Quiz Chapter 11.03: Fourier Transform Pair: Frequency and Time Domain

1. Given two complex numbers: $C_{1}=2-3i$ , and $C_{2}=1+4i$ . The product $P=C_{1} \times C_{2}$ can be computed as

2+5i

-10+5i

-14+5i

14+5i

2. Given the complex number $C_{1} = 3 + 4i$ . In polar coordinates, the complex number can be expressed as $C_{1} = Ae^{i\theta}$ , where $A$ and $\theta$ are called the amplitude and phase angle of $C_{1}$ , respectively. The amplitude $A$ can be computed as

3

4

5

7

3. Given the complex number $C_{1} = 3 + 4i$ . In polar coordinates the complex number can be expressed as $C_{1} = Ae^{i\theta}$ , where $A$ and $\theta$ are called the amplitude and phase angle of $C_{1}$ , respectively. The phase angle $\theta$ in radians can be computed as

0.6435

0.9273

2.864

5.454

4. For the complex number $C_{1} = -3+4i$ , the phase angle $\theta$ in radians can be computed as

0.6435

0.9273

1.206

2.2143

5. Given the function

- - $f_{np}(t) = \delta(t-a) = \left\{\begin{matrix} 1, \, if \, \, t=a\\0,\,elsewhere \end{matrix}\right.$

The Fourier transform $F(iw_{0})$ which will transform the function from time domain to frequency domain can be computed as

\delta(a+t)

e^{-i(2 \pi f)a}

1

\delta(t-a)

6. Given the function

- - $\hat{F}(iw_{0}) = 1$

The inverse Fourier transform $f_{np}(t)$ which will transform the function from frequency domain to time domain can be computed as

e^{it}

e^{-it}

\delta(t-0)

e^{-i (2 \pi f) t}