relationship to the spectrum of a signal.

Reply by ●July 8, 20032003-07-08

Randy Yates wrote:>...> > I also don't see how the number of equations required to solve > for a certain number of unknowns has a relationship to the > spectrum of a signal.That part is easy. Given one period T of a periodic function bandlimited so that no frequency higher than f exists in it, then its spectrum can consist of no more than f*T sines and an equal number of cosines. We know what they are -- harmonics of sin(2*pi/T) and cos(2*pi/T). Determining the spectrum consists of solving for 2*f*T amplitudes, so 2*f*T measurements are needed. The signal and its first (2*f*T - 1)th derivatives at t = zero, for example, suffice. When the measurements are spread uniformly in time and consist of the requisite number either of the waveform alone or the waveform and its derivative, a Fourier transform becomes a convenient way to do the computation. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������