I was thinking of how the j operator is implemented in hardware. this is with respect to complex down conversion and assumes the A/D's for each I and Q channels are present (this is NOT quadrature sampling with digital downconversion). the "j" operator is a mere phase shift of 90 deg in the counterclockwise direction. how is the phase shift introduced ? CORDIC ? thanks
j operator in hardware
Started by ●September 3, 2011
Reply by ●September 3, 20112011-09-03
On Sat, 03 Sep 2011 15:53:25 -0700, Krishnakumar Gurumoorthy wrote:> I was thinking of how the j operator is implemented in hardware. this is > with respect to complex down conversion and assumes the A/D's for each I > and Q channels are present (this is NOT quadrature sampling with digital > downconversion). > > the "j" operator is a mere phase shift of 90 deg in the counterclockwise > direction. how is the phase shift introduced ? CORDIC ?When you get to this level of detail, it is dangerous to think that you are dealing with complex numbers -- you aren't. You're dealing with channels that were demodulated in quadrature. You can do _almost_ all of the math assuming that you're dealing with complex numbers, but it's still not the same thing. The way that I/Q downconversion works is that you have a pair of mixers, each fed by a local oscillator that is shifted 90 degrees from the one feeding the other. So you would get your 'inphase' channel by mixing your incoming signal with a mixer that's fed in phase ('cos wt') with the LO, and you would get your 'quadrature' channel by mixing your incoming signal with a mixer that's fed in quadrature phase ('sin wt') with the LO. -- www.wescottdesign.com
Reply by ●September 3, 20112011-09-03
On Sep 3, 6:53�pm, Krishnakumar Gurumoorthy <krish...@gmail.com> wrote:> I was thinking of how the j operator is implemented in hardware. this > is with respect to complex down conversion and assumes the A/D's for > each I and Q channels are present (this is NOT quadrature sampling > with digital downconversion). > > the "j" operator is a mere phase shift of 90 deg in the > counterclockwise direction. how is the phase shift introduced ? > CORDIC ? > > thanks(a, b) --> (-b, a), maybe?
Reply by ●September 3, 20112011-09-03
Krishnakumar Gurumoorthy wrote:> I was thinking of how the j operator is implemented in hardware. this > is with respect to complex down conversion and assumes the A/D's for > each I and Q channels are present (this is NOT quadrature sampling > with digital downconversion). > > the "j" operator is a mere phase shift of 90 deg in the > counterclockwise direction. how is the phase shift introduced ? > CORDIC ? > > thanks
Reply by ●September 4, 20112011-09-04
> > >Krishnakumar Gurumoorthy wrote:.. and assumes the A/D's for each I and Q channels are present ... .. how is the phase shift introduced ?>> CORDIC ? >> >> thanks >In a "direct conversion" (DC) radio receiver, the "j" operator can be literally implemented in hardware. It works as follows: - get radio frequency signal from the antenna - generate a local oscillator sine wave with twice the frequency - divide by two with a digital divider that gives two phases for the local oscillator signal. Those look as follows: IQ_I = 0011001100110011... IQ_Q = 0110011001100110... - Use them to drive reversing analog switches (mixers) on the analog radio frequency signal. Those will flip the sign at a pace that matches the channel frequency, one switching cycle per sine wave cycle at carrier frequency. - low-pass filter the outputs. The carrier translates to 0 Hz. - A/D conversion of both branches => two real-valued I and Q signals. This is a so-called "double frequency VCO" variant of the DC receiver that's popular in cellular mobiles, for example.
Reply by ●September 4, 20112011-09-04
On Sat, 3 Sep 2011 15:53:25 -0700 (PDT), Krishnakumar Gurumoorthy <krishk24@gmail.com> wrote:>I was thinking of how the j operator is implemented in hardware. this >is with respect to complex down conversion and assumes the A/D's for >each I and Q channels are present (this is NOT quadrature sampling >with digital downconversion). > >the "j" operator is a mere phase shift of 90 deg in the >counterclockwise direction. how is the phase shift introduced ? >CORDIC ? > >thanksThat's one way, if you mean multiplying a real signal by the sin and cos terms that one can achieve with a CORDIC. A DDS/NCO does the same thing. It's no different than in software. In software one keeps separate storage for the I and Q channels or the real and imaginary components of a complex number. Likewise in hardware they can be different paths and registers. Eric Jacobsen http://www.ericjacobsen.org http://www.dsprelated.com/blogs-1//Eric_Jacobsen.php
Reply by ●September 4, 20112011-09-04
On Sep 4, 11:30�am, eric.jacob...@ieee.org (Eric Jacobsen) wrote:> On Sat, 3 Sep 2011 15:53:25 -0700 (PDT), Krishnakumar Gurumoorthy > > <krish...@gmail.com> wrote: > >I was thinking of how the j operator is implemented in hardware. this > >is with respect to complex down conversion and assumes the A/D's for > >each I and Q channels are present (this is NOT quadrature sampling > >with digital downconversion). > > >the "j" operator is a mere phase shift of 90 deg in the > >counterclockwise direction. how is the phase shift introduced ? > >CORDIC ? > > >thanks > > That's one way, if you mean multiplying a real signal by the sin and > cos terms that one can achieve with a CORDIC. � A DDS/NCO does the > same thing. > > It's no different than in software. �In software one keeps separate > storage for the I and Q channels or the real and imaginary components > of a complex number. �Likewise in hardware they can be different paths > and registers. > > Eric Jacobsenhttp://www.ericjacobsen.orghttp://www.dsprelated.com/blogs-1//Eric_Jacobsen.phpWhen designing a chip with imaginary registers it's important to make sure the physical layout of the register is rotated 90 degrees. That way you are gauranteed to have orthogonal signals.
Reply by ●September 4, 20112011-09-04
On 09/04/2011 04:04 PM, Robert Adams wrote:> On Sep 4, 11:30 am, eric.jacob...@ieee.org (Eric Jacobsen) wrote: >> On Sat, 3 Sep 2011 15:53:25 -0700 (PDT), Krishnakumar Gurumoorthy >> >> <krish...@gmail.com> wrote: >>> I was thinking of how the j operator is implemented in hardware. this >>> is with respect to complex down conversion and assumes the A/D's for >>> each I and Q channels are present (this is NOT quadrature sampling >>> with digital downconversion). >> >>> the "j" operator is a mere phase shift of 90 deg in the >>> counterclockwise direction. how is the phase shift introduced ? >>> CORDIC ? >> >>> thanks >> >> That's one way, if you mean multiplying a real signal by the sin and >> cos terms that one can achieve with a CORDIC. A DDS/NCO does the >> same thing. >> >> It's no different than in software. In software one keeps separate >> storage for the I and Q channels or the real and imaginary components >> of a complex number. Likewise in hardware they can be different paths >> and registers. >> >> Eric Jacobsenhttp://www.ericjacobsen.orghttp://www.dsprelated.com/blogs-1//Eric_Jacobsen.php > When designing a chip with imaginary registers it's important to make > sure the physical layout of the register is rotated 90 degrees. That > way you are gauranteed to have orthogonal signals.And use a high-quality protractor when you rotate, otherwise you'll phase and amplitude imbalance! -- Randy Yates % "Watching all the days go by... Digital Signal Labs % Who are you and who am I?" mailto://yates@ieee.org % 'Mission (A World Record)', http://www.digitalsignallabs.com % *A New World Record*, ELO
Reply by ●September 4, 20112011-09-04
On 9/4/2011 7:01 PM, Randy Yates wrote:> On 09/04/2011 04:04 PM, Robert Adams wrote: >> On Sep 4, 11:30 am, eric.jacob...@ieee.org (Eric Jacobsen) wrote: >>> On Sat, 3 Sep 2011 15:53:25 -0700 (PDT), Krishnakumar Gurumoorthy >>> >>> <krish...@gmail.com> wrote: >>>> I was thinking of how the j operator is implemented in hardware. this >>>> is with respect to complex down conversion and assumes the A/D's for >>>> each I and Q channels are present (this is NOT quadrature sampling >>>> with digital downconversion). >>> >>>> the "j" operator is a mere phase shift of 90 deg in the >>>> counterclockwise direction. how is the phase shift introduced ? >>>> CORDIC ? >>> >>>> thanks >>> >>> That's one way, if you mean multiplying a real signal by the sin and >>> cos terms that one can achieve with a CORDIC. A DDS/NCO does the >>> same thing. >>> >>> It's no different than in software. In software one keeps separate >>> storage for the I and Q channels or the real and imaginary components >>> of a complex number. Likewise in hardware they can be different paths >>> and registers. >>> >>> Eric >>> Jacobsenhttp://www.ericjacobsen.orghttp://www.dsprelated.com/blogs-1//Eric_Jacobsen.php >>> >> When designing a chip with imaginary registers it's important to make >> sure the physical layout of the register is rotated 90 degrees. That >> way you are gauranteed to have orthogonal signals. > > And use a high-quality protractor when you rotate, otherwise you'll > phase and amplitude imbalance!All of which goes to show the imaginary numbers don't exist in the real (ahem!) world. But you all know that because I've told you before. Jerry -- Engineering is the art of making what you want from things you can get.
Reply by ●September 5, 20112011-09-05
On Sep 4, 10:53�am, Krishnakumar Gurumoorthy <krish...@gmail.com> wrote:> I was thinking of how the j operator is implemented in hardware. this > is with respect to complex down conversion and assumes the A/D's for > each I and Q channels are present (this is NOT quadrature sampling > with digital downconversion). > > the "j" operator is a mere phase shift of 90 deg in the > counterclockwise direction. how is the phase shift introduced ? > CORDIC ? > > thanksYou use an imaginary wire of course - duh!
