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# ps7-PAM - 6.450 Principles of Digital Communication MIT...

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�� 6.450 Principles of Digital Communication Wednesday, October 17, 2002 MIT, Fall 2002 Handout #24 Due: Wednesday, October 24, 2001 Problem Set 7 Problem 7.1 Prove the following statement using the theorems about linear vector spaces in lecture 10: Every set of n vectors that spans an n -dimensional vector space V is a linearly independent set and is a basis of V . Problem 7.2 Prove that if a set of n vectors uniquely spans a vector space V , in the sense that every v ∈ V can only be represented in one way as a linear combination of the n vectors, then those n vectors are linearly independent and V is an n -dimensional space. Problem 7.3 A discrete memoryless source emits binary equiprobable symbols at a rate of 1000 symbols per second. The symbols from a one second interval are grouped into pairs and sent over a bandlimited channel using 4PAM modulation. In particular, the transmitted signal U ( t ) is given by U ( t ) = 500 k =1 A k sinc t T k (1) where T = 0 . 002, A k takes values in {− 3 d/ 2 , d/ 2 , d/ 2 , 3 d/ 2 } and we

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ps7-PAM - 6.450 Principles of Digital Communication MIT...

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