hw3_filtering_I-Q_modulation - Massachusetts Institute of...

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Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.02 Intro to EECS II Spring 2008 Homework #3: Filtering and I/Q modulation Distributed: February 22, 2008 Due: February 29, 2008 1. In this problem, we will explore the two-stage demodulator shown in Figure 1 below. This system resembles the receiver we have used in labs. In particular, the USRP board can be thought of as providing the first stage of mixing and filtering in hardware, and then Matlab of providing the second stage of mixing and filtering software. Figure 1 a) Given the definition of the Fourier Transform, namely xt () = Xf e j 2 π ft df −∞ and = e j 2 ft dt −∞ show that shifting in frequency corresponds to multiplication in time by a complex exponential: ( ) ( ) 2 shift jft shift ex t X f f ⇔+ b) Given the Fourier Transform property in part (a), plot X 1 f ( ) and X 2 f assuming that rt = e j 2 10 MHz t .
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c) Given your results from part (b), what is an appropriate signal zt () such that the
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hw3_filtering_I-Q_modulation - Massachusetts Institute of...

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