pulsewidth and bandwidth
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From: Fan.Zhang on 26 Jul 2010 21:30 >OK, I am confused even more. The OP said >(without defining what is meant by pulsewidth >or bandwidth) > >OP> bandwidth = 1/pulsewidth. Why? > >to which several people replied, and Robert >Bristow-Johnson said (I think) that the >relationship stated by the OP is true for >Gaussian pulses if pulsewidth and >bandwidth are defined in terms of 92.4% >energy containment. Jitendra Rayala said >in his second post that the OP's relationship >holds for some pulses (but did not specify >which ones he had in mind). He also >said that when bandwidth and pulsewidth >are taken to mean rms bandwidth df and >rms pulsewidth dt, then the inequality > >JR1> dt*df >= 1/2 > >or perhaps > >JR2> dt*df >= 1/(4 pi) > >is applicable to *all* pulses (neither of >which contradict the assertion that the >product equals 1 for some pulses). >For *most* pulses, the inequality would >be strict: dt*df is *larger* than 1/2 or >1/(4 pi). But for a few select pulses >(Gaussians?), it might be that dt*df >*equals* 1/2 or 1/(4 pi). Does it? and >which is the minimum value that is >achieved: 1/2 or 1/(4 pi)? > > --Dilip Sarwate > > Thanks for all your comments on this thread.As the OP owner, I would like to say something about '1/2' and '1'. If we define the bandwidth of a system as the interval of POSITIVE frequencies over which the magnitude |H(f)| remains within a specified value. We may get 2 values for baseband and passband. bandwidth of baseband is (from 0 to Fm). bandwidth of passband is (from Fc-Fm to Fc+Fm). where Fc is the carrier, Fm is the highest frequency of signal. "We need twice as much transmission bandwith to transmit a DSB version of the signal than we do to transmit its baseband counterpart" ----'Digital communications fundamentals and applications 2nd Ed--Bernard Sklar' Section1.7.1 So I personal think it depends on baseband or passband, when we talk about the bandwidth. it may lead to different relation to the pulsewidth. Thanks you all! Fan
From: glen herrmannsfeldt on 26 Jul 2010 21:53
Fan.Zhang <zf624(a)n_o_s_p_a_m.sina.com> wrote: (snip) > Thanks for all your comments on this thread.As the OP owner, I would like > to say something about '1/2' and '1'. > If we define the bandwidth of a system as the interval of POSITIVE > frequencies over which the magnitude |H(f)| remains within a specified > value. > We may get 2 values for baseband and passband. > bandwidth of baseband is (from 0 to Fm). > bandwidth of passband is (from Fc-Fm to Fc+Fm). It is convenient to say that the lower sideband of an AM-DSB signal comes from the negative frequencies of the source. All the fun places you can move the factor of two around to. > where Fc is the carrier, Fm is the highest frequency of signal. > "We need twice as much transmission bandwith to transmit a DSB version of > the signal than we do to transmit its baseband counterpart" Except that you can't transmit, in the usual sense, a baseband signal. > ----'Digital communications fundamentals and applications 2nd Ed--Bernard > Sklar' Section1.7.1 > So I personal think it depends on baseband or passband, > when we talk about the bandwidth. it may lead to different > relation to the pulsewidth. Well, it could also be FM or AM-SSB. But those are modulation choices for the baseband signal, and shouldn't really count. (Unless you actually want to sample them, or use them to modulate another carrier.) -- glen |