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In the windowing design method for FIR filters, the impulse response for the desired frequency response filter is selected with a window. Typically the desired frequency response is a rectangular function in frequency (a brickwall filter, pass a group of frequencies and block the rest), in which case the ideal impulse response is a Sinc function. In this ...



Your first equation is the magnitude of the frequency response. So the squared magnitude of the transfer function becomes $$\big|H(s)\big|^2=\frac{1}{1+\left(\frac{-s^2}{\Omega_c^2}\right)^{N}}\tag{1}$$ Since $|H(s)|^2=H(s)H(-s)$, and since we want a causal and stable transfer function, we assign all poles in the left half-plane to $H(s)$. So for $N=1$ we ...

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