Fourier Pieces
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Let f_1(t) represent a function of continuous time t that is represented by a trigonometric Fourier series:
f_1(t) = \sum_{k=1}^\infty {\sin(kt)\over k}
Part a. What is the average value of f_1(t)? Your answer should be a number or numeric expression that can include common constants (such as \pi). Your answer should not include f_1(t) or any integrals or infinite sums. Briefly explain.
Part b. Determine the numerical value of the following integral:
\int_0^{2\pi}f_1(t)\cos(3t)dt
Your answer should be a number or numeric expression
that can include common constants (such as \pi).
Your answer should not include f_1(t) or any integrals or infinite sums.
Briefly explain.
Part c. Determine the numerical value of the following integral:
\int_0^{2\pi}f_1(t)\sin(5t)dt
Your answer should be a number or numeric expression
that can include common constants (such as \pi).
Your answer should not include f_1(t) or any integrals or infinite sums.
Briefly explain.
Part d. The function f_1(t) can also be expressed as a complex exponential Fourier series as follows:
f_1(t)=\sum_{k=-\infty}^\infty a_ke^{jk\omega_ot}
Determine the numerical values of \omega_o, a_{-2}, a_{-1}, a_0, a_1, a_2.
Each answer should be a number or numeric expression
that can include common constants (such as \pi).
Your answers should not include f_1(t) or any integrals or infinite sums.
Briefly explain.
Please upload a single pdf file that contains your answers to all parts of this problem: No file selected
