problem_set7 - EE 511 Problem Set 7 Due on 16 Nov 2007 1....

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
EE 511 Problem Set 7 Due on 16 Nov 2007 1. Let ˆ X t be the Hilbert transform of the W.S.S. random process X t . Show that (i) S ˆ X ( f ) = S X ( f ), (ii) S X ˆ X ( f ) = - S ˆ XX ( f ), (iii) E [ X t ˆ X t ] = 0, and (iv) for Z t = X t + j ˆ X t , determine S Z ( f ) in terms of S X ( f ). 2. The power spectrum of a W.S.S. band-pass random process X t is as shown in Figure 1. Sketch S X I ( f ), S X Q ( f ) and S X I X Q ( f ) assuming 5 MHz to be the carrier frequency. S (f) X f(MHz) 4 5 7 -7 -5 -4 1 Figure 1: 3. Repeat problem 2 assuming 4 MHz to be the carrier frequency. 4. A narrow-band noise process N t has zero-mean and auto-correlation function R N ( τ ). Its power spectral density S N ( f ) is centered about ± f c . The in-phase and quadrature compo- nents N I t and N Q t are de±ned by N I t = N t cos 2 πf c t + ˆ N t sin 2 πf c t and N Q t = ˆ N t cos 2 πf c t - N t sin 2 πf c t . Show that R N I ( τ ) = R N Q ( τ ) = R N ( τ ) cos 2 πf c τ + ˆ R N ( τ ) sin 2
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 10/26/2011 for the course ECE 171 taught by Professor Tu during the Spring '11 term at Aarhus Universitet.

Page1 / 2

problem_set7 - EE 511 Problem Set 7 Due on 16 Nov 2007 1....

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online