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Unformatted text preview: c = [ c c 1 c 2 c 3 ] T such that s = Vc . S 20.2 ( P 3.1 in textbook). Let α = 1 2 and β = √ 3 2 (i) Determine the complex number z such that the vector v = £ 1 α + jβα + jβ1αjβ αjβ / T equals £ 1 z z 2 z 3 z 4 z 5 / T (ii) If s = £ 3 21 01 2 / T determine the leastsquares approximation ˆ s of s in the form of a linear combination of 1 (i.e., the allones vector), v and v * . Clearly show the numerical values of the elements of ˆ s . S 20.3 ( P 3.2 in textbook). Let v (0) , v (1) and v (7) denote the complex Fourier sinusoids of length N = 8 at frequencies ω = 0, ω = π/ 4 and ω = 7 π/ 4, respectively. Determine the leastsquares approximation ˆ s of s = £ 4 3 2 1 0 1 2 3 / based on v (0) , v (1) and v (7) . Compute the squared approximation error k ˆ ss k 2 ....
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 Spring '08
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 Vector Space, Least Squares, Regression Analysis, Complex number, Linear least squares, Carl Friedrich Gauss

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