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.

  • $\begingroup$ 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, 2021 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, 2021 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, 2021 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, 2021 at 15:46

1 Answer 1


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).


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.