hw2_600(2)

# hw2_600(2) - ECE-600 Introduction to Digital Signal...

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Unformatted text preview: ECE-600 Introduction to Digital Signal Processing Autumn 2010 Homework #2 Oct. 1, 2010 HOMEWORK ASSIGNMENT #2 Due Fri. Oct. 8, 2010 (in class) 1. (a) Prove the CTFT convolution property: integraldisplay ∞-∞ x ( τ ) w ( t- τ ) dτ CTFT ←→ X c ( j Ω) W c ( j Ω). (b) Prove the CTFT multiplication property: x ( t ) w ( t ) CTFT ←→ 1 2 π integraldisplay ∞-∞ X c ( jξ ) W c ( j (Ω- ξ )) dξ (c) Say X ( e jω ) = F DTFT { x [ n ] } is real-valued. Prove x [ n ] = x * [- n ]. (d) Say x [ n ] is real-valued. For X ( e jω ) = F DTFT { x [ n ] } , prove that X ( e jω ) = X * ( e- jω ). Note: For (a)-(b) above, to prove the specified CTFT property, either start with the time domain expression and show that a forward transform yields the frequency domain expression, or you can start with the frequency domain expression and show that an inverse transform yields the time- domain expression. ( Hint : For each sub-problem one of these two approaches may be much easier than the other!)than the other!...
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hw2_600(2) - ECE-600 Introduction to Digital Signal...

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