Quiz Chapter 11.02: Continuous Fourier Transforms

1. Which of the following is an even function of t?

2. A “periodic function” is given by a function which

3. Given the following periodic function, f(t).

The coefficient a_{0} of the continuous Fourier series associated with the above given function f(t) can be computed as

4. For the given periodic function

• • • f(t) =\left\{\begin{matrix} 2t \,\, for \,\, 0 \leq t \leq 2 \\4 \,\, for \,\, 2 \leq t \leq 6\end{matrix}\right.

with a period T=6. The coefficient b_{1} of the continuous Fourier series associated with the given function f(t) can be computed as

5. For the given periodic function

• • • f(t) =\left\{\begin{matrix} 2t \,\, for \,\, 0 \leq t \leq 2 \\4 \,\, for \,\, 2 \leq t \leq 6\end{matrix}\right.

with a period of T=6. The Fourier coefficient a_{1} can be computed as

6. For the given periodic function

• • • f(t) =\left\{\begin{matrix} 2t \,\, for \,\, 0 \leq t \leq 2 \\4 \,\, for \,\, 2 \leq t \leq 6\end{matrix}\right.

with a period of T=6 as shown in Problem 5. The complex form of the Fourier series  can be expressed as

• • • f(t)=\displaystyle\sum_{k=-\infty}^{\infty}\widetilde{C}_{k} e^{ikw_{0}t}

The complex coefficient \widetilde{C}_{1} can be expressed as