hi all, I am having difficulty coming to the mathematical solution to the FT of a periodic clock signal. Simple logic tells me that the signal power should be concentrated at the fundamental frequency (ie the clock freq) present in the signal. But when I solve it using the DTFT, I get the representation as the Sampled sinc function which implies that all my signal informatio(and power) is concentrated in the baseband near the zero frequency , which is contradictory to the prior statement. Similar situation arises when I try to get the spectrum of a periodic triangular wave(which can be thought of as an rough approximation of a sine-wave). Hence the signal power should be centred at the fundamental frequency and not the base freq. But I cannot conclude this result mathematically. Is there a flaw in the basic mathematics involving this? Or am I overlooking something really really fundamental? Can someone help me get a clearer picture of things? Thx and regards apurva
what is the frequncy spectrum of a clock signal?
Started by ●April 23, 2007
Reply by ●April 23, 20072007-04-23
On Apr 23, 11:29 am, apurva <agarwal.apu...@gmail.com> wrote:> hi all, > > I am having difficulty coming to the mathematical solution to the FT > of a periodic clock signal. Simple logic tells me that the signal > power should be concentrated at the fundamental frequency (ie the > clock freq) present in the signal. But when I solve it using the DTFT, > I get the representation as the Sampled sinc function which implies > that all my signal informatio(and power) is concentrated in the > baseband near the zero frequency , which is contradictory to the prior > statement. > > Similar situation arises when I try to get the spectrum of a periodic > triangular wave(which can be thought of as an rough approximation of a > sine-wave). Hence the signal power should be centred at the > fundamental frequency and not the base freq. But I cannot conclude > this result mathematically. Is there a flaw in the basic mathematics > involving this? Or am I overlooking something really really > fundamental? > > Can someone help me get a clearer picture of things? > > Thx and regards > apurvaIs there a non-zero DC offset to your clock signal? Have you tried putting of what you think the clock signal should look like into the FFT and see if you get the results you expect? Dirk
Reply by ●April 23, 20072007-04-23
a. There is no dc offset to any signal b. Yes, I plotted the FFT of the signal in MATLAB but I didn't get what I expected. On Apr 23, 8:36 pm, dbell <bellda2...@cox.net> wrote:> On Apr 23, 11:29 am, apurva <agarwal.apu...@gmail.com> wrote: > > > > > hi all, > > > I am having difficulty coming to the mathematical solution to the FT > > of a periodic clock signal. Simple logic tells me that the signal > > power should be concentrated at the fundamental frequency (ie the > > clock freq) present in the signal. But when I solve it using the DTFT, > > I get the representation as the Sampled sinc function which implies > > that all my signal informatio(and power) is concentrated in the > > baseband near the zero frequency , which is contradictory to the prior > > statement. > > > Similar situation arises when I try to get the spectrum of a periodic > > triangular wave(which can be thought of as an rough approximation of a > > sine-wave). Hence the signal power should be centred at the > > fundamental frequency and not the base freq. But I cannot conclude > > this result mathematically. Is there a flaw in the basic mathematics > > involving this? Or am I overlooking something really really > > fundamental? > > > Can someone help me get a clearer picture of things? > > > Thx and regards > > apurva > > Is there a non-zero DC offset to your clock signal? > > Have you tried putting of what you think the clock signal should look > like into the FFT and see if you get the results you expect? > > Dirk
Reply by ●April 23, 20072007-04-23
On Apr 23, 11:49 am, apurva <agarwal.apu...@gmail.com> wrote:> a. There is no dc offset to any signal > b. Yes, I plotted the FFT of the signal in MATLAB but I didn't get > what I expected. > On Apr 23, 8:36 pm, dbell <bellda2...@cox.net> wrote: >What I was asking, was if you had tried to put in an ideal clock signal (not the real one) and verified that the results matched your expectations? BTW, how many clock cycles are in your FFT input interval and what is the size? Are you doing any windowing or zero padding? Plz give details! Dirk
Reply by ●April 23, 20072007-04-23
apurva wrote:> hi all, > > I am having difficulty coming to the mathematical solution to the FT > of a periodic clock signal. Simple logic tells me that the signal > power should be concentrated at the fundamental frequency (ie the > clock freq) present in the signal. But when I solve it using the DTFT, > I get the representation as the Sampled sinc function which implies > that all my signal informatio(and power) is concentrated in the > baseband near the zero frequency , which is contradictory to the prior > statement. > > Similar situation arises when I try to get the spectrum of a periodic > triangular wave(which can be thought of as an rough approximation of a > sine-wave). Hence the signal power should be centred at the > fundamental frequency and not the base freq. But I cannot conclude > this result mathematically. Is there a flaw in the basic mathematics > involving this? Or am I overlooking something really really > fundamental? > > Can someone help me get a clearer picture of things?Is your clock high for approximately as much time as it is low? If so, it has the approximate harmonic structure of a square wave, which would then do for a model. Is it unipolar; that is, all positive or negative? If so, then it has a strong DC component, amounting (if truly square) to half of the total power. [(V/2)^2/(V^2/2) = 1/2] Since there are some harmonics, clearly less than half the power can reside in the fundamental. The series [1 + 1/9 + 1/25 ... + 1/(2n+1)^2 + ... is proportional to half the power in a square pulse train. The first term alone represents fundamental power. Jerry -- Engineering is the art of making what you want from things you can get. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Reply by ●April 23, 20072007-04-23
apurva wrote:> a. There is no dc offset to any signalWhat kind of clock is bipolar? ... Jerry -- Engineering is the art of making what you want from things you can get. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Reply by ●April 23, 20072007-04-23
> I am having difficulty coming to the mathematical solution to the FT > of a periodic clock signal. Simple logic tells me that the signal > power should be concentrated at the fundamental frequency (ie the > clock freq) present in the signal. But when I solve it using the DTFT, > I get the representation as the Sampled sinc function which implies > that all my signal informatio(and power) is concentrated in the > baseband near the zero frequency , which is contradictory to the prior > statement.That's the thing; sometimes "simple logic" just isn't right. If your signal was a sinusoid, then you would be right; you would have a concentration near the fundamental frequency. However, a pulse train is not a sinusoid, and it therefore contains other frequency content. It just so happens that it contains a lot of other frequencies, and, as you found, less than half of the signal power is concentrated at the frequency that corresponds with the pulse period. It's just one of those things that's not perfectly intuitive, but that's the way the math works out. Jason
Reply by ●April 25, 20072007-04-25
apurva wrote:> hi all, > > I am having difficulty coming to the mathematical solution to the FT > of a periodic clock signal. Simple logic tells me that the signal > power should be concentrated at the fundamental frequency (ie the > clock freq) present in the signal. But when I solve it using the DTFT,You mean the Fourier series?> I get the representation as the Sampled sinc function which implies > that all my signal informatio(and power) is concentrated in the > baseband near the zero frequency , which is contradictory to the prior > statement.That's not a contradiction. If you ignore DC offset, the fundamental harmonic has the highest amplitude. As the ratio (pulse width ) / (clock period) moves away from 1/2, the main lobe of the sinc gets sampled denser, thus the power in the overtones increases. The ratio with the lowest distortion factor (most power concentrated at fundamental) is 1/2. Regards, Andor
Reply by ●April 25, 20072007-04-25
Andor wrote:> apurva wrote: >> hi all, >> >> I am having difficulty coming to the mathematical solution to the FT >> of a periodic clock signal. Simple logic tells me that the signal >> power should be concentrated at the fundamental frequency (ie the >> clock freq) present in the signal. But when I solve it using the DTFT, > > You mean the Fourier series? > >> I get the representation as the Sampled sinc function which implies >> that all my signal informatio(and power) is concentrated in the >> baseband near the zero frequency , which is contradictory to the prior >> statement. > > That's not a contradiction. If you ignore DC offset, the fundamental > harmonic has the highest amplitude. As the ratio > > (pulse width ) / (clock period) > > moves away from 1/2, the main lobe of the sinc gets sampled denser, > thus the power in the overtones increases. The ratio with the lowest > distortion factor (most power concentrated at fundamental) is 1/2.He isn't ignoring the DC offset. He's puzzled that there's more power there than at the fundamental. Jerry -- Engineering is the art of making what you want from things you can get. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Reply by ●April 25, 20072007-04-25
Jerry Avins <jya@ieee.org> writes:> Andor wrote: >> apurva wrote: >>> hi all, >>> >>> I am having difficulty coming to the mathematical solution to the FT >>> of a periodic clock signal. Simple logic tells me that the signal >>> power should be concentrated at the fundamental frequency (ie the >>> clock freq) present in the signal. But when I solve it using the DTFT, >> You mean the Fourier series? >> >>> I get the representation as the Sampled sinc function which implies >>> that all my signal informatio(and power) is concentrated in the >>> baseband near the zero frequency , which is contradictory to the prior >>> statement. >> That's not a contradiction. If you ignore DC offset, the fundamental >> harmonic has the highest amplitude. As the ratio >> (pulse width ) / (clock period) >> moves away from 1/2, the main lobe of the sinc gets sampled denser, >> thus the power in the overtones increases. The ratio with the lowest >> distortion factor (most power concentrated at fundamental) is 1/2. > > He isn't ignoring the DC offset. He's puzzled that there's more power > there than at the fundamental.He shouldn't be. First-semester circuit analysis revealed that the power of a DC level v(t) = A is A^2 / R, and the power of a sinusoid of amplitude A is A^2 / (2*R). -- % Randy Yates % "Midnight, on the water... %% Fuquay-Varina, NC % I saw... the ocean's daughter." %%% 919-577-9882 % 'Can't Get It Out Of My Head' %%%% <yates@ieee.org> % *El Dorado*, Electric Light Orchestra http://home.earthlink.net/~yatescr
