On Mon, May 07, 2012 at 08:54:16PM -0500, Daniel J Sebald wrote: > 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?
The answer to this is yes, you can define your own window function and pass in the window as a vector to either fir1 or fir2 rather than a string. This way you can define the window any way you like. And as Dan noted, the length of the window you create must be 1 more than the filter order. > > 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? The formula in [1] is correct, it's just that the indexing and the signs on the terms need to agree. If your indexing is from -N/2 to +N/2, the a1 and a3 terms are positive. If your indexing is from 0 to N, the a1 and a3 terms are negative, which is what [1] shows. > 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? But actually both the current and this behavior do not match ML's blackmanharris function, at least in the version I have at my disposal. Can anyone verify? I just ran it with a couple different lengths and it always returns an asymmetric window, whether the length is even or odd. Can't say whether this is intentional, other window functions seem to be symmetric. -- mike ------------------------------------------------------------------------------ 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
