symmetric 2D function....
in [DSP]
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From: Tim Wescott on 28 May 2010 18:18 On 05/28/2010 02:50 PM, dbd wrote: > On May 28, 11:19 am, Tim Wescott<t...(a)seemywebsite.now> wrote: >> On 05/28/2010 06:55 AM, dbd wrote: >> >>> On May 28, 5:43 am, "fisico32"<marcoscipioni1(a)n_o_s_p_a_m.gmail.com> >>> wrote: >>>> ... >>>> fisico > >>> Is your question a (continuous/infinite) theoretical one or do you >>> want a (sampled/finite) DSP answer? Your first sentence is not true in >>> the finite sampled domain for some definitions of even. > >> Which ones? Examples? AFAIK it's a universally accepted definition. > >> Tim Wescott > > DFT-even You're still confusing me. Do you mean the output of a usual DFT function (i.e. 'fft' in Matlab or Scilab), where it's even about the midpoint of the data set, and even about zero when you take the frequency mod length, and allow negative frequencies? I liked Dirk Bell's augmentation, 'even about something', i.e. (x - 10)^2 is even about 10. -- Tim Wescott Control system and signal processing consulting www.wescottdesign.com
From: dbd on 28 May 2010 21:24
On May 28, 3:18 pm, Tim Wescott <t...(a)seemywebsite.now> wrote: .... > > You're still confusing me. ... My concern is that the " f(t)=f(-t) " expression is only valid in an interval in the continuous domain. Since fiscio32 has a history of wandering between domains without warning (and this -is- comp.dsp) I wanted to understand where his question was c\o\m\i\n\g\ f\r\o\m\ going to. > Do you mean the output of a usual DFT > function (i.e. 'fft' in Matlab or Scilab), where it's even about the > midpoint of the data set, and even about zero when you take the > frequency mod length, and allow negative frequencies? > > I liked Dirk Bell's augmentation, 'even about something', i.e. (x - > 10)^2 is even about 10. > > -- > Tim Wescott I was assuming something like Dirk Bell's augmentation. And I was concerned about the problematic assumption we often see that the symmetry applies within the sequence. Where the sequence is [0 1 2 3 2 1 0] and "even about something" refers to the sample with value 3. The sequence is then certainly "even". >> fft([0 1 2 3 2 1 0]).' ans = 9 -4.54891733952231 - 2.19064313376741i 0.192021471630095 + 0.240787309403764i -0.14310413210779 - 0.626980168831352i -0.14310413210779 + 0.626980168831352i 0.192021471630095 - 0.240787309403764i -4.54891733952231 + 2.19064313376741i But the DFT of this real "even" sequence is neither real nor symmetric >> fft([0 1 2 3 2 1]).' ans = 9 -4 0 -1 0 -4 This "DFT-even" sequence does not satisfy "even about something" within the sequence but the fft output is real and symmetric and the sequence represents samples of the same triangle wave. A time modulo length definition provides a solution. The term used to refer to this solution is "DFT-even" The problem with letting " f(t)=f(-t) " alone stand is that it often leads to the choice of the wrong length in the discrete domain in the amazing event that someone tries to act on a comp.dsp answer. Dale B. Dalrymple |