Quiz Chapter 11.02: Continuous Fourier Transforms

MULTIPLE CHOICE TEST

(All Tests)

CONTINUOUS FOURIER TRANSFORMS

(More on Continuous Fourier Transforms)

FAST FOURIER TRANSFORMS

(More on Fast Fourier Transforms)


Pick the most appropriate answer


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