N:32;
gamma:48/20;
M:N+1;
alpha:cosh(acosh(10^gamma)/N);
A(m):=abs(alpha*cos(%pi*m/N));
W(m):=((-1)^m)*chebyshev_t(N,A(m)); makelist(''ev(ratsimp(W(n)),numer),n,0,N-1);
freq= [251.1886431509343, - 105.9392735931824, 0.4193242363116815, - 0.6394550815653592, 0.01522099347604597, 0.3856457167948537, 0.5997410704897626, 0.7320135982679906, 0.8183989191419395, 0.8771985186325758, 0.9183630436608434, 0.9478210284728955, 0.9668451541730011, 1.000472238713574, 0.8156703834037801, 2.638631937232813, - 11.99999999999998, 2.638631937232824, 0.8156703834037801, 1.000472238713574, 0.966845154173002, 0.9478210284728955, 0.9183630436608434, 0.8771985186325758, 0.8183989191419395,
td=ifft(freq);
td=real(td);
N=32;
te=[td(1)/2,td(2:N),td(1)/2];
tf=te/max(te);
0.05060350341419111,0.09318854394997424,0.0891740552692859,0.180542307461633,0.194132939061669,0.306667930702plotting this shows wiggles, unsure why.
4942,0.334105377095744,0.4643736917713142,0.497180244238745,0.6369967107549066,0.6630579828897345,0.800695027
2395862,0.8068400400763767,0.9292125330996996,0.9046336599899251,1,0.9393020597770186,1,0.9046336599899251,0.
9292125330996994,0.8068400400763767,0.8006950272395861,0.6630579828897345,0.6369967107549066,0.49718024423874
5,0.4643736917713142,0.334105377095744,0.3066679307024942,0.194132939061669,0.180542307461633,0.0891740552692
859,0.09318854394997422,0.05060350341419111
Nevermind.. it seems the gamma needs2be integer.
Hello Johann Klammer. I just now saw your posts.
As far as I know, variable 'gamma' does not have to be an integer.
Looking at your Feb. 13 post, using N = 32 and gamma = 48/20, my MATLAB software computes exactly the same frequency vector as your posted "freq" vector. That is a good thing.
When I execute your code to compute your 'tf' vector (the final window sequence) I obtain the same result as my MATLAB code. As far as I can tell your computed 'tf' sequence is the correct final Chebeshev window sequence.
My computation of your code to compute your 'tf' vector produces:
tf =
0.0627, 0.0740, 0.1135, 0.1629, 0.2223, 0.2910, 0.3677, 0.4507,
0.5375, 0.6252, 0.7106, 0.7904, 0.8611, 0.9197, 0.9636, 0.9908,
1.0000, 0.9908, 0.9636, 0.9197, 0.8611, 0.7904, 0.7106, 0.6252,
0.5375, 0.4507, 0.3677, 0.2910, 0.2223, 0.1629, 0.1135, 0.0740,
0.0627.
When I plot your 'tf' window sequence it looks good to me.
[-Rick-]
Hi Johann.
I think the problem may be your 'chebyshev_t()' command. My MATLAB 'A(m)' sequence is equal to your 'A(m)' sequence, but my MATLAB 'W(m)' frequency-domain sequence is NOT equal to your 'freq' sequence. My 'W(m)' sequence is:
W(m) =
251.1886 -105.9393, 0.4193 -0.6395, 0.0152, 0.3856, 0.5997,
0.7320, 0.8184, 0.8772, 0.9184, 0.9477, 0.9685, 0.9831, 0.9927,
0.9982, 1.0000, 0.9982, 0.9927, 0.9831, 0.9685, 0.9477, 0.9184,
0.8772, 0.8184, 0.7320, 0.5997, 0.3856, 0.0152 -0.6395,
0.4193, -105.9393.
Perhaps you could use the processing in my blog's Step# 5 to compute your 'freq' sequence, and see what happens.
[-Rick-]
cheby_t.m
function retval = cheby_t (n,v)
if(abs(v)>1)
retval=cosh(n*acosh(v));
else
retval=cos(n*acos(v));
endif
endfunction
Hello Johann.
I can only make your Feb 26, 2020 code work if I multiply your final 'retval' sequence by an n-length sequence of 1, -1, 1, -1, ... . That is, in MATLAB code:
retval = (-1).^(0:n-1).*retval;
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