Filter and inverse filter =/ timedelay?
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From: Jerry Avins on 26 Jul 2010 14:28 On 7/26/2010 2:13 PM, Tim Wescott wrote: ... > In the mathematical world you can take a minimum-phase transfer > function, you can find a stable, causal inverse, you can multiply this > by the original transfer function, and you can get a cascade of transfer > functions whose impulse response is unity. > > You can do this regardless of whether you're in discrete or continuous > time. > > Then you can go and simulate this behavior, and if you don't pay > attention to all the points that I raised, you can get a simulation that > "tells" you that a real system really is perfectly invertible. The only > problem with it is that it is wrong. There will be the obvious delay if you actually build a cascade of the minimum-phase filter and its stable, causal inverse. In the Mathemagic Kingdom, when poles and zeros cancel, they just go away. The real world isn't so obliging. ... Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
From: Demus on 26 Jul 2010 14:46 >There will be the obvious delay if you actually build a cascade of the >minimum-phase filter and its stable, causal inverse. In the Mathemagic >Kingdom, when poles and zeros cancel, they just go away. The real world >isn't so obliging. > > ... > >Jerry How would one go about computing this delay (just to see if I understand this correctly)?
From: Vladimir Vassilevsky on 26 Jul 2010 14:59 Jerry Avins wrote: > There will be the obvious delay if you actually build a cascade of the > minimum-phase filter and its stable, causal inverse. In the Mathemagic > Kingdom, when poles and zeros cancel, they just go away. The real world > isn't so obliging. Jerry, Once you said very good phrase; I remembered it: "Digits are the models of numbers" (c) Jerry Avins VLV
From: Jerry Avins on 26 Jul 2010 15:11 On 7/26/2010 2:46 PM, Demus wrote: >> There will be the obvious delay if you actually build a cascade of the >> minimum-phase filter and its stable, causal inverse. In the Mathemagic >> Kingdom, when poles and zeros cancel, they just go away. The real world >> isn't so obliging. >> >> ... >> >> Jerry > How would one go about computing this delay (just to see if I understand > this correctly)? Compute the separate delays and add them up. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
From: Jerry Avins on 26 Jul 2010 15:16
On 7/26/2010 2:59 PM, Vladimir Vassilevsky wrote: > > > Jerry Avins wrote: > > >> There will be the obvious delay if you actually build a cascade of the >> minimum-phase filter and its stable, causal inverse. In the Mathemagic >> Kingdom, when poles and zeros cancel, they just go away. The real >> world isn't so obliging. > > Jerry, > > Once you said very good phrase; I remembered it: > > "Digits are the models of numbers" (c) Jerry Avins Did I really? How clever of me! Jerry -- Engineering is the art of making what you want from things you can get. ����������������������������������������������������������������������� |