If f(x) is continuous and periodic function of x, with fundamental period T = 1 second. Let the {a} be the complex Fourier series coefficients of f(x), where k is integer valued. Consider the following statements about f(3x): I. The complex Fourier series coefficients of f(3x) are {a} where k is integer valued. II. The complex Fourier series coefficients of f(3x) are {3ak} where k is integer valued. III. The fundamental angular frequency (wo) of f(3x) is 6π rad/s. For the three statements above, which one of the following is correct?
If f(x) is continuous and periodic function of x, with fundamental period T = 1 second. Let the {a} be the complex Fourier series coefficients of f(x), where k is integer valued. Consider the following statements about f(3x): I. The complex Fourier series coefficients of f(3x) are {a} where k is integer valued. II. The complex Fourier series coefficients of f(3x) are {3ak} where k is integer valued. III. The fundamental angular frequency (wo) of f(3x) is 6π rad/s. For the three statements above, which one of the following is correct?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:If f(x) is continuous and periodic function of x, with fundamental period T = 1 second.
Let the {a} be the complex Fourier series coefficients of f(x), where k is integer valued.
Consider the following statements about f(3x):
I. The complex Fourier series coefficients of f(3x) are {a} where k is integer valued.
II. The complex Fourier series coefficients of f(3x) are {3ak} where k is integer valued.
III. The fundamental angular frequency (wo) of f(3x) is 6π rad/s.
For the three statements above, which one of the following is correct?
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