Hello forum, I have a few questions about bandwidth: Take a finite time signal, like a pulse. It must be composed of a band of Fourier frequencies. The notion of a single pure frequency belongs only to a sinusoidal signal, which is infinite in duration. To measure a frequency we need to have periodicity of an event forever. That is just theory, an abstraction. 1) Back to the pulse: are those composing Fourier frequencies somewhat real? How does the hardware measure them, since they only belong to abstract functions? Maybe the hardware just does some math with the received data...? If we could use a infinitely narrow-band tunable detector, would we see energy at each of those Fourier frequencies proportional to their amplitude? 2) There is another definition of frequency: instantaneous frequency. That measures not the re-occurrence of the exactly the same event but the reappearance of the same state (peak), regardless of its maximum amplitude. Is there a relation between Fourier and Instantaneous frequency? 3) Modulation (AM) is a nonlinear process. If I start with a local oscillator that outputs a clean sinusoid and then chop that, we get those new Fourier frequencies.... How are they physically produced? The modulator interacts with signal and.....? thanks a LOT and admiration to anyone able and willing to answer, fisico30
true meaning of bandwidth
Started by ●February 17, 2009
Reply by ●February 17, 20092009-02-17
On Feb 17, 9:37�am, "fisico30" <marcoscipio...@gmail.com> wrote:> Hello forum, > I have a few questions about bandwidth: > > Take a finite time signal, like a pulse. It must be composed of a band of > Fourier frequencies. > The notion of a single pure frequency belongs only to a sinusoidal signal, > which is infinite in duration. To measure a frequency we need to have > periodicity of an event forever. That is just theory, an abstraction. > 1) Back to the pulse: are those composing Fourier frequencies somewhat > real? How does the hardware measure them, since they only belong to > abstract functions? Maybe the hardware just does some math with the > received data...?I'm not sure what hardware you're referring to, but it sounds like a spectrum analyzer. A spectrum analyzer, like all test equipment, generates an *estimate* of the input signal's power spectral density. The actual method for doing so may vary; older models would actually sweep across the entire band with a fixed IF filter, then measure the power coming out at each tune frequency. Modern analyzers most likely do more processing digitally (e.g. using the FFT as a filterbank to estimate power in each bin, then sweeping in larger chunks across the analyzer's bandwidth). So, to answer your question, yes, the Fourier transform is "real" in the sense that you could synthesize a time- domain signal by adding up enough appropriately-weighted sinusoids. It just so happens that "enough" usually means "infinitely many", so it's often not practical.> If we could use a infinitely narrow-band tunable detector, would we see > energy at each of those Fourier frequencies proportional to their > amplitude?Yes.> 2) There is another definition of frequency: instantaneous frequency. > That measures not the re-occurrence of the exactly the same event but the > reappearance of the same state (peak), regardless of its maximum > amplitude. > Is there a relation between Fourier and Instantaneous frequency?I'm not sure what you're referring to. Instantaneous frequency is a term used often in frequency-modulated systems, referring to the transmitted frequency at any given instant. Otherwise, I'm not sure what your question is.> 3) Modulation (AM) is a nonlinear process. If I start with a local > oscillator that outputs a clean sinusoid and then chop that, we get those > new Fourier frequencies.... How are they physically produced? The modulator > interacts with signal and.....?Again, I'm not sure what you're asking. They are physically produced by the distortion that you apply to the signal. Those new frequencies don't add energy (unless you're amplifying it in the process); some energy is merely "stolen" from the pure sinusoidal input and shoved over to other frequencies. Sounds like you could benefit from studying a signals and systems text. I don't have a particularly good one; maybe someone else can suggest a reference. Jason
Reply by ●February 17, 20092009-02-17
On 17 Feb, 15:37, "fisico30" <marcoscipio...@gmail.com> wrote:> Hello forum, > I have a few questions about bandwidth: > > Take a finite time signal, like a pulse. It must be composed of a band of > Fourier frequencies. > The notion of a single pure frequency belongs only to a sinusoidal signal, > which is infinite in duration. To measure a frequency we need to have > periodicity of an event forever. That is just theory, an abstraction.Nope. That's reality. If you want to determine the frequency with infinite precision, based on the spectrum.> 1) Back to the pulse: are those composing Fourier frequencies somewhat > real? How does the hardware measure them, since they only belong to > abstract functions? Maybe the hardware just does some math with the > received data...?Thta's what happens, at least in digital systems: Data are numbers, DSP operators are functions working on those numbers to produuce other numbers.> If we could use a infinitely narrow-band tunable detector, would we see > energy at each of those Fourier frequencies proportional to their > amplitude?Watch out! The question might be intuitive, but is in fact an abstract, meaningless questions: You can't make a filter with infinitely narrow passband. Don't go there.> 2) There is another definition of frequency: instantaneous frequency.'Instantaneous frequency' is a meaningless term. If I tell you that a sample at one isntance had value 1, could you determine the signal's frequency from that information? Of course not. You need at least two samples, that is, measurements over some interval, to make any meaningful statements about frequency.> That measures not the re-occurrence of the exactly the same event but the > reappearance of the same state (peak), regardless of its maximum > amplitude. > Is there a relation between Fourier and Instantaneous frequency?No. Rune
Reply by ●February 17, 20092009-02-17
> Again, I'm not sure what you're asking. They are physically produced > by the distortion that you apply to the signal. Those new frequencies > don't add energy (unless you're amplifying it in the process); some > energy is merely "stolen" from the pure sinusoidal input and shoved > over to other frequencies. >I disagree. In the case of AM, the "carrier" remains the same amplitude at all times. When modulation is applied, the sidebands ARE ADDED power amounting to a total of 50% additional AVERAGE power at 100% modulation. It takes a 50 Watt audio amp to plate modulate a 100 Watt RF transmitter, and that 50 Watts of audio goes into the sidebands. CQ DX Mark
Reply by ●February 17, 20092009-02-17
On Feb 17, 11:26�am, makol...@yahoo.com wrote:> > Again, I'm not sure what you're asking. They are physically produced > > by the distortion that you apply to the signal. Those new frequencies > > don't add energy (unless you're amplifying it in the process); some > > energy is merely "stolen" from the pure sinusoidal input and shoved > > over to other frequencies. > > I disagree. > > In the case of AM, the "carrier" remains the same amplitude at all > times. �When modulation �is applied, the sidebands ARE ADDED power > amounting to a total of 50% additional AVERAGE power at 100% > modulation. > > It takes a 50 Watt audio amp to plate modulate a 100 Watt RF > transmitter, and that 50 Watts of audio goes into the sidebands. > > CQ DX > > MarkI was talking about the case that he mentioned where he runs a pure sinusoid into a clipping circuit. The clipping operation won't add energy, but it does introduce content at new frequencies. I agree with you, in the traditional AM case, you're correct. Jason
Reply by ●February 17, 20092009-02-17
fisico30 wrote:> Hello forum, > I have a few questions about bandwidth: > > Take a finite time signal, like a pulse. It must be composed of a band of > Fourier frequencies.I don't know what a Fourier frequency is. I don't think you do either; I guess you mean something else. Can you clarify?> The notion of a single pure frequency belongs only to a sinusoidal signal, > which is infinite in duration. To measure a frequency we need to have > periodicity of an event forever. That is just theory, an abstraction.True. So?> 1) Back to the pulse: are those composing Fourier frequencies somewhat > real?To comment, I have to guess that by "Fourier frequency", you mean those component frequencies that Fourier analysis would reveal. They are absolutely, not somewhat, real.> How does the hardware measure them, since they only belong to > abstract functions? Maybe the hardware just does some math with the > received data...?What hardware? A radio receiver could measure them by tuning to each of them in turn.> If we could use a infinitely narrow-band tunable detector, would we see > energy at each of those Fourier frequencies proportional to their > amplitude?An infinitely narrow tuned circuit needs infinite time to respond. Neither you nor I want to wait that long.> 2) There is another definition of frequency: instantaneous frequency. > That measures not the re-occurrence of the exactly the same event but the > reappearance of the same state (peak), regardless of its maximum > amplitude. > Is there a relation between Fourier and Instantaneous frequency?Instantaneous frequency is associated with a signal that changes frequency, such as an FM carrier.> 3) Modulation (AM) is a nonlinear process.Some people call it a linear time-varying process. Linear modulation results in an envelope that reproduces the modulating signal. That doesn't make modulation itself linear.> If I start with a local > oscillator that outputs a clean sinusoid and then chop that, we get those > new Fourier frequencies....What are Fourier frequencies? Harmonics?> How are they physically produced?Abrupt changes in a current require high frequencies to represent them. Chopping creates sharp corners; abruptness, and thereby introduces high frequencies.> The modulator interacts with signal and.....?What modulator?> thanks a LOT and admiration to anyone able and willing to answer, > fisico30May I suggest a book to supply the basics? Good texts are expensive, but the ARRL Handbook is reasonably priced and provides good explanations. http://www.arrl.org/catalog/?item=9760#top Is now a bargain, even with $7 shipping to US addresses. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●February 17, 20092009-02-17
fisico30 wrote:> Take a finite time signal, like a pulse. It must be composed of a band of > Fourier frequencies. > The notion of a single pure frequency belongs only to a sinusoidal signal, > which is infinite in duration. To measure a frequency we need to have > periodicity of an event forever. That is just theory, an abstraction.There is another choice in the Fourier case, and that is periodic boundary conditions. In addition to the use here, periodic boundary conditions are used in solid state physics when working on the bulk properties of crystalline solids, while ignoring the boundary effects. (Especially in the beginning classes.)> 1) Back to the pulse: are those composing Fourier frequencies somewhat > real? How does the hardware measure them, since they only belong to > abstract functions? Maybe the hardware just does some math with the > received data...? > If we could use a infinitely narrow-band tunable detector, would we see > energy at each of those Fourier frequencies proportional to their > amplitude?As the finite duration increases in length, the result gets closer to the infinite time solution. Eventually it is close enough, especially in noisy signals.> 2) There is another definition of frequency: instantaneous frequency. > That measures not the re-occurrence of the exactly the same event but the > reappearance of the same state (peak), regardless of its maximum > amplitude. > Is there a relation between Fourier and Instantaneous frequency?I would say not directly. In the case of FM signals, with sufficiently low modulation frequency, you could use instantaneous frequency in the description. I believe you can trace that through derivatives of Fourier transforms, or Fourier transforms of derivatives.> 3) Modulation (AM) is a nonlinear process. If I start with a local > oscillator that outputs a clean sinusoid and then chop that, we get those > new Fourier frequencies.... How are they physically produced? The modulator > interacts with signal and.....?In the easy cases, though the non-linear operator of multiplication (by a time varying signal). -- glen
Reply by ●February 17, 20092009-02-17
On Feb 17, 11:40�am, cincy...@gmail.com wrote:> On Feb 17, 11:26�am, makol...@yahoo.com wrote: > > > > > > > > Again, I'm not sure what you're asking. They are physically produced > > > by the distortion that you apply to the signal. Those new frequencies > > > don't add energy (unless you're amplifying it in the process); some > > > energy is merely "stolen" from the pure sinusoidal input and shoved > > > over to other frequencies. > > > I disagree. > > > In the case of AM, the "carrier" remains the same amplitude at all > > times. �When modulation �is applied, the sidebands ARE ADDED power > > amounting to a total of 50% additional AVERAGE power at 100% > > modulation. > > > It takes a 50 Watt audio amp to plate modulate a 100 Watt RF > > transmitter, and that 50 Watts of audio goes into the sidebands. > > > CQ DX > > > Mark > > I was talking about the case that he mentioned where he runs a pure > sinusoid into a clipping circuit. The clipping operation won't add > energy, but it does introduce content at new frequencies. I agree with > you, in the traditional AM case, you're correct. > > Jason- Hide quoted text - > > - Show quoted text -ok agreed... thanks Mark
Reply by ●February 18, 20092009-02-18
fisico30 wrote:> Hello forum, > I have a few questions about bandwidth: > > Take a finite time signal, like a pulse. It must be composed of a > band of Fourier frequencies.***No. It has an infinite Fourier Transform because you define it as time-limited (finite time).> The notion of a single pure frequency belongs only to a sinusoidal > signal, which is infinite in duration.***Yes.>To measure a frequency we need > to have periodicity of an event forever. That is just theory, an > abstraction.***??? A measurement isn't usually an abstraction. A time-limited sinsuoid can have its frequency determined rather precisely. ***How do "event" and "forever" relate? Poor terminology will only get you in trouble.> > 1) Back to the pulse: are those composing Fourier frequencies somewhat > real?***Like totally. You compute the Fourier Transform of "the pulse" and that's all there is to it.>How does the hardware measure them, since they only belong to > abstract functions?***What hardware? Any hardware or algorithm? What abstract functions? You mean the infinite-length sinusoids? OK. They are what they are in the analytical sense. Perhaps it will help you to split your "world" into "analytical" considerations and "practical" considerations.>Maybe the hardware just does some math with the > received data...?***It surely does; one way or another.> If we could use a infinitely narrow-band tunable detector, would we > see energy at each of those Fourier frequencies proportional to their > amplitude?***You imply practical hardware and then you introduce an impossibility. Also, you mean "set of" detectors - one for each frequency. Not likely because an infinitely narrow filter has an impulse response that's infinite. There would be no steady state output unless the input were also infinite in length. ***However, the Fourier Transform does exactly this in an analytical sense.> > 2) There is another definition of frequency: instantaneous frequency.***Not a commonly accepted one!!> That measures not the re-occurrence of the exactly the same event but > the reappearance of the same state (peak), regardless of its maximum > amplitude.***????????????? (makes no sense).> Is there a relation between Fourier and Instantaneous frequency?***First, what is "Fourier frequency"? Not a known term. If you mean "frequency" resulting from a Fourier Transform then it's just "frequency". ***Second. If Fourier Frequency just means frequency then you're asking if there's a relationship between the frequency and Instantaneous frequency. What's implied but not stated is: "of a particular waveform or temporal record". ***The answer is a qualified "yes" in the sense that a GIVEN waveform will have a Fourier Transform. If the given waveform is a sinusoidal sweep then the Fourier Transform will reflect this. After that, it's dependent on how you define "instantaneous", the temporal window on the data, etc. etc.> > 3) Modulation (AM) is a nonlinear process.***OK.>If I start with a local > oscillator that outputs a clean sinusoid and then chop that, we get > those new Fourier frequencies.... How are they physically produced?***With a chopper.> The modulator interacts with signal and.....?***And what? What are you looking for here? Perhaps it's better to say that an amplitude modulator *multiplies* a sinusoid with another signal. That's a lot clearer. A chopper might be a multiplier input of +1, -1, +1, -1, ...... ***You can do the math if you multiply one sinusoid by another as the modulating signal. If the modulation index is less than 100% then there will be few new frequencies introduced. If it's greater then there will be a multiplicity of new frequencies introduced. ***Actually, an AM modulator with a constant sinusoid as one input can be viewed as a linear system (linear time-varying) but that's another and involved discussion. Where are the questions about bandwidth? Fred
Reply by ●February 18, 20092009-02-18
On Feb 17, 12:03�pm, Jerry Avins <j...@ieee.org> wrote:> fisico30 wrote: > > Hello forum, > > I have a few questions about bandwidth: > > > Take a finite time signal, like a pulse. It must be composed of a band of > > Fourier frequencies. > > I don't know what a Fourier frequency is. I don't think you do either; I > guess you mean something else. Can you clarify?it's standard terminology in harmonic analysis, read http://books.google.com/books?id=zQsupRg5rrAC&pg=PA37&lpg=PA37&dq=%22fourier+frequencies%22&source=web&ots=SuxllrEC0i&sig=bslLkLihXNKE2ch0KDdC4cBzFqg&hl=en&ei=qEacSYqDMYmGsQOe-qGsAg&sa=X&oi=book_result&resnum=10&ct=result
