# FL10quiz16 - series, we decompose the time function, f ( t...

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ESE 351 Quiz 16 Name: 11/2/10 Sections 10.1–10.5 a. Can we derive an exponential Fourier series from the trigonometric Fourier series? Answer yes or no. b. We will ﬁnd the Fourier spectrum of f ( t ) = 3 + 10 cos(2 πt ) = 3 + 5 e i 2 πt + 5 e - i 2 πt . Let ω 1 = 2 π be the fundamental frequency. First, ﬁnd the Fourier coeﬃcient, F (0), for the zero frequency. c. Now, ﬁnd the Fourier coeﬃcients, F (1) and F ( - 1). d. When we studied the convolutions and the impulses, we decomposed the time function, f ( t ) = -∞ f ( τ ) δ ( t - τ ) or f ( k ) = = -∞ f ( ) δ ( k - ), into impulses, δ ( t - τ ) or δ ( k - ), at diﬀerent times, t = τ or k = . In the continuous-time exponential Fourier
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Unformatted text preview: series, we decompose the time function, f ( t ), into at dierent . Fill in the blanks. e. The Fourier coecients for function f ( t ) over the interval between 0 and T are found from the following formula: F ( n ) = 1 T T f ( t ) e-in 1 t dt, where the basic frequency is 1 = 2 T . Assume that the function f ( t ) is periodic with period T . Is it true that the coecient can be computed from the following formula as well? F ( n ) = 1 T T 2-T 2 f ( t ) e-in 1 t dt. Answer yes or no....
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