On Oct 19, 5:26�pm, Jerry Avins <j...@ieee.org> wrote:> Tim Wescott wrote: > > On Mon, 19 Oct 2009 11:17:09 -0400, Jerry Avins wrote: > > >> Tim Wescott wrote: > > >> � �... > > >>> A time-varying system will add frequencies to the spectrum, because it > >>> multiplies the signal by a time-varying parameter. �The effect on the > >>> spectrum is to convolve the signal's spectrum with the time-varying > >>> parameter's spectrum. > > >>> So a time varying system can't generate frequencies from _nothing_, but > >>> it can certainly have more frequencies at the output than at the input. > >> Can a nonlinear system generate frequencies from _nothing_? > > > Define "nothing". > > > A time-varying system cannot generate an output signal with spectral � > > components that are unrelated to the spectrum of the input signal. �A > > nonlinear system can -- define the system > > > y = h(x, t) > > > as y = sin(w*t) > > > It's time-varying, it's nonlinear (it certainly doesn't obey > > superposition!), and it generates an output signal from as close to > > nothing as you can get. > > You lost me. (That's not hard.) As far as I can see, you're setting up > sin(w*t) = h(x, t). Then the innards of h(x, t) are immaterial; y is > given. Where's the non-linearity? Are you describing an oscillator with > dummy input terminals? If so, we agree. > > A balanced diode bridge is non-linear. No x emerges at all, only its > harmonics. It's so bad that the term "distortion" hardly applies. > Nevertheless, when no signal is applied, none emerges. > > Jerry > -- > Engineering is the art of making what you want from things you can get. > �����������������������������������������������������������������������As a first approximation (which most of the time is all you're bothered about with a bridge rectifier) a diode bridge is something like abs(x). Is that a nonlinear function?
time variant or invariant output?
Started by ●October 17, 2009
Reply by ●October 21, 20092009-10-21
Reply by ●October 21, 20092009-10-21
Fully Half Baked wrote:> On Oct 19, 2:28 am, Jerry Avins <j...@ieee.org> wrote:...>> To continue in a simplistic vein, imagine an amplifier with time-varying >> gain; the input is a single sinusoid of 2KHz, and the gain varies >> sinusoidally at a frequency of 50 Hz. What is the output spectrum?...> You got me there.A two KHz carrier modulated at 50 Hz. The (positive) spectrum consists of three spikes; one each at 1950, 2000, and 2050 Hz. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●October 21, 20092009-10-21
Fully Half Baked wrote: ...> As a first approximation (which most of the time is all you're > bothered about with a bridge rectifier) a diode bridge is something > like abs(x). Is that a nonlinear function?Yes. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●October 21, 20092009-10-21
Fully Half Baked wrote: ...> Maybe it's more like this > http://en.wikipedia.org/wiki/Nonlinear_systemMore like in what way> Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●October 21, 20092009-10-21
On Oct 21, 8:12�pm, Jerry Avins <j...@ieee.org> wrote:> Fully Half Baked wrote: > > On Oct 19, 2:28 am, Jerry Avins <j...@ieee.org> wrote: > > � �... > > >> To continue in a simplistic vein, imagine an amplifier with time-varying > >> gain; the input is a single sinusoid of 2KHz, and the gain varies > >> sinusoidally at a frequency of 50 Hz. What is the output spectrum? > > � �... > > > You got me there. > > A two KHz carrier modulated at 50 Hz. The (positive) spectrum consists > of three spikes; one each at 1950, 2000, and 2050 Hz. > > Jerry > -- > Engineering is the art of making what you want from things you can get. > �����������������������������������������������������������������������I meant you proved me wrong. What happened to 50Hz?
Reply by ●October 21, 20092009-10-21
On Oct 21, 8:15�pm, Jerry Avins <j...@ieee.org> wrote:> Fully Half Baked wrote: > > � �... > > > Maybe it's more like this > >http://en.wikipedia.org/wiki/Nonlinear_system > > More like in what way> > > Jerry > -- > Engineering is the art of making what you want from things you can get. > �����������������������������������������������������������������������In way of an official definition that I was happily ignoring.
Reply by ●October 21, 20092009-10-21
On Wed, 21 Oct 2009 10:40:15 -0700, Fully Half Baked wrote:> On Oct 19, 5:26 pm, Jerry Avins <j...@ieee.org> wrote: >> Tim Wescott wrote: >> > On Mon, 19 Oct 2009 11:17:09 -0400, Jerry Avins wrote: >> >> >> Tim Wescott wrote: >> >> >> ... >> >> >>> A time-varying system will add frequencies to the spectrum, because >> >>> it multiplies the signal by a time-varying parameter. The effect >> >>> on the spectrum is to convolve the signal's spectrum with the >> >>> time-varying parameter's spectrum. >> >> >>> So a time varying system can't generate frequencies from _nothing_, >> >>> but it can certainly have more frequencies at the output than at >> >>> the input. >> >> Can a nonlinear system generate frequencies from _nothing_? >> >> > Define "nothing". >> >> > A time-varying system cannot generate an output signal with spectral >> > components that are unrelated to the spectrum of the input signal. A >> > nonlinear system can -- define the system >> >> > y = h(x, t) >> >> > as y = sin(w*t) >> >> > It's time-varying, it's nonlinear (it certainly doesn't obey >> > superposition!), and it generates an output signal from as close to >> > nothing as you can get. >> >> You lost me. (That's not hard.) As far as I can see, you're setting up >> sin(w*t) = h(x, t). Then the innards of h(x, t) are immaterial; y is >> given. Where's the non-linearity? Are you describing an oscillator with >> dummy input terminals? If so, we agree. >> >> A balanced diode bridge is non-linear. No x emerges at all, only its >> harmonics. It's so bad that the term "distortion" hardly applies. >> Nevertheless, when no signal is applied, none emerges. >> >> Jerry >> -- >> Engineering is the art of making what you want from things you can get. >> ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ > > As a first approximation (which most of the time is all you're bothered > about with a bridge rectifier) a diode bridge is something like abs(x). > Is that a nonlinear function?Does it obey superposition? Hmm. Let's put it to the test. Let x = x1 + x2. Does abs(x1 + x2) = abs (x1) + abs(x2) for any arbitrary x1 and x2? What about when x1 and x2 are different signs? No? Then abs(x) isn't a linear function. -- www.wescottdesign.com
Reply by ●October 21, 20092009-10-21
Fully Half Baked wrote:> On Oct 21, 8:12 pm, Jerry Avins <j...@ieee.org> wrote: >> Fully Half Baked wrote: >>> On Oct 19, 2:28 am, Jerry Avins <j...@ieee.org> wrote: >> ... >> >>>> To continue in a simplistic vein, imagine an amplifier with time-varying >>>> gain; the input is a single sinusoid of 2KHz, and the gain varies >>>> sinusoidally at a frequency of 50 Hz. What is the output spectrum? >> ... >> >>> You got me there. >> A two KHz carrier modulated at 50 Hz. The (positive) spectrum consists >> of three spikes; one each at 1950, 2000, and 2050 Hz. >> >> Jerry >> -- >> Engineering is the art of making what you want from things you can get. >> ����������������������������������������������������������������������� > > I meant you proved me wrong. What happened to 50Hz?No 50 Hz was never created. jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
