I came across this confusion in Chapter 16,"Book - The Scientist and Engineers guide to DSP" and Topic is "Windowed Sinc-Filters". I am doing some calculations for designing the sinc filter and came across these doubts:
M = 4/BW
where "M" is the filter kernel length and "BW" is the transition bandwidth. The author says that "The BW must be expressed as a fraction of sampling rate with a value between 0 to 0.5 and same goes with the cut off frequency". For the values of M = 20, 40, 200, the BW is 0.2, 0.1, 0.02 and like we can see, it satisfies the condition of 0 to 0.5.
After I searched online, I understood that the value of cut off frequency and BW to exist between 0 to 0.5 has to do something with the power (dB) and presumed that 0 is 0db and 0.5 is -3 dB, since 10log(0.5) = -3dB.
My question is, what is the relationship between the cutoff of frequency and BW being a fraction of the sampling rate and between the values 0 to 0.5? What does it mean?. Is it something to do with the frequency components present beyond the cut off freq or BW being attenuated?
For example: If my sampling rate is 100sps, so the cut off frequency and BW must be a fraction of 100 sps with a value between 0 to 0.5?