On 05/07/2012 07:39 PM, James Steward wrote: > On 08/05/12 09:39, James Steward wrote: >> Hi, >> >> Regarding the fir1 function and the "blackmanharris" window; >> >> If I specify an even number of coefficients (n) it produces a symmetric >> filter with an odd number of coefficients (n+1). >> >> If I specify an odd number of coefficients it produces a non symmetric >> filter with an even number of coefficients.
N is the order, not the number of coefficients. E.g., second order equation would have three coefficients. >> octave:39> version >> ans = 3.0.5 >> octave:40> b=fir1(8, 0.5, "blackmanharris") >> b = >> >> Columns 1 through 8: >> >> -7.1851e-08 -2.8280e-03 2.6042e-04 2.7158e-01 6.1193e-01 >> 2.7158e-01 2.6042e-04 -2.8280e-03 >> >> Column 9: >> >> -7.1851e-08 >> >> octave:41> b=fir1(7, 0.5, "blackmanharris") >> b = >> >> -3.8206e-04 -5.2516e-04 2.6785e-02 3.8140e-01 6.1393e-01 >> 1.2791e-01 -1.5875e-02 -3.8206e-04 >> >> octave:42> >> >> Is there some trick to producing a symmetric "blackmanharris" windowed >> filter with an even number of coefficients? >> > > In reply to myself, I looked at the wikipedia page [1] that describes > the Blackman-Harris filter, and wrote my own blackmanharris.m function > from that. It seems to work just fine, though with no parameter > sensibility checking. > > Then out of curiosity I checked my installed signal library function [2] > and found that it is certainly different. > > [1] > http://en.wikipedia.org/wiki/Window_function#Blackman.E2.80.93Harris_window > [2] /usr/share/octave/packages/signal-1.0.10/blackmanharris.m Good catch James. The first thing I recognize is that the formula doesn't appear to match what is listed in the Wikipedia reference. In the file [2] is the code a0 = 0.35875; a1 = 0.48829; a2 = 0.14128; a3 = 0.01168; n = -ceil(N/2):N/2; w = a0 + a1.*cos(2.*pi.*n./N) + a2.*cos(4.*pi.*n./N) + a3.*cos(6.*pi.*n./N); But according to [1], it should be "- a1" and "- a3". HOWEVER, I made that change and ended up with a window where the tail is weighted more than the center, so I think that Wikipedia might have the wrong formula. Agreed? Also, this formula inside of blackmanharris.m: n = -ceil(N/2):N/2; does not produce the desired result for N odd. octave:33> N=7 N = 7 octave:34> n = -ceil(N/2):N/2 n = -4 -3 -2 -1 0 1 2 3 Instead of defining 'n' the way the code does, it might be better to use the description from the Wiki page that says "w(n) = w_0(n - (N-1)/2)", this N not being the same as the N in the lines above. Note that blackmanharris.m uses an input L which is the length of window and N = L - 1. I think the definition of n inside blackmanharris.m should be: n = (0:N) - N/2; Does that produce the result you are expecting James? Dan > > Regards, > James. > > ------------------------------------------------------------------------------ > Live Security Virtual Conference > Exclusive live event will cover all the ways today's security and > threat landscape has changed and how IT managers can respond. Discussions > will include endpoint security, mobile security and the latest in malware > threats. http://www.accelacomm.com/jaw/sfrnl04242012/114/50122263/ > _______________________________________________ > Octave-dev mailing list > Octave-dev@lists.sourceforge.net > https://lists.sourceforge.net/lists/listinfo/octave-dev > -- Dan Sebald email: daniel(DOT)sebald(AT)ieee(DOT)org URL: http://www(DOT)dansebald(DOT)com ------------------------------------------------------------------------------ Live Security Virtual Conference Exclusive live event will cover all the ways today's security and threat landscape has changed and how IT managers can respond. Discussions will include endpoint security, mobile security and the latest in malware threats. http://www.accelacomm.com/jaw/sfrnl04242012/114/50122263/ _______________________________________________ Octave-dev mailing list Octave-dev@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/octave-dev
