Complex FIR coefficients
in [DSP]
|
From: Rune Allnor on 30 Mar 2010 23:53 On 30 Mar, 18:24, Tim Wescott <t...(a)seemywebsite.now> wrote: > Randy Yates wrote: > > HardySpicer <gyansor...(a)gmail.com> writes: > > >> So I suppose it is complex because the imaginary part also has > >> frequency-selective properties as well as real. > > > Not exactly. It is complex because F(w) != F*(-w), i.e., the frequency > > response isn't Hermitian symmetric. Note I use "*" here to denote > > conjugation. > > That's not a _physical_ interpretation, because no physical system has a > frequency response that isn't Hermitian symmetric. Wrong. 1) 2D signals from antenna arrays are physical. 2) After DFT along the time axis the physical signal exist in (w,x) domain 3) Each vector along the x direction consits of complex-valued samples 4) Spatial narrow-band filters, e.g. for DoA or velocity filtering, needs to be complex-valued Physical as anything. Complex as it comes. In any sense of the word. Rune
From: Peter O. Brackett on 6 Apr 2010 13:52 Tim: [snip] > That's not a _physical_ interpretation, because no physical system has a > frequency response that isn't Hermitian symmetric. > > -- > Tim Wescott [snip] That is a common misconception but untrue. 'Physical' systems with non Hermitian symmetry are not only possible, indeed they have practical uses. Complex physical systems are rarely addressed in common textbooks and so remain somewhat obscure. Just because they are uncommon does not mean they don't exist! So called complex systems have been synthesized, designed, prototyped and even manufactured. Addmittedly they are uncommon, especially in natural form, but man can make them easily. This is more difficult to do (exactly) in analogue form than in digital form, but even complex analogue systems have been built. There have been numerous [OK... several] professional technical papers written about such systems over the years, beginning way back 40-50 years ago. Search for subjects such as "complex analogue filters", etc... will turn up some references. I have worked on and wrtten about complex analogue filters myself. -- Pete Indialantic By-the-Sea, FL
From: Mikolaj on 7 Apr 2010 03:38 On 31-03-2010 o 06:53:53 Rune Allnor <allnor(a)tele.ntnu.no> wrote: > Wrong. > > 1) 2D signals from antenna arrays are physical. > 2) After DFT along the time axis the physical signal exist > in (w,x) domain > 3) Each vector along the x direction consits of complex-valued > samples > 4) Spatial narrow-band filters, e.g. for DoA or velocity filtering, > needs to be complex-valued > > Physical as anything. Complex as it comes. In any sense of the word. > > Rune I can just put 'j' or 'i' befor any physical value and than interpret it at will. I can fit j to anything I want. But when we have description of something than partial imaginary result numbers can have no physical interpretation. Can you interpret imaginary impulse response? I can travel back in time on a paper. -- Mikolaj
From: glen herrmannsfeldt on 7 Apr 2010 06:53 Mikolaj <sterowanie_komputerowe(a)poczta.onet.pl> wrote: (snip) > I can just put 'j' or 'i' befor any physical value > and than interpret it at will. > I can fit j to anything I want. > But when we have description of something > than partial imaginary result numbers > can have no physical interpretation. I believe that in some cases complex physical quantities that are in exponents have a physical interpretation. As examples, the dielectric constant and its square root, the index of refraction. Other than in exponents, the use of complex numbers for physical quantities, such as describing phase shifts, seems more of a convenience, and not something with a physical interpretation. > Can you interpret imaginary impulse response? > I can travel back in time on a paper. -- glen
From: Mikolaj on 7 Apr 2010 06:03
on 07-04-2010 o 13:53:36 glen herrmannsfeldt <gah(a)ugcs.caltech.edu> wrote: (...) > I believe that in some cases complex physical quantities > that are in exponents have a physical interpretation. > As examples, the dielectric constant and its square root, > the index of refraction. Other than in exponents, > the use of complex numbers for physical quantities, > such as describing phase shifts, seems more of a > convenience, and not something with a physical > interpretation. (...) It seems that sometimes, luckily when you use complex (compressed, packed, combined, compact) way of describing few dependent physical things their imaginary part (additional dimension used for compression) can be human understandable and could have interpretation. But you can always decompress complex matrix to it's scalar version equations. -- Mikolaj |