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mat210-exercises2

# mat210-exercises2 - Review Problems ll 1 Given the...

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Unformatted text preview: Review Problems ll 1.) Given the following trusses, ﬁnd out Whether they are stable or unstable. If they are unstable, ﬁnd 1 2.) Given < f,g >= / on continuous functions on [0,1]. 0 a.) Show that <, > is an inner product. b.) Find a, b, c such that {1,110 + a,:r2 + bar + c} is an orthogonal set i.e. each element is orthogonal to the others. 0.) Find the projection of \$3 to the space spanned by 17 x + a, m2 + bx + 0 found in 3.) a.) Find all roots of .28 = M1 and plot them. b.) Show that if Z122 and 21 + 22 are both real, then zl = 2—2. c.) Find cos(4x) in terms of cos(:c) and sin(q:) using complex exponentials. 4.) Compute the Fourier Series of the following functions Whose one period is given. a.) f(x)m6(a:+72r) 6(x)16(a: 72‘) f(x+27r)=f(:r) 0 for—WSxS"§f 1 for—§f<:t —% b.) m): 0 for—gsxgg f(m+27r)=f<x) 1 for§<x<iif 0 foréfgargﬁ 0 for—7r33:<7r - c.) ﬂat): 27r—x for7r£zzi<27r f(aﬁ+47T)=f(\$) —27T—95 for—27rfa:<—7r xe"“’ for0<at<7r d. : 2 2 we) {0 “Mgr/ESQ” f(x+7r) ms) DO 271' 5.) Say/ |f(a:)[2d:v = 11. Suppose that f(:13)= 2 016617”, and co : 1,c1 2 CW1 : 0 [6:700 Show that 10k! S V; for all k. ( Hint : Use Parseval’s Identity ) 6.) a.) Write F6 and F671. b.) Express as a linear combination of the columns of F6. 1 c.) Find the matrices A, B so that 7.) Let ﬂat) 2 005(205) a.) Discretize f for N : 4 to get 7 b.) Find the DFT of j? and plot it. c.) Find the continuous complex F T of f and compare with its DFT. 8.) Given 0 = (3,1,—1,4) and d = (—1,0, 5, 3). a.) Compute c * d and 0 ® d for N = 4 b.) For N = 4, write a ﬁlter that takes the signal 00 00 c c . . 1 —> 1 in the frequency domain. (32 0 03 0 ...
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mat210-exercises2 - Review Problems ll 1 Given the...

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