| Line 21: | Line 21: | ||
\bar x(t) = sin(6 \pi t), \omega_{o} = 6\pi \\ | \bar x(t) = sin(6 \pi t), \omega_{o} = 6\pi \\ | ||
x(t) = 2 + cos(6 \pi t) - \frac{1}{2} sin(3 \pi t), \omega_{o} = 3\pi \\ | x(t) = 2 + cos(6 \pi t) - \frac{1}{2} sin(3 \pi t), \omega_{o} = 3\pi \\ | ||
| − | x(t) = cos(\frac{2\pi}{10}t), \omega_{o} = \frac{\pi}{10} | + | x(t) = cos(\frac{2\pi}{10}t), \omega_{o} = \frac{\pi}{10} \\ |
x(t) = | x(t) = | ||
\begin{cases} | \begin{cases} | ||
| Line 43: | Line 43: | ||
x[n] = 1 + sin(\frac{2\pi}{8}n) + 3cos(\frac{2\pi}{8}n), N=8 --> \omega_{o} = \frac{2\pi}{8} \\ | x[n] = 1 + sin(\frac{2\pi}{8}n) + 3cos(\frac{2\pi}{8}n), N=8 --> \omega_{o} = \frac{2\pi}{8} \\ | ||
x[n] = -j^n, \omega_o = \frac{\pi}{2} \\ | x[n] = -j^n, \omega_o = \frac{\pi}{2} \\ | ||
| − | x | + | x[n] = |
\begin{cases} | \begin{cases} | ||
| − | + | sin(\pi t), & \text{if}\ a=1 \\ | |
0, & \text{otherwise} | 0, & \text{otherwise} | ||
\end{cases}\\ | \end{cases}\\ | ||
| − | x | + | x[n] = |
\begin{cases} | \begin{cases} | ||
| − | + | 4, & \text{if}\ a=1 \\ | |
| − | + | -4, & \text{otherwise} | |
\end{cases} | \end{cases} | ||
Revision as of 21:04, 25 April 2019
A project by Kalyan Mada
Introduction
I am going to compute some fourier series coefficients.
CT signals
$ \begin{align} \bar x(t) = sin(6 \pi t), \omega_{o} = 6\pi \\ x(t) = 2 + cos(6 \pi t) - \frac{1}{2} sin(3 \pi t), \omega_{o} = 3\pi \\ x(t) = cos(\frac{2\pi}{10}t), \omega_{o} = \frac{\pi}{10} \\ x(t) = \begin{cases} 3, & \text{if}\ a=1 \\ 0, & \text{otherwise} \end{cases} \end{align} $
DT signals
$ \begin{align} f(x) &= \oint_S g(x) dx \\ &= \int_a^b g(x) dx \\ &= \frac{\mu_0}{2 \pi a \cdot b}\\ & = \int_a^{-\infty} jzdhfbvzjhvz dt \\ & = \sum_{k=0}^{-\infty} kzdjfgdzjkfg \\ x[n] = 1 + sin(\frac{2\pi}{8}n) + 3cos(\frac{2\pi}{8}n), N=8 --> \omega_{o} = \frac{2\pi}{8} \\ x[n] = -j^n, \omega_o = \frac{\pi}{2} \\ x[n] = \begin{cases} sin(\pi t), & \text{if}\ a=1 \\ 0, & \text{otherwise} \end{cases}\\ x[n] = \begin{cases} 4, & \text{if}\ a=1 \\ -4, & \text{otherwise} \end{cases} \end{align} $
Questions and comments
If you have any questions, comments, etc. please post them here.
[to 2019 Spring ECE 301 Boutin]
