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I came across this problem while designing a FIR filter for given $\omega_p = 0.4\pi$ and $\omega_s = 0.6\pi$ along with the minimum stop-band attenuation $\delta_s$.

I have worked out some examples of design of FIR filters using Kaiser's window, where the filter length M is approximately:

$$M=\frac{A-8}{2.285\,\Delta\omega}\tag{1}$$

I found this similar question here in SE:What is the relation of the transition band's width and the filter order for the FIR windowing method, but in the accepted answer, it is explicitly specified

For the Kaiser window...

but no specification whether this specific formula in equation (1) can still be applied to other windowing methods too.

I know that I can still use other heuristics formulae like Fred Harris rule (as mentioned here: Filter Order Rule of Thumb), but my question is whether the formula in equation (1) be applied to my case or not.

EDIT

I have seen somewhere that the main lobe width of Hamming window used to find the filter length. For example, main lobe width in Hamming Window is $\frac{8\pi}{M}$ and equating this with transition band $\Delta \omega = 0.2\pi$ in my example, I get $M=40$. Can this also be used?

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