Three-Term Blackman-Harris

Properties:

• $\alpha_0 = 0.4243801$ $\alpha_1 = 0.4973406$ , and $\alpha_2 = 0.0782793$ .
• Side-lobe level $-71.5$ dB.
• Side lobes roll off $\approx 6$ dB per octave in the absence of aliasing (like rectangular and Hamming).
• All degrees of freedom (scaling aside) are used to minimize side lobes (like Chebyshev-Hamming $\approx$ Hamming).

Matlab:

N = 101; L = 3; No2 = (N-1)/2; n=-No2:No2;
ws = zeros(L,3*N); z = zeros(1,N);
for l=0:L-1
  ws(l+1,:) = [z,cos(l*2*pi*n/N),z];
end
% 3-term Blackman-Harris(-Nuttall):
alpha = [0.4243801, 0.4973406, 0.0782793];
w = alpha * ws;