Theory
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  Filter Design - Theory

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.

  Filter Design - Windows

The equations of various Windows used in FIR Filter Design section are presented below:

  1. Rectangular: w(n) = 1 for n = 0, 1,….., N-1

  2. Bartlett: w(n) = 1- (|n-N/2| / N/2) for n = 0 to N-1

  3. Hann: w(n) = 0.5- 0.5*cos(2*pi*n/N) for n = 0 to N-1

  4. Hamming: w(n) = 0.54 - 0.46*cos(2*pi*n/N) for n = 0 to N-1

  5. Blackman: w(n) = 0.42 - 0.5*cos(2*k*n/(N-1)) + 0.08*cos(4*pi*k/(N-1))

  6. Gaussian: w(n) = exp(-.5* (((alpha*(n-N/2))/(N/2)).^2))

  7. Dolph-Chebyshev : beta = cosh ( ( acosh (10^alpha) /N ) ) W(k)= ( (-1) ^k) * cos(N * acos( ( beta * cos(pi * k/N) ) ) ) / cosh(len * acosh(beta) )

  8. Lanczos: w(n) = sin( (n-N/2) *pi / N)

  9. Kaiser:

Harris, F. J. "On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform." Proceedings of the IEEE. Vol. 66 (January 1978)

  Filter Design - Parks-McClellan

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.

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