# When does a Window function's sidelobe level become out of band attenuation?

Another question I'm struggling to answer by myself.

For a Window function, say Blackman (response pictured), what is the out of band attenuation? If I'm designing a filter with out of band attenuation of 40dB, is it the level of the first sidelobe that I'm interested in? Or is the out of band attenuation dictated by something else (like 3rd sidelobe level for example?)

Thanks!

• That depends on what you define to be "your" band. It's not a property of the filter, but of how you defined your bands. – Marcus Müller Nov 10 '17 at 7:38

Windows with low sidelobe levels have large transition bandwidth's. Transition bandwidth is inversely proportional to N for a given window. Indeed, the ratio of transition width over sidelobe level in dB for fixed length N is virtually a constant.

We can use the following empirical formula to estimate the required filter length

where,

• N is filter length,
• A is the out of band attenuation in dB
• fs is the sampling frequency
• Hi, yes I understand this. What I really want to know is what defines the out of band attenuation. Is is the height of the first sidelobe? Or some other metric? – dsp_yes Nov 10 '17 at 7:15
• this is not an answer to OP's question, I'm afraid. – Marcus Müller Nov 10 '17 at 7:37