Hi, Can anyone give me a rigorous math definition of the term "even symmetric filter"? TIA, Matt
Does anyone know the Mathematical Definition of Even Symmetric Filter?
Started by ●December 13, 2006
Reply by ●December 13, 20062006-12-13
"junoexpress" <MTBrenneman@gmail.com> wrote in news:1166038177.991529.323410@t46g2000cwa.googlegroups.com:> Hi, > > Can anyone give me a rigorous math definition of the term "even > symmetric filter"? > > TIA, > > Matt > >For some value of j, x[j+k]=x[j-k] for every k -- Scott Reverse name to reply
Reply by ●December 13, 20062006-12-13
junoexpress wrote:> Hi, > > Can anyone give me a rigorous math definition of the term "even > symmetric filter"?Back up a bit. Do you know the meanings of "even symmetry" and "odd symmetry"? A cosine has even symmetry about the origin, while a sine has odd symmetry. Can you take it from there? Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●December 13, 20062006-12-13
Nope. Doesn't work. For [1 2 2 1], what is j if k is an integer? Dirk Scott Seidman wrote:> "junoexpress" <MTBrenneman@gmail.com> wrote in > news:1166038177.991529.323410@t46g2000cwa.googlegroups.com: > > > Hi, > > > > Can anyone give me a rigorous math definition of the term "even > > symmetric filter"? > > > > TIA, > > > > Matt > > > > > > For some value of j, x[j+k]=x[j-k] for every k > > -- > Scott > Reverse name to reply
Reply by ●December 13, 20062006-12-13
"dbell" <bellda2005@cox.net> wrote in news:1166039602.604314.83630 @t46g2000cwa.googlegroups.com:> Nope. Doesn't work. > > For [1 2 2 1], what is j if k is an integer? > > Dirk > > Scott Seidman wrote: >> "junoexpress" <MTBrenneman@gmail.com> wrote in >> news:1166038177.991529.323410@t46g2000cwa.googlegroups.com: >> >> > Hi, >> > >> > Can anyone give me a rigorous math definition of the term "even >> > symmetric filter"? >> > >> > TIA, >> > >> > Matt >> > >> > >> >> For some value of j, x[j+k]=x[j-k] for every k >> >> -- >> Scott >> Reverse name to reply > >OK, one of either the above or x[j+.5 +(k+.5)] = x[j+.5 -(k+.5)] must be true -- Scott Reverse name to reply
Reply by ●December 13, 20062006-12-13
I'm a mathematician working on a problem with a colleague. She's trying to find the center freq of the FFT of a discrete BPSK signal. The problem is that the PSD at the center freq (i.e. your estimate for the "true" signal freq) is often not the local max: instead what often happens is that the FFT gets "split" about the true center freq, with the max FFT values occuring on both sides of the center freq. So using the max PSD value is not a good method for finding the center frequency. The one thing that struck me when she showed me the FFT about the center freq (for a simulated BPSK signal), was how symmetric it was. When I used some Monte-Carlo simulations and played around with different measures of "symmetry" for some window (of say n pts) around the center freq, like skewness, odd moments, etc. , what I found was that the following function ALWAYS performed superior ro any other function. This function always located the true center freq _exactly_. The function was: S(k) = Sum on k from k=1 to n of [F(k-j) - F(j+k)]^2 where F(*) = PSD at pt (*) So this function is essentially minimizing the rms deviation of the PSD and its image inverted about pt k. I am wondering if in DSP this is a type of "even symmetric filter", which was what motivated my original question. TA, Matt Scott Seidman wrote:> "dbell" <bellda2005@cox.net> wrote in news:1166039602.604314.83630 > @t46g2000cwa.googlegroups.com: > > > Nope. Doesn't work. > > > > For [1 2 2 1], what is j if k is an integer? > > > > Dirk > > > > Scott Seidman wrote: > >> "junoexpress" <MTBrenneman@gmail.com> wrote in > >> news:1166038177.991529.323410@t46g2000cwa.googlegroups.com: > >> > >> > Hi, > >> > > >> > Can anyone give me a rigorous math definition of the term "even > >> > symmetric filter"? > >> > > >> > TIA, > >> > > >> > Matt > >> > > >> > > >> > >> For some value of j, x[j+k]=x[j-k] for every k > >> > >> -- > >> Scott > >> Reverse name to reply > > > > > > OK, one of either the above or > x[j+.5 +(k+.5)] = x[j+.5 -(k+.5)] must be true > > > -- > Scott > Reverse name to reply
Reply by ●December 13, 20062006-12-13
> S(k) = Sum on k from k=1 to n of [F(k-j) - F(j+k)]^2Should read with the summation index being j not k, so the correct eqn is: S(k) = Sum on j from j=1 to n of [F(k-j) - F(j+k)]^2 Sorry, Matt
Reply by ●December 14, 20062006-12-14
Matt wrote:> I am wondering if in DSP this is a type of "even symmetric filter", > which was what motivated my original question.The symmetry property is w.r.t. the impulse response of the filter, and has (almost) nothing to do with the shape of the frequency response. Regards, Andor
Reply by ●December 14, 20062006-12-14
junoexpress wrote:> I'm a mathematician working on a problem with a colleague. She's trying > to find the center freq of the FFT of a discrete BPSK signal. The > problem is that the PSD at the center freq (i.e. your estimate for the > "true" signal freq) is often not the local max: instead what often > happens is that the FFT gets "split" about the true center freq, with > the max FFT values occuring on both sides of the center freq. So using > the max PSD value is not a good method for finding the center > frequency.Since you seem to be running into FFT resolution issues, is zero-padding the time domain signal to generate more points in the FFT an option? If your frequency bins are more finely spaced, you're more likely to get a good estimate for the peak. Jason
Reply by ●December 14, 20062006-12-14
Andor wrote:> Matt wrote: > > > I am wondering if in DSP this is a type of "even symmetric filter", > > which was what motivated my original question. > > The symmetry property is w.r.t. the impulse response of the filter, and > has (almost) nothing to do with the shape of the frequency response. > > Regards, > AndorThank you. That defintely answers my question. Matt
