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Say passband edge frequency=0.25 $\pi$

Stopband edge frequency=0.35 $\pi$

What is the cut off frequency? Do we average these 2 frequencies and write the answer or what is the procedure to find cut off frequency?

This is the question I want to solve-:

Use hamming window method to design a digital low pass filter with pass band edge frequency=0.25$\pi$, stopband edge frequency=0.35$\pi$ where main lobe width of hanning window is 8*$\pi$/M M is filter length.

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  • $\begingroup$ If the filter is FIR then it's the arithmetic mean, if it's of an IIR-type then it's the geometric mean. $\endgroup$ Sep 5 at 6:02
  • $\begingroup$ First you have to define what you mean by "cut-off frequency". If you don't say "$X$ dB cut-off" for some $X$ (e.g., $3$dB) then the term has no clearly defined meaning. There's no reason why "cut-off frequency" shouldn't be the same as "pass band edge". $\endgroup$
    – Matt L.
    Sep 5 at 10:49
  • $\begingroup$ The question is-:Use hamming window method to design a digital low pass filter with pass band edge frequency=0.25pi, stopband edge frequency=0.35pi where main lobe width of hanning window is 8pi/M M is filter length. @MattL. $\endgroup$
    – abdulkhan
    Sep 5 at 11:23
  • $\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$
    – Community Bot
    Sep 5 at 15:46
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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 case, the transition in the frequency response maps to a -6 dB cutoff after the windowing operation which will be half way between a passband edge frequency and stopband edge frequency.

The graphic below demonstrates this for a rectangular window. For other windows, the transition band will increase for a given number of taps, but the relationship between $f_c$ in the desired rectangular frequency response and $f_c$ that is midway in the transition band still applies.

rectangular window

For other design methods such as Parks-McClellan and Least Squares, the passband edge and stopband edge is provided to the design algorithm. The resulting 6 dB cutoff will similarly be half way between the passband edge and stopband edge. Generally it needs to be clarified as to what we mean by "cut-off" as this can refer to a -3 dB cutoff or -6 dB cutoff (or any dB cutoff).

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