Bode's Amplitude/Phase relation for discrete time systems
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From: Demus on 21 May 2010 20:00 Could someone please show me what the discrete-time version of Bode's amplitude/phase relation looks like?
From: HardySpicer on 21 May 2010 23:03 On May 22, 12:00 pm, "Demus" <sodemus(a)n_o_s_p_a_m.hotmail.com> wrote: > Could someone please show me what the discrete-time version of Bode's > amplitude/phase relation looks like? Discrete-time is an approximation to analogue so Bodes Theorem is the same. There are no quick short-cuts for plotting Bode-plots however such as asmyptotic approximations ie straight line approximations with slopes multiples of +/- 20ndB/decade where n is 1,2,3etc Hardy
From: Tim Wescott on 22 May 2010 00:41 On 05/21/2010 08:03 PM, HardySpicer wrote: > On May 22, 12:00 pm, "Demus"<sodemus(a)n_o_s_p_a_m.hotmail.com> wrote: >> Could someone please show me what the discrete-time version of Bode's >> amplitude/phase relation looks like? > > Discrete-time is an approximation to analogue so Bodes Theorem is the > same. Eh? Aside from being completely wrong that's a very sensible and wise statement. Discrete time is discrete time, and within discrete time the z transform is exact. The Bode theorem is exact within discrete time control because the z transform is exact. There's absolutely no reason at all that one has to make any approximations when doing discrete time control of a continuous-time plant (ask me how before you start your flame). Sometimes the approximations are convenient, but they are not necessary. > There are no quick short-cuts for plotting Bode-plots however > such as asmyptotic approximations ie straight line approximations with > slopes multiples of +/- 20ndB/decade where n is 1,2,3etc Too true, at least for traditional "on paper" short cuts. Fortunately Scilab/Matlab/Octave/etc. make _really good_ short cuts, and even Excel can be coerced to do the job. -- Tim Wescott Control system and signal processing consulting www.wescottdesign.com
From: Tim Wescott on 22 May 2010 00:45 On 05/21/2010 05:00 PM, Demus wrote: > Could someone please show me what the discrete-time version of Bode's > amplitude/phase relation looks like? A heck of a lot like the continuous-time version. The interpretation of a Bode plot of a sampled-time control system is exactly the same as the interpretation of one for a continuous-time system -- only the fact that the thing repeats at Fs/2 and beyond is different (and handy -- you're never left worrying if you've ignored something important). Here's some examples: http://www.wescottdesign.com/articles/zTransform/z-transforms.html That paper got cut up and scattered around in two or three chapters of my book, which has a much more complete treatment of just about everything the paper touches: http://www.wescottdesign.com/actfes/actfes.html, http://www.elsevier.com/wps/find/bookdescription.cws_home/707797/description#description. -- Tim Wescott Control system and signal processing consulting www.wescottdesign.com
From: HardySpicer on 22 May 2010 04:05
On May 22, 4:41 pm, Tim Wescott <t...(a)seemywebsite.now> wrote: > On 05/21/2010 08:03 PM, HardySpicer wrote: > > > On May 22, 12:00 pm, "Demus"<sodemus(a)n_o_s_p_a_m.hotmail.com> wrote: > >> Could someone please show me what the discrete-time version of Bode's > >> amplitude/phase relation looks like? > > > Discrete-time is an approximation to analogue so Bodes Theorem is the > > same. > > Eh? Aside from being completely wrong that's a very sensible and wise > statement. > > Discrete time is discrete time, and within discrete time the z transform > is exact. The Bode theorem is exact within discrete time control > because the z transform is exact. > > There's absolutely no reason at all that one has to make any > approximations when doing discrete time control of a continuous-time > plant (ask me how before you start your flame). Sometimes the > approximations are convenient, but they are not necessary. > > > There are no quick short-cuts for plotting Bode-plots however > > such as asmyptotic approximations ie straight line approximations with > > slopes multiples of +/- 20ndB/decade where n is 1,2,3etc > > Too true, at least for traditional "on paper" short cuts. Fortunately > Scilab/Matlab/Octave/etc. make _really good_ short cuts, and even Excel > can be coerced to do the job. > > -- > Tim Wescott > Control system and signal processing consultingwww.wescottdesign.com Actually no. There is nothing special because you sample a system or a signal. If you sample fast enought you get back to analogue. Digital is just an approximation to analogue, nothing more. For example, take an integrator K/s. Use the Bilinear transform and sample high enough and it will have a slope of -20dB/decade just as the analogue case and a phase of -90 degrees.. However, if you are thinking of special contrived digital systems eg FIR then I might agree. Hardy |