Equivalent Noise Bandwidth

[derick007]

Please find attached my derivation of the equivalent noise bandwidth of a filter which produces a sinc x response i.e. H(f) = hT sin (ΠfT) / ΠfT.

I find the equivalent noise bandwidth, f = 1 / 2T ? i.e. halfway between zero and the first null of the sinc x response ?

 

[pancho_hideboo]

Consider Frequency response of Moving Average Filter is Sinc.

Moving Average Filter or CIC Filter is a most simple LPF.

 

[derick007]

Done some research - see first 2 attachments. Now convinced fenbw = 1/2T.

The third attachment is a variation on the same theme and I get the same result i.e. 1/2T ? Which I think should be 1/T, but I cannot see were I am going wrong in the attached derivation ? This time the frequency response of the practical filter is the same at that when you multiply the rectangular pulse of height h and width T, by a cosine of amplitude a, and frequency fc.