(New page: == Memory and Memoryless Systems == '''Memoryless System:''' A system is memoryless if for any '''<math>t_o \in \mathbb{R}</math>''' the output of the system, '''<big><math>Y(t_o)</math><...) |
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'''Memoryless System:''' A system is memoryless if for any '''<math>t_o \in \mathbb{R}</math>''' the output of the system, '''<big><math>Y(t_o)</math></big>''', only depends on the input at '''<big><big><math>t_o</math></big></big>'''. In other words, the system has no past or future dependance. | '''Memoryless System:''' A system is memoryless if for any '''<math>t_o \in \mathbb{R}</math>''' the output of the system, '''<big><math>Y(t_o)</math></big>''', only depends on the input at '''<big><big><math>t_o</math></big></big>'''. In other words, the system has no past or future dependance. | ||
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Example of memoryless system: '''<big><math>Y(t) = 2*X(t)</math></big>'''. This system is memoryless because at '''<big><math>Y(0) = 2*X(0)</math></big>''', it does not show any future or past dependancy. | Example of memoryless system: '''<big><math>Y(t) = 2*X(t)</math></big>'''. This system is memoryless because at '''<big><math>Y(0) = 2*X(0)</math></big>''', it does not show any future or past dependancy. | ||
Latest revision as of 10:05, 19 September 2008
Memory and Memoryless Systems
Memoryless System: A system is memoryless if for any $ t_o \in \mathbb{R} $ the output of the system, $ Y(t_o) $, only depends on the input at $ t_o $. In other words, the system has no past or future dependance.
Example of memoryless system: $ Y(t) = 2*X(t) $. This system is memoryless because at $ Y(0) = 2*X(0) $, it does not show any future or past dependancy.
Memory System: A system has memory if for any $ t_o \in \mathbb{R} $ , its output $ Y(t_o) $ depends on $ t_o \pm n \in \mathbb{R} $, which means it has past or future dependance.
Example of a system with memory: $ Y(t) = X(t) + X(t - 1) $. This system has memory because at $ Y(0) = X(0) + X(-1) $, $ X(-1) $ shows past dependance.
