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Unformatted text preview: The Cooper Union Department of Electrical Engineering ECE111 Signal Processing & Systems Analysis Problem Set II: Basic Systems Analysis Solution Key Spring 2010 1. A 5 MHz (real) sinewave is input to a 20 MHz A/D converter. (a) List all frequencies up to 60 MHz that would alias into 5 MHz if proper anti- aliasing &ltering is not used. The answer is & f input + mf s , yields: 5 ; 25 ; 45 MHz and 15 ; 35 ; 55 MHz (b) What is the proper cut-o frequency for the anti-aliasing &lter? (Not for this speci&c signal; I mean what the A/D converter should employ, in general) f s = 2 = 10 MHz (c) Specify the input signal on the following frequency scales: analog radian fre- quency; normalized digital radian frequency; digital frequency normalized to the sampling rate; digital frequency normalized to the Nyquist bandwidth. 5 MHz , ! analog = 2 &f = 3 : 14 10 7 rad= sec ; ! dig = 2 &f=f s = 2 &= 4 = &= 2 rad , f=f s = 5 = 20 = 1 = 4 , f=B Nyq = f= [ f s = 2] = 5 = 10 = 1 = 2 . The latter two are unitless....
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- Spring '08