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# hwB22 - z 1 and z 2(iii Compute the amplitude and phase...

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ENEE 241 02 * HOMEWORK ASSIGNMENT 22 Due Wed 04/02 The real-valued signal vector s has DFT S = £ 6 z 1 3 + 2 j - 7 z 2 - 5 + 3 j / T (i) (2 pts.) What are the values of z 1 and z 2 ? (ii) (3 pts.) Without using complex algebra (or MATLAB), determine the sum of the entries of s . (iii) (4 pts.) Display the amplitude ( | S [ k ] | ) and phase ( S [ k ]) spectra as vectors. (iv) (7 pts.) Write an expression for s [ n ] (where n = 0 : 5) in the form of a constant plus three real-valued sinusoids with frequencies in the range (0 , π ]. (v) (4 pts.) In MATLAB, generate the vector s given by the equation found in part (iv) and verify that fft(s) agrees with S . Solved Examples S 22.1 ( P 3.7 in textbook). A five-point real-valued signal x has DFT given by X = £ 4 1 + j 3 - j z 1 z 2 / T (i) Compute x [0] + x [1] + x [2] + x [3] + x [4] using one entry of X only . (ii) Determine the values of
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Unformatted text preview: z 1 and z 2 . (iii) Compute the amplitude and phase spectra of x , displaying each as a vector. (iv) Express x [ n ] as a linear combination of three real-valued sinusoids. S 22.2 ( P 3.8 in textbook). Consider the real-valued signal x given by x [ n ] = 3(-1) n + 7cos ‡ πn 4 + 1 . 2 · + 2cos ‡ πn 2-. 8 · , n = 0 ,..., 7 (i) Which Fourier frequencies (for an eight-point sample) are present in the signal x ? (ii) Determine the amplitude spectrum of x , displaying your answer in the form £ A A 1 A 2 A 3 A 4 A 5 A 6 A 7 / T (iii) Determine the phase spectrum of x , displaying your answer in the form £ φ φ 1 φ 2 φ 3 φ 4 φ 5 φ 6 φ 7 / T...
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