Boston University, College of Engineering
Electrical and Computer Engineering Department
EC515 Digital Communications
Fall 2009
Problem Set 1
Out: 9/2/2009
Due: 9/11/2009
Linear Algebra
Problem 1.
This problem tests your understanding of basis functions.
1.
We are given three vectors (a, b, c), (0, b, 0) and (a, 0, c). Construct a vector space, V, of
smallest dimension containing all the vectors. Construct the basis vectors of this space
and express the three vectors as a linear combination of the basis vectors.
2.
We are given a 2 dimensional Euclidean space with basis vectors (1, 0), (0, 1) and a
vector (1/3, 2/3). We now choose vectors (1/
2, 1/
2), (0, 1). Does this form a basis for
the 2 dimensional Euclidean space? If so, what are the coordinates of the vector in the old
and new basis? Can you come up with a general rule for coordinate transformation based
on this example?
3.
Check whether the space of periodic discrete time signals, s[n], with period, N, forms a
vector space. What is its dimension? Find the Fourier series coefficients of the DT signal.
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 Fall '09
 VenkateshSaligrama
 Linear Algebra, Vector Space, basis vectors, dimensional Euclidean space

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