solns2_600

solns2_600 - ECE-600 Introduction to Digital Signal...

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

View Full Document Right Arrow Icon

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

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

Unformatted text preview: ECE-600 Introduction to Digital Signal Processing Autumn 2011 Homework #2 Oct. 7, 2011 HOMEWORK SOLUTIONS #2 1. (a) CTFT modulation property: F CTFT { x ( t ) e j Ω t } = integraldisplay ∞-∞ x ( t ) e j Ω t e- j Ω t dt = integraldisplay ∞-∞ x ( t ) e- j (Ω- Ω ) t dt = X c ( j (Ω- Ω )) via the CTFT definition (b) CTFT shift property: F CTFT { x ( t- τ ) } = integraldisplay ∞-∞ x ( t- τ ) e- j Ω t dt = integraldisplay ∞-∞ x ( q ) e- j Ω( q + τ ) dq via substitution q = t- τ (limits don’t change) = e- j Ω τ integraldisplay ∞-∞ x ( q ) e- j Ω q = e- j Ω τ X c ( j Ω) via the CTFT definition (c) DTFT property of real-valued x [ n ]: X * ( e- jω ) = parenleftBigg summationdisplay n x [ n ] e- j (- ω ) n parenrightBigg * using DTFT definition = summationdisplay n x * [ n ] e- jωn distributing the conjugation & ( e jωn ) * = e- jωn = summationdisplay n x [ n ] e- jωn since real-valued x [ n ] implies x * [ n ] = x [ n ] = X ( e jω ) using DTFT definition 2. (a) The Fourier series says that we can write any T-period signal p ( t ) as...
View Full Document

This note was uploaded on 10/29/2011 for the course ECE 600 taught by Professor Clymer,b during the Fall '08 term at Ohio State.

Page1 / 3

solns2_600 - ECE-600 Introduction to Digital Signal...

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