How to rapidly read a Pole-Zero Diagram?
in [DSP]
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From: Shenzhi on 23 Mar 2010 08:09 When there are only one or two poles or zeros in a diagram(for a digital filter), it's easy to know its frequency response, the method have been introduced by Many DSP books. But when many poles and zeros appear in one diagram, how can we see its frequency response at a glance? Is there any book about it?
From: Rune Allnor on 23 Mar 2010 08:20 On 23 Mar, 13:09, "Shenzhi" <zhi.m.s...(a)gmail.com> wrote: > When there are only one or two poles or zeros in a diagram(for a digital > filter), it's easy to know its frequency response, the method have been > introduced by Many DSP books. > But when many poles and zeros appear in one diagram, how can we see its > frequency response at a glance? The basic principles still apply: - Poles must be inside the unit circle, for the filter to be causal and stable - The zeros must be inside the unit circle for the filter to have a causal and stable inverse - There are often many poles in the vicinity of the passband - There are often many zeros in the vicinity of the stoppand - Pole-zero patterns tend to become cluttered in the vicinity of notches or narrow transition bands The main difference between lower and higher orders are in the fine details, which you can not spot at a glance anyway. > Is there any book about it? No. If you *really* want to get into this, play with the pole- zero diagrams and frequency responses, and build intuition: First plot the pole-zero diagram of a filter, sketch how you think the frequency response will look like, and only then plot the frequency response. See how close you got. Do that a couple of times, with a few filter designs, and you will quickly start building intuition. But don't spend too much time on this! Rune
From: Shenzhi on 23 Mar 2010 08:49 Thanks so much for your help! I will do as your suggestions to test more filters. In many DSP materials, the authors just slightly adjust the poles and zeros in the diagram to achieve their goals. That always confused to me. "Rune Allnor" <allnor(a)tele.ntnu.no> e19c7858660f(a)x12g2000yqx.googlegroups.com... > On 23 Mar, 13:09, "Shenzhi" <zhi.m.s...(a)gmail.com> wrote: >> When there are only one or two poles or zeros in a diagram(for a digital >> filter), it's easy to know its frequency response, the method have been >> introduced by Many DSP books. >> But when many poles and zeros appear in one diagram, how can we see its >> frequency response at a glance? > > The basic principles still apply: > > - Poles must be inside the unit circle, for the filter to > be causal and stable > - The zeros must be inside the unit circle for the filter to > have a causal and stable inverse > - There are often many poles in the vicinity of the passband > - There are often many zeros in the vicinity of the stoppand > - Pole-zero patterns tend to become cluttered in the vicinity > of notches or narrow transition bands > > The main difference between lower and higher orders are in > the fine details, which you can not spot at a glance anyway. > >> Is there any book about it? > > No. If you *really* want to get into this, play with the pole- > zero diagrams and frequency responses, and build intuition: > First plot the pole-zero diagram of a filter, sketch how you > think the frequency response will look like, and only then > plot the frequency response. See how close you got. > > Do that a couple of times, with a few filter designs, and you > will quickly start building intuition. But don't spend too > much time on this! > > Rune
From: Tim Wescott on 23 Mar 2010 11:56 Shenzhi wrote: (top posting fixed) > > "Rune Allnor" <allnor(a)tele.ntnu.no> > e19c7858660f(a)x12g2000yqx.googlegroups.com... >> On 23 Mar, 13:09, "Shenzhi" <zhi.m.s...(a)gmail.com> wrote: >>> When there are only one or two poles or zeros in a diagram(for a digital >>> filter), it's easy to know its frequency response, the method have been >>> introduced by Many DSP books. >>> But when many poles and zeros appear in one diagram, how can we see its >>> frequency response at a glance? >> The basic principles still apply: >> >> - Poles must be inside the unit circle, for the filter to >> be causal and stable >> - The zeros must be inside the unit circle for the filter to >> have a causal and stable inverse >> - There are often many poles in the vicinity of the passband >> - There are often many zeros in the vicinity of the stoppand >> - Pole-zero patterns tend to become cluttered in the vicinity >> of notches or narrow transition bands >> >> The main difference between lower and higher orders are in >> the fine details, which you can not spot at a glance anyway. >> >>> Is there any book about it? >> No. If you *really* want to get into this, play with the pole- >> zero diagrams and frequency responses, and build intuition: >> First plot the pole-zero diagram of a filter, sketch how you >> think the frequency response will look like, and only then >> plot the frequency response. See how close you got. >> >> Do that a couple of times, with a few filter designs, and you >> will quickly start building intuition. But don't spend too >> much time on this! > > Thanks so much for your help! > I will do as your suggestions to test more filters. > In many DSP materials, the authors just slightly adjust the poles > and zeros in the diagram to achieve their goals. > That always confused to me. > Well, they're really adjusting the poles and zeros in the _filter_, then showing you a diagram. They may have forgotten how hard it was to develop their intuition, or they may be subtly encouraging you to develop yours. Don't be afraid to just plug the numbers into a math package and run a Bode plot. -- Tim Wescott Control system and signal processing consulting www.wescottdesign.com
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