FL10quiz17 - c Now ﬁnd the magnitude | F(0 | and the...

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ESE 351 Quiz 17 Name: 11/4/10 Sections 10.6-10.8 (continuous-time only) a. What kinds of functions is the Fourier series useful in approximating? (i) a periodic function over the real line from -∞ to ; (ii) a function over a ﬁxed ﬁnite interval from t 0 to t 1 ; (iii) both (i) and (ii); (iv) none of the above. b. We will ﬁnd the Fourier spectrum of f ( t ) = - 8 + 6 cos(5 πt + π ) = - 8 + 3 e i 5 πt + π + 3 e - i 5 πt + π . Let ω 1 = 5 π be the fundamental frequency. First, ﬁnd the Fourier coeﬃcient, F (0), for the zero frequency.
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Unformatted text preview: c. Now, ﬁnd the magnitude | F (0) | and the phase 6 F (0) of the Fourier coeﬃcient F (0) . d. Finally, ﬁnd the Fourier coeﬃcients, F (1) and F (-1). e. See Figure 1 for a graph of another function f ( t ). Find the zeroth Fourier coeﬃcient, F (0) for the zero frequency.-20-15-10-5 5 10 15 20-4-3-2-1 1 2 3 4 5 6 7 Time t Time function f(t) Periodic Wave Figure 1: Continuous-time time function....
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This document was uploaded on 05/15/2011.

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