Please refer to "Discrete-Time Signal Processing" by Alan V. Oppenheim and Ronald W. Schafer , for a detailed explanation of the theoretical concepts presented in this GUI.
The equations of various Windows used in FIR Filter Design section are presented below:
Rectangular: w(n) = 1 for n = 0, 1,….., N-1
Bartlett: w(n) = 1- (|n-N/2| / N/2) for n = 0 to N-1
Hann: w(n) = 0.5- 0.5*cos(2*pi*n/N) for n = 0 to N-1
Hamming: w(n) = 0.54 - 0.46*cos(2*pi*n/N) for n = 0 to N-1
Blackman: w(n) = 0.42 - 0.5*cos(2*k*n/(N-1)) + 0.08*cos(4*pi*k/(N-1))
Gaussian: w(n) = exp(-.5* (((alpha*(n-N/2))/(N/2)).^2))
Dolph-Chebyshev : beta = cosh ( ( acosh (10^alpha) /N ) ) W(k)= ( (-1) ^k) * cos(N * acos( ( beta * cos(pi * k/N) ) ) ) / cosh(len * acosh(beta) )
The Parks-McClellan designs an optimum FIR filter given a set of specifications and uses Remez Iterations in order to design the filter. The Parks-McClellan algorithm for the design is referred from Chapter-7 of "Discrete-Time Signal Processing" by Alan V. Oppenheim and Ronald W. Schafer.