Dirichlet Conditions: Difference between revisions
Jump to navigation
Jump to search
| (2 intermediate revisions by the same user not shown) | |||
| Line 3: | Line 3: | ||
===Condition 1.=== |
===Condition 1.=== |
||
Over any period <math> [t, t + T],\,f(t)</math> must have the property: <math> \int_t^{t+T} \ |
Over any period <math> [t, t + T],\,f(t)</math> must have the property: <math> \int_t^{t+T} \vert f(t)\vert \, dt < \infty </math> |
||
In other words, <math> f(t) </math> is abosolutely integrable. The result of this property is that each of the Fourier coefficients <math> c_n </math> is finite. |
In other words, <math> f(t) </math> is abosolutely integrable. The result of this property is that each of the Fourier coefficients <math> c_n </math> is finite. |
||
| Line 14: | Line 14: | ||
Over any period, <math> f(t) </math> can have only a finite number of discontinuities. |
Over any period, <math> f(t) </math> can have only a finite number of discontinuities. |
||
<small> Information Referenced from <u>Linear Circuit Analysis <math> 2^{nd} </math> Edition</u> by DeCarlo & Lin |
|||
Latest revision as of 22:01, 3 October 2006
Dirichlet Conditions
Condition 1.
Over any period must have the property:
![{\displaystyle [t,t+T],\,f(t)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cd70e3aa757b2525b6e1fbcca5434a0c559b3c27)
In other words, is abosolutely integrable. The result of this property is that each of the Fourier coefficients is finite.
Condition 2.
Over any period of the signal, there must be only a finite number of minima and maxima. in other words, functions like are excluded. These functions are known as bounded variations.
Condition 3.
Over any period, can have only a finite number of discontinuities.
Information Referenced from Linear Circuit Analysis Edition by DeCarlo & Lin
