process of averaging is equivalent to lowpass filtering in the frequency domain

[pankaj jha]

Hello everyone!!!
Can anyone give me the derivation/logic behind the statement---- "The process of averaging is equivalent to lowpass filtering in the frequency domain."

 

[FvM]

I can accept the statement as a first guess. Strictly spoken, you have to ask for the exact averaging method applied. You can describe it by an impulse response h(t) and calculate the fourier transform to get the involved frequency domain characteristic. A rectangular impulse response according to a "boxcar" averager e.g. results in a sin(x)/x frequency characteristic, which is somewhat different from a simple lowpass.

 

[pankaj jha]

I can accept the statement as a first guess. Strictly spoken, you have to ask for the exact averaging method applied. You can describe it by an impulse response h(t) and calculate the fourier transform to get the involved frequency domain characteristic. A rectangular impulse response according to a "boxcar" averager e.g. results in a sin(x)/x frequency characteristic, which is somewhat different from a simple lowpass.

Dear FvM,
Thanks again for ur promptness.
My averaging process pertains to the decimation done in sigma delta modulators. Plz suggest any paper or text to understand the averaging through decimation.