> On the other hand, I do agree that curve fitting to points > on the V(t) curve doesn't seem like rectification, and does allow > one to compute the amplitude, though not easily the envelope for > an AM modulated carrier.
> -- glen
I think the key point is not about rectification or linear vs non linear.
I think the key point is that the usual "rectification" methods require some kind of explicit or implicit (in the case of a heaters) low pass filtering to remove the carrier component and keep the modulation component. The Hilbert method describe by R. Lyons requires no filtering and returns an exact result regardless of the relationship between the carrier frequency and the modulation.
That is the beauty of it.
That is the problem I saw many years ago, if you applied a lot of filtering to the diode detector to completely remove the 455 kHz IF signal, you would loose some of the high frequency audio components. Of course I was using simple RC filters, I know better now of course.
But, to me, that is the ___fundamental__ advantage of the Hilbert method over the "rectifier" methods.
Hello Rick, I already have the received the errata from you. thank you.
In comp.dsp Mark <makol...@yahoo.com> wrote: (snip, I wrote)
>> On the other hand, I do agree that curve fitting to points >> on the V(t) curve doesn't seem like rectification, and does allow >> one to compute the amplitude, though not easily the envelope for >> an AM modulated carrier. > I think the key point is not about rectification or linear vs non > linear. > I think the key point is that the usual "rectification" methods > require some kind of explicit or implicit (in the case of a heaters) > low pass filtering to remove the carrier component and keep the > modulation component. The Hilbert method describe by R. Lyons > requires no filtering and returns an exact result regardless of the > relationship between the carrier frequency and the modulation. > That is the beauty of it.
Hmm, interesting and a different question. It does remind me of asking here about synchronous demodulation of AM signals, such that you get the right result when the modulation index is greater than one. I will guess that the Hilbert method can also do that.
> That is the problem I saw many years ago, if you applied a lot of > filtering to the diode detector to completely remove the 455 kHz IF > signal, you would loose some of the high frequency audio components. > Of course I was using simple RC filters, I know better now of > course. > But, to me, that is the ___fundamental__ advantage of the Hilbert > method over the "rectifier" methods.
> > You can put the signal through almost any non-linear operation, > You can put the signal into the heater and measure the temperature. > Where is nonlinearity?
It would be hard to claim _that_ was "non linear" in even the least sophisticated sense of the term.
That isn't the issue, however. The issue is rectification.
If some operation results in the same + sign of the magnitude of some +/- signal then that operation could be broadly construed as "rectification."
> You can put the signal into a into a solenoid and measure the force > attracting a piece of ferrous material.
Same as the heater. The operation outputs a + magnitude for a +/- signal.
> Or, for that matter, the force > between two solenoids with the same current running in them. > There is a zillion of ways to measure AC without any nonlinearity or > rectification involved.
Maybe there are several if the wave form is known.
>> Poorly written OP. The goal is getting the amplitude _without_ >> rectification. Rectification" is to be very broadly construed and >> includes anything that results in the final "signal" being positive at >> all times.
>> Maybe peak to peak wil work if you know the wave form.
>I still have my Heathkit VTVM, christmas present from when >I was in high school. The manual includes an explanation of >the form of rectifier used, and why the result is peak-to-peak. >Other than that, it seems unusual to rectify as peak-to-peak.
>-- glen
Hi glen, Good God!! When you mention a Heathkit VTVM you strike a nerve with me. I had one of those, with its cigar-sized probe and alligator ground clip.
When I was in high school (yes I played on the baseball team and got into trouble like any other knuckleheaded high school student), I became interested in electronics.
I mostly used my VTVM to test the filaments of vacuum tubes from the old radios and televisions that my neighbors threw away and gave to me.
Back then you could buy all sorts of electronic parts from Radio Shack At that time Radio Shack was about radios and electronics hobbyists. Now Radio Shack is geared toward cell phones and digital cameras. It's too bad, really too bad.
It's a shame but American teenage boys are now far more interested in playing video games than experimenting with electronics.
glen, are you old enough to remember the chintzy little crystal radios that had a simple tuning coil, capacitor (I think), diode, earphone, and NO BATTERY? With those little crystal radios you could "pick up" local AM radio while lying in your bed at night.
> In comp.dsp Vladimir Vassilevsky <nos...@nowhere.com> wrote:
>> Bret Cahill wrote:
>>> Is there anyway to get an amplitude of an ac signal averaged over >>> time w/o some kind of rectification?
>> Sure. Connect the AC to a heater and measure the temperature.
>>> This doesn't include the trivial, i.e., dc offsets or partial >>> cycles. The rectification could be analog, digital or software.
> You need some non-linear operation, which may or may not be > considered rectification. I believe the heater/temperature > measurement has been used for RF power measurements for many years.
> In comp.dsp Fred Marshall<fmarshall_xremove_the...@xacm.org> wrote: > (snip)
>> Multiplying by other than a constant or a stable periodic waveform is a >> non-linear operation. Multiplying by a constant or a sinusoid or a sum >> of sinusoids is a linear operation.... believe it or not.
> Hmmm. As I understand it (longer ago than I remember) they used > to make rectifiers out of synchronous motor driven commutators.
> That is, multiply by a square wave (sum of sines) of the appropriate > frequency. The result doesn't seem like a linear function of > the input anymore.
> -- glen
Well, Jerry and I argued about this at length here some time ago. The key is in the tests for linearity. It rather surprised me too and it didn't "seem like a linear system" but it worked out.
In all these things we're talking about a 2-port situation and asking whether the 2-port system is linear or not.
So, if the 2-port system is a 4-quadrant multiplier with a stable sinusoidal input (which is not one of the "ports") then the result of a signal on the "input" port is a sinusoid of amplitude proportional to that input. And, if a different input is applied, same thing. And, if the sum of those two inputs is applied, the output is the sum of the two independent outputs. etc.
Now, I must say that I was pulling from memory about the composite sinusoidal modulating function .. but I think it still holds with that being used instead of a simple sinusoid...
On 2010-11-05, Bret Cahill <BretCah...@peoplepc.com> wrote:
> The goal is getting the amplitude _without_ > rectification. Rectification" is to be very broadly construed and > includes anything that results in the final "signal" being positive at > all times.
<fmarshall_xremove_the...@xacm.org> wrote: >On 11/5/2010 5:26 PM, glen herrmannsfeldt wrote: >> In comp.dsp Fred Marshall<fmarshall_xremove_the...@xacm.org> wrote: >> (snip)
>>> Multiplying by other than a constant or a stable periodic waveform is a >>> non-linear operation. Multiplying by a constant or a sinusoid or a sum >>> of sinusoids is a linear operation.... believe it or not.
>> Hmmm. As I understand it (longer ago than I remember) they used >> to make rectifiers out of synchronous motor driven commutators.
>> That is, multiply by a square wave (sum of sines) of the appropriate >> frequency. The result doesn't seem like a linear function of >> the input anymore.
>> -- glen
>Well, Jerry and I argued about this at length here some time ago. The >key is in the tests for linearity. It rather surprised me too and it >didn't "seem like a linear system" but it worked out.
>In all these things we're talking about a 2-port situation and asking >whether the 2-port system is linear or not.
>So, if the 2-port system is a 4-quadrant multiplier with a stable >sinusoidal input (which is not one of the "ports") then the result of a >signal on the "input" port is a sinusoid of amplitude proportional to >that input. And, if a different input is applied, same thing. And, if >the sum of those two inputs is applied, the output is the sum of the two >independent outputs. >etc.
>Now, I must say that I was pulling from memory about the composite >sinusoidal modulating function .. but I think it still holds with that >being used instead of a simple sinusoid...
I think this depends on what you mean by "linear". Most of the time, IMHO, we mean "no new frequencies produced in the output". Multiplying two sinusoids violates this, because you end up with sum and difference frequencies.
Think about amplifiers. We talk about "nonlinear distortion" when we get new frequency components (THD, IMD, slew limiting, etc), while "linear distortion" (which is a rarely used term) means only changes in amplitudes or phases of the original frequency components.
Best regards,
Bob Masta
DAQARTA v5.10 Data AcQuisition And Real-Time Analysis www.daqarta.com Scope, Spectrum, Spectrogram, Sound Level Meter Frequency Counter, FREE Signal Generator Pitch Track, Pitch-to-MIDI DaqMusic - FREE MUSIC, Forever! (Some assembly required) Science (and fun!) with your sound card!
On Fri, 5 Nov 2010 13:00:54 -0700 (PDT) Bret Cahill <Bret_E_Cah...@yahoo.com> wrote in Message id: <e6a620ac-ec32-4ae8-8f56-6f948ed1f...@x7g2000prj.googlegroups.com>:
>Is there anyway to get an amplitude of an ac signal averaged over time >w/o some kind of rectification?
> On Sat, 06 Nov 2010 09:52:02 -0700, Fred Marshall > <fmarshall_xremove_the...@xacm.org> wrote:
>> On 11/5/2010 5:26 PM, glen herrmannsfeldt wrote: >>> In comp.dsp Fred Marshall<fmarshall_xremove_the...@xacm.org> wrote: >>> (snip)
>>>> Multiplying by other than a constant or a stable periodic waveform is a >>>> non-linear operation. Multiplying by a constant or a sinusoid or a sum >>>> of sinusoids is a linear operation.... believe it or not.
>>> Hmmm. As I understand it (longer ago than I remember) they used >>> to make rectifiers out of synchronous motor driven commutators.
>>> That is, multiply by a square wave (sum of sines) of the appropriate >>> frequency. The result doesn't seem like a linear function of >>> the input anymore.
>>> -- glen
>> Well, Jerry and I argued about this at length here some time ago. The >> key is in the tests for linearity. It rather surprised me too and it >> didn't "seem like a linear system" but it worked out.
>> In all these things we're talking about a 2-port situation and asking >> whether the 2-port system is linear or not.
>> So, if the 2-port system is a 4-quadrant multiplier with a stable >> sinusoidal input (which is not one of the "ports") then the result of a >> signal on the "input" port is a sinusoid of amplitude proportional to >> that input. And, if a different input is applied, same thing. And, if >> the sum of those two inputs is applied, the output is the sum of the two >> independent outputs. >> etc.
>> Now, I must say that I was pulling from memory about the composite >> sinusoidal modulating function .. but I think it still holds with that >> being used instead of a simple sinusoid...
> I think this depends on what you mean by "linear". Most of > the time, IMHO, we mean "no new frequencies produced in the > output". Multiplying two sinusoids violates this, because > you end up with sum and difference frequencies.
That is true for time-invariant systems. Look at my previous post and, for instance, http://en.wikipedia.org/wiki/Linear for the mathematical definition of linearity.
The operation "multiplying by m(t)" is a linear but time-_variant_ operation and is common in communication systems, such as any frequency conversion process:
> Think about amplifiers. We talk about "nonlinear > distortion" when we get new frequency components (THD, IMD, > slew limiting, etc), while "linear distortion" (which is a > rarely used term) means only changes in amplitudes or phases > of the original frequency components.
> Best regards,
> Bob Masta
> DAQARTA v5.10 > Data AcQuisition And Real-Time Analysis > www.daqarta.com > Scope, Spectrum, Spectrogram, Sound Level Meter > Frequency Counter, FREE Signal Generator > Pitch Track, Pitch-to-MIDI > DaqMusic - FREE MUSIC, Forever! > (Some assembly required) > Science (and fun!) with your sound card!
> Poorly written OP. The goal is getting the amplitude _without_ > rectification. Rectification" is to be very broadly construed and > includes anything that results in the final "signal" being positive at > all times.
If your signal x(t) is described by x(t) = A·(cos wt + fi), then A is called the amplitude and is positive (at all times, since it does not depend on t) by definition.
From your rewritten question it seems you want something that does not make sense (even) in the sinusoidal case.
> On 11/05/2010 01:00 PM, Bret Cahill wrote: >> Is there anyway to get an amplitude of an ac signal averaged over time >> w/o some kind of rectification?
>> This doesn't include the trivial, i.e., dc offsets or partial cycles.
>> The rectification could be analog, digital or software.
> On Nov 7, 11:25 am, Fred Abse<excretatau...@invalid.invalid> wrote: >> On Sun, 07 Nov 2010 04:22:16 +0000, Jasen Betts wrote: >>> show me a signal with negative amplitude.
>> a sin x at x>pi<2*pi
>> -- > I searched all of the posts here to see if anyone caught that.
> Posters are using the terms "amplitude" and "magnitude" as if they are > the same.
> Dirk
Dirk,
Good point. I've probably done that! So you got me thinking....
It occurs to me that there's another: "value of a function" or "value of a signal" which, obviously can be negative.
This goes along with:
"magnitude of a signal or function" (which I don't think implies any time frame).... as in "abs(value of a function)"
"amplitude of a wave" as in "a sin x" or, amplitude of noise perhaps... where we most often use "a" as a positive number in physics but don't *have to* in mathematics, eh? In the latter case it could be said to have a negative amplitude but that would be most unusual wouldn't it? Or maybe it's just implied that 0=<a ??
I'm not sure how "amplitude" really applies otherwise:
What's the "amplitude" of a*sin(wt) + b*cos(pi*w*t) ????
Then things like "rms value" or "rms whatever" usually imply a time frame over which the sum or integral is taken - often a single period but could be just some arbitrary time frame.
In comp.dsp Fred Marshall <fmarshall_xremove_the...@xacm.org> wrote: (snip, someone wrote)
>> Posters are using the terms "amplitude" and "magnitude" as if >> they are the same. > Good point. I've probably done that! So you got me thinking.... > It occurs to me that there's another: > "value of a function" or "value of a signal" which, obviously can be > negative. > This goes along with: > "magnitude of a signal or function" (which I don't think implies any > time frame).... as in "abs(value of a function)" > "amplitude of a wave" as in "a sin x" > or, amplitude of noise perhaps... > where we most often use "a" as a positive number in physics but don't > *have to* in mathematics, eh? In the latter case it could be said to > have a negative amplitude but that would be most unusual wouldn't it? > Or maybe it's just implied that 0=<a ??
In physics, at least in optics and QM, amplitude is signed.
For example, "for coherent sources add the amplitude, for incoherent sources add the intensity."
Though another way to look at it is that amplitude is unsigned, but that one has to include the appropriate phase difference when adding.
> I'm not sure how "amplitude" really applies otherwise: > What's the "amplitude" of a*sin(wt) + b*cos(pi*w*t) ????
> >> -- > > I searched all of the posts here to see if anyone caught that.
> > Posters are using the terms "amplitude" and "magnitude" as if they are > > the same.
> > Dirk
> Dirk,
> Good point. I've probably done that! So you got me thinking....
> It occurs to me that there's another: > "value of a function" or "value of a signal" which, obviously can be > negative.
> This goes along with:
> "magnitude of a signal or function" (which I don't think implies any > time frame).... as in "abs(value of a function)"
> "amplitude of a wave" as in "a sin x" > or, amplitude of noise perhaps... > where we most often use "a" as a positive number in physics but don't > *have to* in mathematics, eh? In the latter case it could be said to > have a negative amplitude but that would be most unusual wouldn't it? > Or maybe it's just implied that 0=<a ??
> I'm not sure how "amplitude" really applies otherwise:
> What's the "amplitude" of a*sin(wt) + b*cos(pi*w*t) ????
> Then things like "rms value" or "rms whatever" usually imply a time > frame over which the sum or integral is taken - often a single period > but could be just some arbitrary time frame.
The term "time ave." in the header implies the quantity is over some time period.
If peak to peak or rms or any other measure of amplitude increases by some percent during that time period then the magnitude of the low pass or integral will increase by that same percent.
