I am working on a tutorial about IQ modulation and demodulation. I have been thinking about this topic for a long time and have begun putting together some stuff. Here is an interactive page (exclusively for comp.dsp to look at :-) This shows the difference between an FFT that is stuffed with real data and an FFT that is stuffed with complex data. This has been real eye opening for me to see that the Nyquist sampling rate is blown away with complex data :-) http://www.fourier-series.com/fun/IQdemod.html
Difference between real data and complex FFT
Started by ●April 29, 2011
Reply by ●April 29, 20112011-04-29
On Apr 29, 10:24�am, brent <buleg...@columbus.rr.com> wrote:> I am working on a tutorial about IQ modulation and demodulation. �I > have been thinking about this topic for a long time and have begun > putting together some stuff. �Here is an interactive page (exclusively > for comp.dsp to look at :-) > > This shows the difference between an FFT that is stuffed with real > data and an FFT that is stuffed with complex data. �This has been real > eye opening for me to see that the Nyquist sampling rate is blown away > with complex data :-) > > http://www.fourier-series.com/fun/IQdemod.htmlBTW, this is preliminary stuff with no audio. It will be incorporated into larger tutorial later.
Reply by ●April 29, 20112011-04-29
On Apr 29, 10:24�am, brent <buleg...@columbus.rr.com> wrote:> I am working on a tutorial about IQ modulation and demodulation. �I > have been thinking about this topic for a long time and have begun > putting together some stuff. �Here is an interactive page (exclusively > for comp.dsp to look at :-) > > This shows the difference between an FFT that is stuffed with real > data and an FFT that is stuffed with complex data. �This has been real > eye opening for me to see that the Nyquist sampling rate is blown away > with complex data :-) > > http://www.fourier-series.com/fun/IQdemod.htmlThe sampling requirement is unchanged. You need something more than two samples per cycle of the highest frequency being sampled. It doesn't matter if those samples are sequential, in-phase and quadrature, function and derivative, or just about any other mathematically related pair. Jerry -- Engineering is the art of making what you want from things you can get.
Reply by ●April 29, 20112011-04-29
On Apr 29, 10:31�am, Jerry Avins <j...@ieee.org> wrote:> On Apr 29, 10:24�am, brent <buleg...@columbus.rr.com> wrote: > > > I am working on a tutorial about IQ modulation and demodulation. �I > > have been thinking about this topic for a long time and have begun > > putting together some stuff. �Here is an interactive page (exclusively > > for comp.dsp to look at :-) > > > This shows the difference between an FFT that is stuffed with real > > data and an FFT that is stuffed with complex data. �This has been real > > eye opening for me to see that the Nyquist sampling rate is blown away > > with complex data :-) > > >http://www.fourier-series.com/fun/IQdemod.html > > The sampling requirement is unchanged. You need something more than > two samples per cycle of the highest frequency being sampled. It > doesn't matter if those samples are sequential, in-phase and > quadrature, function and derivative, or just about any other > mathematically related pair. > > Jerry > -- > Engineering is the art of making what you want from things you can get.Depends how you look at it. Sampling rate is the same, but complex samples are applied to the FFT
Reply by ●April 29, 20112011-04-29
On Apr 29, 8:43�am, brent <buleg...@columbus.rr.com> wrote:> On Apr 29, 10:31�am, Jerry Avins <j...@ieee.org> wrote: > > > > > On Apr 29, 10:24�am, brent <buleg...@columbus.rr.com> wrote: > > > > I am working on a tutorial about IQ modulation and demodulation. �I > > > have been thinking about this topic for a long time and have begun > > > putting together some stuff. �Here is an interactive page (exclusively > > > for comp.dsp to look at :-) > > > > This shows the difference between an FFT that is stuffed with real > > > data and an FFT that is stuffed with complex data. �This has been real > > > eye opening for me to see that the Nyquist sampling rate is blown away > > > with complex data :-) > > > >http://www.fourier-series.com/fun/IQdemod.html > > > The sampling requirement is unchanged. You need something more than > > two samples per cycle of the highest frequency being sampled. It > > doesn't matter if those samples are sequential, in-phase and > > quadrature, function and derivative, or just about any other > > mathematically related pair. > > > Jerry > > -- > > Engineering is the art of making what you want from things you can get. > > Depends how you look at it. �Sampling rate is the same, but complex > samples are applied to the FFTSampling times are the same but two samples per time doubles the rate. Nyquist hasn't changed, you've just applied it to a two channel system. Dale B. Dalrymple
Reply by ●April 29, 20112011-04-29
On 04/29/2011 08:43 AM, brent wrote:> On Apr 29, 10:31 am, Jerry Avins<j...@ieee.org> wrote: >> On Apr 29, 10:24 am, brent<buleg...@columbus.rr.com> wrote: >> >>> I am working on a tutorial about IQ modulation and demodulation. I >>> have been thinking about this topic for a long time and have begun >>> putting together some stuff. Here is an interactive page (exclusively >>> for comp.dsp to look at :-) >> >>> This shows the difference between an FFT that is stuffed with real >>> data and an FFT that is stuffed with complex data. This has been real >>> eye opening for me to see that the Nyquist sampling rate is blown away >>> with complex data :-) >> >>> http://www.fourier-series.com/fun/IQdemod.html >> >> The sampling requirement is unchanged. You need something more than >> two samples per cycle of the highest frequency being sampled. It >> doesn't matter if those samples are sequential, in-phase and >> quadrature, function and derivative, or just about any other >> mathematically related pair. >> >> Jerry >> -- >> Engineering is the art of making what you want from things you can get. > > Depends how you look at it. Sampling rate is the same, but complex > samples are applied to the FFTYes, it does depend on how you look at it -- but if you don't look at it the way the math demands, you'll get it wrong. A complex number gives you twice as much information as a real number, so it counts as two samples. Sampling the signal and it's derivative, ditto. It's very simple, if you just hold your mouth right. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Do you need to implement control loops in software? "Applied Control Theory for Embedded Systems" was written for you. See details at http://www.wescottdesign.com/actfes/actfes.html
Reply by ●April 29, 20112011-04-29
On Apr 29, 8:43 am, brent <buleg...@columbus.rr.com> wrote:> On Apr 29, 10:31 am, Jerry Avins <j...@ieee.org> wrote: > > > > > On Apr 29, 10:24 am, brent <buleg...@columbus.rr.com> wrote: > > > > I am working on a tutorial about IQ modulation and demodulation. I > > > have been thinking about this topic for a long time and have begun > > > putting together some stuff. Here is an interactive page (exclusively > > > for comp.dsp to look at :-) > > > > This shows the difference between an FFT that is stuffed with real > > > data and an FFT that is stuffed with complex data. This has been real > > > eye opening for me to see that the Nyquist sampling rate is blown away > > > with complex data :-) > > > >http://www.fourier-series.com/fun/IQdemod.html > > > The sampling requirement is unchanged. You need something more than > > two samples per cycle of the highest frequency being sampled. It > > doesn't matter if those samples are sequential, in-phase and > > quadrature, function and derivative, or just about any other > > mathematically related pair. > > > Jerry > > -- > > Engineering is the art of making what you want from things you can get. > > Depends how you look at it. Sampling rate is the same, but complex > samples are applied to the FFTthe most general form of the sampling theorem is this, for a bandlimited signal of B hz, over a length T seconds , you need 2BT independent pieces of information to completely reconstruct the signal
Reply by ●April 29, 20112011-04-29
steve <bungalow_steve@yahoo.com> wrote: (snip, someone wrote)>> Depends how you look at it. Sampling rate is the same, but complex >> samples are applied to the FFT> the most general form of the sampling theorem is this, for a > bandlimited signal of B hz, over a length T seconds , you need 2BT > independent pieces of information to completely reconstruct the signalYou have to be pretty careful when defining the sampling theorem over a finite interval. That is usually ignored, and for a sufficiently long interval, usually close enough. Otherwise, you need N >= 2BT in the limit as N and T go to infinity. -- glen
Reply by ●April 29, 20112011-04-29
On Apr 29, 11:43�am, brent <buleg...@columbus.rr.com> wrote:> On Apr 29, 10:31�am, Jerry Avins <j...@ieee.org> wrote:...> Depends how you look at it. �Sampling rate is the same, but complex > samples are applied to the FFTHow many sample-and-holds are needed to get a complex sample? Jerry -- Engineering is the art of making what you want from things you can get.
Reply by ●April 29, 20112011-04-29
On Apr 29, 11:57 am, glen herrmannsfeldt <g...@ugcs.caltech.edu> wrote:> steve <bungalow_st...@yahoo.com> wrote: > > (snip, someone wrote) > > >> Depends how you look at it. Sampling rate is the same, but complex > >> samples are applied to the FFT > > the most general form of the sampling theorem is this, for a > > bandlimited signal of B hz, over a length T seconds , you need 2BT > > independent pieces of information to completely reconstruct the signal > > You have to be pretty careful when defining the sampling theorem > over a finite interval. That is usually ignored, and for a sufficiently > long interval, usually close enough. > > Otherwise, you need N >= 2BT in the limit as N and T go to infinity. > > -- glendon't understand what you are getting at, it is >2BT for any size T, large or small practically speaking your correct because for real analog signals B is always infinite
