Linear Time Invarient System - Revision history

68.113.10.142: /* LTI system properties */

2006-11-06T00:08:07Z

LTI system properties

← Older revision		Revision as of 17:08, 5 November 2006
Line 13:		Line 13:
	for any scalar values of A and B.		for any scalar values of A and B.

	Time invariance of a system means that ~~for~~ any input <math>x(t)</math> by some amount of time T the out put will also be adjusted by that amount of time. This implies that for,		Time invariance of a system means that if any input <math>x(t)</math> is shifted by some amount of time T the out-put will also be adjusted by that amount of time. This implies that for,

	::<math>x(t ~~- T~~)\!</math>		::<math>H(x(t))=y(t)\!</math>
	::<math>y(t - T) = ~~H(x~~(t - T))\!</math>		::<math>H(x(t - T))=y(t-T)\!</math>

	<br>		<br>

Nathan: /* LTI system properties */

2006-10-13T05:31:13Z

LTI system properties

← Older revision		Revision as of 22:31, 12 October 2006
Line 6:		Line 6:
	A system is considered to be a Linear Time Invariant when it satisfies the two basic criteria implied in its name, one it must be linear and two it must be time invariant. A Linear system is characterized by two properties superposition (additivity) and scaling (homogeneity). The superposition principal says that for any linear system a linear combination of solutions to the system is also a solution to the same linear system. The principal of scaling implies that if you adjust your scale an input by N amount, your output will also be adjusted by N amount. An example of a linear system then would be,		A system is considered to be a Linear Time Invariant when it satisfies the two basic criteria implied in its name, one it must be linear and two it must be time invariant. A Linear system is characterized by two properties superposition (additivity) and scaling (homogeneity). The superposition principal says that for any linear system a linear combination of solutions to the system is also a solution to the same linear system. The principal of scaling implies that if you adjust your scale an input by N amount, your output will also be adjusted by N amount. An example of a linear system then would be,

	::<math>x_1(t)</math>		::<math>x_1(t)\!</math>
	::<math>x_2(t)</math>		::<math>x_2(t)\!</math>
	::<math>y_1(t) = H(x_1(t))</math>		::<math>y_1(t) = H(x_1(t))\!</math>
	::<math>y_2(t) = H(x_2(t))</math>		::<math>y_2(t) = H(x_2(t))\!</math>
	::<math>Ay_1(t) + By_2(t) = H(Ax_2(t) + Bx_1(t))</math>		::<math>Ay_1(t) + By_2(t) = H(Ax_2(t) + Bx_1(t))\!</math>
	for any scalar values of A and B.		for any scalar values of A and B.

	Time invariance of a system means that for any input <math>x(t)</math> by some amount of time T the out put will also be adjusted by that amount of time. This implies that for,		Time invariance of a system means that for any input <math>x(t)</math> by some amount of time T the out put will also be adjusted by that amount of time. This implies that for,

	::<math>x(t - T)</math>		::<math>x(t - T)\!</math>
	::<math>y(t - T) = H(x(t - T))</math>		::<math>y(t - T) = H(x(t - T))\!</math>

	<br>		<br>

Sherna at 03:53, 10 October 2006

2006-10-10T03:53:50Z

← Older revision		Revision as of 20:53, 9 October 2006
Line 17:		Line 17:
	::<math>x(t - T)</math>		::<math>x(t - T)</math>
	::<math>y(t - T) = H(x(t - T))</math>		::<math>y(t - T) = H(x(t - T))</math>

			<br>
			<br>
			Related Links
			*[[The Game]]

Smitry at 21:49, 8 October 2006

2006-10-08T21:49:49Z

← Older revision		Revision as of 14:49, 8 October 2006
Line 1:		Line 1:
			*[[Signals and systems\|Signals and Systems]]
	==LTI systems==		==LTI systems==
	LTI System theory is a powerful and widely used concept in electrical engineering. It has applictions in circuit anlysis, control theory , and our main topic of interest signal processing.		LTI System theory is a powerful and widely used concept in electrical engineering. It has applictions in circuit anlysis, control theory , and our main topic of interest signal processing.

Smitry: /* LTI system properties */

2006-10-08T21:48:35Z

LTI system properties

← Older revision		Revision as of 14:48, 8 October 2006
Line 3:		Line 3:

	===LTI system properties===		===LTI system properties===
	A system is considered to be a Linear Time ~~Invarient~~ when it ~~satifies~~ the two basic criteria implied in its name, one it must be linear and two it must be time ~~invarient~~. A Linear system is ~~charterized~~ by two ~~propeties~~ superposition (~~additvity~~) and scaling (~~homegeneity~~). The ~~superpostion~~ principal says that for any linear system a linear combination of solutions to the system is also a solution to the same linear system. The principal of scaling implies that if you adjust your scale an input by N amount, your output will also be adjusted by N amount. An example of a ~~Linear~~ system then would be,		A system is considered to be a Linear Time Invariant when it satisfies the two basic criteria implied in its name, one it must be linear and two it must be time invariant. A Linear system is characterized by two properties superposition (additivity) and scaling (homogeneity). The superposition principal says that for any linear system a linear combination of solutions to the system is also a solution to the same linear system. The principal of scaling implies that if you adjust your scale an input by N amount, your output will also be adjusted by N amount. An example of a linear system then would be,

	::<math>x_1(t)</math>		::<math>x_1(t)</math>
Line 12:		Line 12:
	for any scalar values of A and B.		for any scalar values of A and B.

	Time ~~invarience~~ of a system means that for any input <math>x(t)</math> by some ~~amout~~ of time T the out put will also be adjusted by that amount of time. This implies that for,		Time invariance of a system means that for any input <math>x(t)</math> by some amount of time T the out put will also be adjusted by that amount of time. This implies that for,

	::<math>x(t - T)</math>		::<math>x(t - T)</math>
	::<math>y(t - T) = H(x(t - T))</math>		::<math>y(t - T) = H(x(t - T))</math>

172.16.18.250: /* LTI system properties */

2006-10-08T21:35:49Z

LTI system properties

← Older revision		Revision as of 14:35, 8 October 2006
Line 12:		Line 12:
	for any scalar values of A and B.		for any scalar values of A and B.

	Time invarience of a system means that for ~~adjust~~ any input <math>x(t)</math> by some amout of time T the out put will also be adjusted by that amount of time. This ~~impies~~ that for,		Time invarience of a system means that for any input <math>x(t)</math> by some amout of time T the out put will also be adjusted by that amount of time. This implies that for,

	::<math>x(t - T)</math>		::<math>x(t - T)</math>
	::<math>y(t - T) = H(x(t - T))</math>		::<math>y(t - T) = H(x(t - T))</math>

172.16.18.250: /* LTI system properties */

2006-10-08T21:29:50Z

LTI system properties

← Older revision		Revision as of 14:29, 8 October 2006
Line 3:		Line 3:

	===LTI system properties===		===LTI system properties===
	A system is considered to be a Linear Time Invarient when it satifies the two basic criteria implied in its name, one it must be linear and two it must be time invarient. A Linear system is charterized by two propeties superposition (additvity) and scaling (homegeneity). The superpostion principal says that for any linear system a linear combination of solutions to the system is also a solution to the same linear system. The principal of scaling implies that if you adjust your scale ~~and~~ input by N amount, your output will also be adjusted by N amount. An example of a Linear system then would be,		A system is considered to be a Linear Time Invarient when it satifies the two basic criteria implied in its name, one it must be linear and two it must be time invarient. A Linear system is charterized by two propeties superposition (additvity) and scaling (homegeneity). The superpostion principal says that for any linear system a linear combination of solutions to the system is also a solution to the same linear system. The principal of scaling implies that if you adjust your scale an input by N amount, your output will also be adjusted by N amount. An example of a Linear system then would be,

	::<math>x_1(t)</math>		::<math>x_1(t)</math>

172.16.18.250: /* LTI system properties */

2006-10-08T21:29:17Z

LTI system properties

← Older revision		Revision as of 14:29, 8 October 2006
Line 3:		Line 3:

	===LTI system properties===		===LTI system properties===
	A system is considered to be a Linear Time Invarient when it satifies the two basic criteria implied in its name, one it must be linear and two it must be time invarient. A Linear system is charterized by two propeties superposition (additvity) and scaling (homegeneity). The superpostion principal says that for any linear system a linear combination of solutions to the system is also a solution to the same linear system. The principal of scaling implies that if you adjust ~~you~~ scale ~~you~~ input by N amount your output will also be adjusted by N amount. An example of a Linear system then would be,		A system is considered to be a Linear Time Invarient when it satifies the two basic criteria implied in its name, one it must be linear and two it must be time invarient. A Linear system is charterized by two propeties superposition (additvity) and scaling (homegeneity). The superpostion principal says that for any linear system a linear combination of solutions to the system is also a solution to the same linear system. The principal of scaling implies that if you adjust your scale and input by N amount, your output will also be adjusted by N amount. An example of a Linear system then would be,

	::<math>x_1(t)</math>		::<math>x_1(t)</math>

Fonggr: /* LTI system properties */

2006-10-04T13:13:18Z

LTI system properties

← Older revision		Revision as of 06:13, 4 October 2006
Line 3:		Line 3:

	===LTI system properties===		===LTI system properties===
	A system is considered to be a Linear Time Invarient when it satifies the two basic criteria implied in its name, one it must be linear and two it must be time invarient. A Linear system is charterized by two propeties superposition and scaling. The superpostion principal says that for any linear system a linear combination of solutions to the system is also a solution to the same linear system. The principal of scaling implies that if you adjust you scale you input by N amount your output will also be adjusted by N amount. An example of a Linear system then would be,		A system is considered to be a Linear Time Invarient when it satifies the two basic criteria implied in its name, one it must be linear and two it must be time invarient. A Linear system is charterized by two propeties superposition (additvity) and scaling (homegeneity). The superpostion principal says that for any linear system a linear combination of solutions to the system is also a solution to the same linear system. The principal of scaling implies that if you adjust you scale you input by N amount your output will also be adjusted by N amount. An example of a Linear system then would be,

	::<math>x_1(t)</math>		::<math>x_1(t)</math>

Adkich: /* LTI systems */

2006-10-04T06:00:03Z

LTI systems

← Older revision		Revision as of 23:00, 3 October 2006
Line 1:		Line 1:
	==LTI systems==		==LTI systems==
	LTI System theory is a powerful and widely used concept in electrical engineering. It has applictions in circuit anlysis, control theory , and our main topic of ~~intrest~~ signal processing.		LTI System theory is a powerful and widely used concept in electrical engineering. It has applictions in circuit anlysis, control theory , and our main topic of interest signal processing.

	===LTI system properties===		===LTI system properties===