Forums

Rectified FFT

Started by Benjamin M. Stocks December 5, 2003
Bevan Weiss wrote:

   ...

> I agree that adding some DC bias to the input signal (to ensure it remains > positive at all times, hence avoiding the nonlinearity of the rectifier) is > the best method. Then assuming the remaining circuitry is linear, you could > use superposition to remove the effect of the DC bias, simply by subtracting > the DC response from the response of the DC biased AC signal. That will > leave you with just the remaining circuitries response, ie it will ignore > the rectification circuit.
All well and good if the system passes DC to the rectifier. We don't actually know the makeup of the system or its response. Suppose, at the worst, that the system is transformer coupled at the input. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
"Fred Marshall" <fmarshallx@remove_the_x.acm.org> wrote in message 
> Is that the case? Do you know that it's a linear system? Your descriptions > have really been too cryptic for people to respond very well.
I apologize for the cryptic nature (I didn't think I was being that cryptic but maybe I was) but this is a work related question so I need to be careful about how much I describe, I'm sure you can understand. It is a linear system except for a device at the input that prevents any DC and any positive voltages from entering.
> You have not said if you want the frequency response of the system in the > general case or if you want the frequency response of the system to the > input signal.
To the specific input signal. I want to know the system's response at a specified frequency.
> If the system is linear and if you input a full-wave rectified sinusoid then > you can do this: > 0) You must know the frequency and amplitude of the full-wave rectified > sinusoid
I'm the one generating the full-wave rectified signal and I can use just about any frequency or amplitude I desire.
> 1) Represent the full-wave rectified sinusoid as a Fourier Series. > 2) Assuming a reasonably long sample of the output, Fourier Transform the > output with this special input present. > 3) Sample the Fourier Transform at the frequencies represented in the > Fourier Series you calculated in (1) for those frequencies where the Fourier > Series coefficients of (1) are not zero.
If I understand what you are saying here I should take the Fourier Transform of the output signals at the same frequencies as the input signals? I tried this but I get distortion. Ben
Benjamin M. Stocks wrote:

> "Fred Marshall" <fmarshallx@remove_the_x.acm.org> wrote in message > >>Is that the case? Do you know that it's a linear system? Your descriptions >>have really been too cryptic for people to respond very well. > > > I apologize for the cryptic nature (I didn't think I was being that > cryptic but maybe I was) but this is a work related question so I need > to be careful about how much I describe, I'm sure you can understand. > It is a linear system except for a device at the input that prevents > any DC and any positive voltages from entering. > > >>You have not said if you want the frequency response of the system in the >>general case or if you want the frequency response of the system to the >>input signal. > > > To the specific input signal. I want to know the system's response at > a specified frequency. > > >>If the system is linear and if you input a full-wave rectified sinusoid then >>you can do this: >>0) You must know the frequency and amplitude of the full-wave rectified >>sinusoid > > > I'm the one generating the full-wave rectified signal and I can use > just about any frequency or amplitude I desire. > > >>1) Represent the full-wave rectified sinusoid as a Fourier Series. >>2) Assuming a reasonably long sample of the output, Fourier Transform the >>output with this special input present. >>3) Sample the Fourier Transform at the frequencies represented in the >>Fourier Series you calculated in (1) for those frequencies where the Fourier >>Series coefficients of (1) are not zero. > > > If I understand what you are saying here I should take the Fourier > Transform of the output signals at the same frequencies as the input > signals? I tried this but I get distortion. > > Ben
There's a conceptual gap somewhere. A rectifier creates distortion. The FT merely shows it. Jerry -- Engineering is the art of making what you want from things you can get. &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
In article <3fd60c6a$0$14969$61fed72c@news.rcn.com>,
Jerry Avins <jya@ieee.org> wrote:

>Subject: Re: Rectified FFT >From: Jerry Avins <jya@ieee.org> >Reply-To: jya@ieee.org >Organization: The Hectic Eclectic >Date: Tue, 09 Dec 2003 12:54:49 -0500 >Newsgroups: comp.dsp > >Benjamin M. Stocks wrote: > >> "Fred Marshall" <fmarshallx@remove_the_x.acm.org> wrote in message >> >>>Is that the case? Do you know that it's a linear system? Your descriptions >>>have really been too cryptic for people to respond very well. >> >> >> I apologize for the cryptic nature (I didn't think I was being that >> cryptic but maybe I was) but this is a work related question so I need >> to be careful about how much I describe, I'm sure you can understand. >> It is a linear system except for a device at the input that prevents >> any DC and any positive voltages from entering. >> >> >>>You have not said if you want the frequency response of the system in the >>>general case or if you want the frequency response of the system to the >>>input signal. >> >> >> To the specific input signal. I want to know the system's response at >> a specified frequency. >> >> >>>If the system is linear and if you input a full-wave rectified sinusoid then >>>you can do this: >>>0) You must know the frequency and amplitude of the full-wave rectified >>>sinusoid >> >> >> I'm the one generating the full-wave rectified signal and I can use >> just about any frequency or amplitude I desire. >> >> >>>1) Represent the full-wave rectified sinusoid as a Fourier Series. >>>2) Assuming a reasonably long sample of the output, Fourier Transform the >>>output with this special input present. >>>3) Sample the Fourier Transform at the frequencies represented in the >>>Fourier Series you calculated in (1) for those frequencies where the Fourier >>>Series coefficients of (1) are not zero. >> >> >> If I understand what you are saying here I should take the Fourier >> Transform of the output signals at the same frequencies as the input >> signals? I tried this but I get distortion. >> >> Ben > >There's a conceptual gap somewhere. A rectifier creates distortion. The >FT merely shows it.
One must agree that this has been a rather good imitation of being confused on the concepts. The basic concept is that Linear Time Invariant (LTI) systems lead to convolutions and Fourier analysis. But we keep being told that the system is "nonlinear". Either it has the properties of a rectifier or it is being probed with a rectified signal but it has not been explicitly and totally clear. You can not just pick up the notion of frequency response developed for LTI systems and apply it blindly to anything and everything without a very long set of caviates, restrictions, gotchas and howevers. Does this system behave like a linear system as long as the input is positive but has some sort of nonlinearity when the input goes negtive, with the confusion being that the discussion goes to rectifiers because that is a convenient source of signals with no negative part? What hapens if one sums a value 2 offset and a sine wave of amplitude 1 so the signal lies between 1 and 3? Is the output a nice sine wave with some offset? That means pure sine wave output and not periodic with the input period.
>Jerry >-- >Engineering is the art of making what you want from things you can get. >&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095; >
"Jerry Avins" <jya@ieee.org> wrote in message
news:3fd60c6a$0$14969$61fed72c@news.rcn.com...
> Benjamin M. Stocks wrote: > > > "Fred Marshall" <fmarshallx@remove_the_x.acm.org> wrote in message > > > >>Is that the case? Do you know that it's a linear system? Your
descriptions
> >>have really been too cryptic for people to respond very well. > > > > > > I apologize for the cryptic nature (I didn't think I was being that > > cryptic but maybe I was) but this is a work related question so I need > > to be careful about how much I describe, I'm sure you can understand. > > It is a linear system except for a device at the input that prevents > > any DC and any positive voltages from entering. > > > > > >>You have not said if you want the frequency response of the system in
the
> >>general case or if you want the frequency response of the system to the > >>input signal. > > > > > > To the specific input signal. I want to know the system's response at > > a specified frequency. > > > > > >>If the system is linear and if you input a full-wave rectified sinusoid
then
> >>you can do this: > >>0) You must know the frequency and amplitude of the full-wave rectified > >>sinusoid > > > > > > I'm the one generating the full-wave rectified signal and I can use > > just about any frequency or amplitude I desire. > > > > > >>1) Represent the full-wave rectified sinusoid as a Fourier Series. > >>2) Assuming a reasonably long sample of the output, Fourier Transform
the
> >>output with this special input present. > >>3) Sample the Fourier Transform at the frequencies represented in the > >>Fourier Series you calculated in (1) for those frequencies where the
Fourier
> >>Series coefficients of (1) are not zero. > > > > > > If I understand what you are saying here I should take the Fourier > > Transform of the output signals at the same frequencies as the input > > signals? I tried this but I get distortion. > > > > Ben > > There's a conceptual gap somewhere. A rectifier creates distortion. The > FT merely shows it.
Ben and Jerry :-) No gap but perhaps another qualification for Ben: See step 1. This will generate a series of sinusoids that are harmonically related with the fundamental frequency the same as 2x the frequency of the original rectified sine wave. Terms at the fundamental, f0, and 2*f0, 3*f0, etc. all with different amplitudes and phases. This is the input to the linear system - a superposition of sinusoids. The output of the linear system will also be a superposition of those same sinusoids but weighted by the frequency response of the linear system - amplitude and phase again..... So, if one computes the Fourier Transform of the output of the linear system at each of the input frequencies, and divides by the amplitude of the input and takes the phase difference, one will have the linear system transfer function at those frequencies - and at those frequencies only. Example: I put in a full-wave rectified sinusoid with original frequency f0/2 and fundamental frequency of f0. Let's examine the 3rd harmonic, 3*f0: It is input to the linear system with let's say amplitude 3/4 and phase pi/4. The Fourier Transform of the output of the linear system at 3*f0 is of amplitude 1/2 and phase of pi/2. So, the linear system has reduced the amplitude to 2/3 and has added a phase shift of pi/2-pi/4=pi/4. This is the value of the transfer function of the linear system at 3*f0. So, Ben, if you know the amplitude and frequency of the input rectified sinusoid, you can determine the amplitudes and the frequencies at the output of the linear system. An exhaustive measurement process may allow you to fully characterize the linear system. Otherwise, you can make measurements at all the frequencies of interest and do this calculation. Interpolation of results comes to mind.... You use this then by saying: Here is the amplitude and frequency of the input. Now I can look up the amplitudes and frequencies of the output in my table of results as generated above. If the amplitude changes, the output scales directly. If the frequency changes, you need to do another look up from your table of results. The result is independent of input amplitude but not of the input frequency in general. Also, I've neglected the effect of "there is no dc passed to the input". You should be careful about this. If you start with a zero average sinusoid (no dc term) and then rectify it, then there will be a dc term resulting. If you start with a zero average sinusoid (no dc term), rectify it and *then* remove the dc term, that's a different waveform - but the method above still works. Fred
stocksb@ieee.org (Benjamin M. Stocks) wrote in message news:<132e56ad.0312090748.4c829fe@posting.google.com>...
> "Fred Marshall" <fmarshallx@remove_the_x.acm.org> wrote in message > > Is that the case? Do you know that it's a linear system? Your descriptions > > have really been too cryptic for people to respond very well. > > I apologize for the cryptic nature (I didn't think I was being that > cryptic but maybe I was) but this is a work related question so I need > to be careful about how much I describe, I'm sure you can understand. > It is a linear system except for a device at the input that prevents > any DC and any positive voltages from entering. > > > You have not said if you want the frequency response of the system in the > > general case or if you want the frequency response of the system to the > > input signal. > > To the specific input signal. I want to know the system's response at > a specified frequency. > > > If the system is linear and if you input a full-wave rectified sinusoid then > > you can do this: > > 0) You must know the frequency and amplitude of the full-wave rectified > > sinusoid > > I'm the one generating the full-wave rectified signal and I can use > just about any frequency or amplitude I desire. > > > 1) Represent the full-wave rectified sinusoid as a Fourier Series. > > 2) Assuming a reasonably long sample of the output, Fourier Transform the > > output with this special input present. > > 3) Sample the Fourier Transform at the frequencies represented in the > > Fourier Series you calculated in (1) for those frequencies where the Fourier > > Series coefficients of (1) are not zero. > > If I understand what you are saying here I should take the Fourier > Transform of the output signals at the same frequencies as the input > signals? I tried this but I get distortion. > > Ben
So am I correct in thinking that the output of the rectifier (which is the input to your linear system) is not observable and that the input to the rectifier is know (ie. waveform shape)? If that is the case my suggestion would be to construct a model of the rectifier in code and input the model with the same signal as the real rectifier. Then you just perform transfer function analysis by measuring the cross spectrum of the system output with your virtual input and divide that by the power spectrum of the input to get the frequency response. The only caveat with this approach is that you need sufficient whiteness in your input signal to be able to measure the freuqnecy response so you may have to add some noise to your sinusoid, or if your system can handle pure noise then just use rectified noise. Regards, Paavo Jumppanen Author of AtSpec : A 2 channel PC based FFT spectrum analyzer http://www.taquis.com

"Benjamin M. Stocks" wrote:

> It is a linear system except for a device at the input that prevents > any DC and any positive voltages from entering.
Well, everyone is still guessing as to what it is that you are really observing. It has been suggested that you input a periodic waveform with a DC bias (sounds like negative bias would be appropiate here) - have you tried that? What does the resulting output look like? If the input is AC coupled as you suggest then the DC gets removed and its no different than if you inputed the signal without a DC bias - is that what you are observing? If thatis the case then inputing a rectified signal (inverted I guess) would be of no help either since the DC component of that signal will also be removed and you would have just doubled the distortion. -jim -----= Posted via Newsfeeds.Com, Uncensored Usenet News =----- http://www.newsfeeds.com - The #1 Newsgroup Service in the World! -----== Over 100,000 Newsgroups - 19 Different Servers! =-----
Benjamin M. Stocks wrote:

(snip)

> I'm the one generating the full-wave rectified signal and I can use > just about any frequency or amplitude I desire.
>>1) Represent the full-wave rectified sinusoid as a Fourier Series. >>2) Assuming a reasonably long sample of the output, Fourier Transform the >>output with this special input present. >>3) Sample the Fourier Transform at the frequencies represented in the >>Fourier Series you calculated in (1) for those frequencies where the Fourier >>Series coefficients of (1) are not zero.
> If I understand what you are saying here I should take the Fourier > Transform of the output signals at the same frequencies as the input > signals? I tried this but I get distortion.
The first thing that happens is that the frequency is doubled. The sound people are used to calling "60Hz hum" is actually 120Hz. The vibrations of transformer wires are at twice the line frequency. There is also a non-linear effect, which generates an infinite series of harmonics of decreasing amplitude. If you square the rectified signal, you should get pretty much the FT with each component at twice the original frequency, and some phase information lost. I haven't tried to figure out what the phase information does. -- glen
Benjamin M. Stocks wrote:

   ...


> It is a linear system except for a device at the input that prevents > any DC and any positive voltages from entering.
I just reread that. It sounds like a half-wave rectifier. You wrote originally that that positive voltages are inverted. Now you write that they are blocked. Was that a slip? Jerry -- Engineering is the art of making what you want from things you can get. &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
stocksb@ieee.org (Benjamin M. Stocks) wrote in message news:<132e56ad.0312090748.4c829fe@posting.google.com>...
> "Fred Marshall" <fmarshallx@remove_the_x.acm.org> wrote in message > > Is that the case? Do you know that it's a linear system? Your descriptions > > have really been too cryptic for people to respond very well. > > I apologize for the cryptic nature (I didn't think I was being that > cryptic but maybe I was) but this is a work related question so I need > to be careful about how much I describe, I'm sure you can understand. > It is a linear system except for a device at the input that prevents > any DC and any positive voltages from entering. > > > You have not said if you want the frequency response of the system in the > > general case or if you want the frequency response of the system to the > > input signal. > > To the specific input signal. I want to know the system's response at > a specified frequency. >
a) Generate a frequency sweep. b) Lowpass filter the output. c) Plot the measured amplitude against the input frequencies. voila! you have the frequency response. Unless we're all missing something... regards Robert