求助AD和采样混淆问题

1.<br />Assume&nbsp;a&nbsp;Sigma-Delta&nbsp;ADC&nbsp;has&nbsp;a&nbsp;sampling&nbsp;rate&nbsp;of&nbsp;1MHz.&nbsp;The&nbsp;interested&nbsp;signal&nbsp;band&nbsp;is<br />from&nbsp;0&nbsp;to&nbsp;8kHz.<br />a.&nbsp;What&nbsp;value&nbsp;of&nbsp;R&nbsp;and&nbsp;C&nbsp;in&nbsp;an&nbsp;RC&nbsp;anti-aliasing&nbsp;filter&nbsp;should&nbsp;be&nbsp;used&nbsp;to&nbsp;assure&nbsp;that&nbsp;the<br />signal&nbsp;distortion&nbsp;within&nbsp;the&nbsp;interested&nbsp;band&nbsp;has&nbsp;less&nbsp;than&nbsp;-80dB.<br />b.&nbsp;Suppose&nbsp;there&nbsp;is&nbsp;a&nbsp;white&nbsp;noise&nbsp;presence&nbsp;between&nbsp;0&nbsp;to&nbsp;1MHz&nbsp;with&nbsp;magnitude&nbsp;of&nbsp;10uV<br />RMS.&nbsp;With&nbsp;your&nbsp;RC&nbsp;filter,&nbsp;what&nbsp;kind&nbsp;of&nbsp;extra&nbsp;noise&nbsp;level&nbsp;will&nbsp;be&nbsp;seen&nbsp;by&nbsp;the&nbsp;ADC&nbsp;due&nbsp;to<br />the&nbsp;aliasing&nbsp;effect?<br />2&nbsp;.<br />Suppose&nbsp;a&nbsp;signal&nbsp;is&nbsp;sampled&nbsp;at&nbsp;the&nbsp;sampling&nbsp;rate&nbsp;Fs.&nbsp;Now&nbsp;you&nbsp;want&nbsp;to&nbsp;resample&nbsp;it&nbsp;at&nbsp;half<br />the&nbsp;rate&nbsp;1/2Fs.&nbsp;From&nbsp;the&nbsp;lecture,&nbsp;one&nbsp;needs&nbsp;to&nbsp;insert&nbsp;a&nbsp;low&nbsp;pass&nbsp;filter&nbsp;with&nbsp;cut&nbsp;off<br />frequency&nbsp;at&nbsp;&frac14;Fs&nbsp;and&nbsp;beyond&nbsp;before&nbsp;the&nbsp;down&nbsp;sampling.&nbsp;This&nbsp;combined&nbsp;process&nbsp;is&nbsp;called<br />decimation.&nbsp;Please&nbsp;explain&nbsp;why&nbsp;the&nbsp;low&nbsp;pass&nbsp;filter&nbsp;is&nbsp;needed.<br /><br />~~谢谢您通俗的解释.