| (8 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
== "Guessing the Periodic Signal" == | == "Guessing the Periodic Signal" == | ||
| + | |||
| + | |||
Supposing we are given a signal x(t) | Supposing we are given a signal x(t) | ||
| + | |||
1) x(t) is real and odd | 1) x(t) is real and odd | ||
| + | |||
2) x(t) is periodic with period T = 2 and has Fourier coefficients <math> ak </math> | 2) x(t) is periodic with period T = 2 and has Fourier coefficients <math> ak </math> | ||
| + | |||
3) <math> ak = 0 </math> for |k| > 1 | 3) <math> ak = 0 </math> for |k| > 1 | ||
| − | 4) <math> \frac{1}{2} \ | + | |
| + | 4) <math> \frac{1}{2} * \int_{0}^{2} |x(t)|^2 dt = 1 </math> | ||
| + | |||
| + | |||
| + | We are told to specify two different signals that satisfy the given conditions. | ||
| + | |||
| + | 1) since it is odd the function can be a sin wave | ||
| + | |||
| + | 2)the signal has a period of 2 | ||
| + | |||
| + | 3) <math> ak </math> is always greater than 1 (except 0) | ||
| + | |||
| + | 4) w= <math> \frac{2*\pi}{2} = \pi </math> | ||
| + | |||
| + | |||
| + | |||
| + | signal = <math> 4*sin(\frac{2\pi}{2} * t) + 4 </math> | ||
Latest revision as of 16:51, 25 September 2008
"Guessing the Periodic Signal"
Supposing we are given a signal x(t)
1) x(t) is real and odd
2) x(t) is periodic with period T = 2 and has Fourier coefficients $ ak $
3) $ ak = 0 $ for |k| > 1
4) $ \frac{1}{2} * \int_{0}^{2} |x(t)|^2 dt = 1 $
We are told to specify two different signals that satisfy the given conditions.
1) since it is odd the function can be a sin wave
2)the signal has a period of 2
3) $ ak $ is always greater than 1 (except 0)
4) w= $ \frac{2*\pi}{2} = \pi $
signal = $ 4*sin(\frac{2\pi}{2} * t) + 4 $
