Does this system have memory or memoryless?and why?

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The system described by the equation Y[n+1] + 4Y[n] = 3X[n+1] - X[n] is determined to have memory. A memoryless system's output at a given time depends solely on the input at that same time, which does not apply here. The output Y[t1] relies on previous input values, indicating that the system retains information from past inputs. Therefore, the conclusion is that this system exhibits memory. Understanding the definitions of memory and memoryless systems is crucial for analyzing such equations.
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does this system have memory or memoryless??and why??

Y[n+1] + 4Y[n] = 3 X[n+1] - X[n]
 
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I moved this to the homework forums. Angel23, as you know, you need to show some of your own work to get help from the PF community. What are the definitions of DSP with and without memory?
 
ok a memoryless system is the system in which the value of output at t1 depends only on the value of the input at t1.

now i want to apply this on the given system how can i do?
 
angel23 said:
ok a memoryless system is the system in which the value of output at t1 depends only on the value of the input at t1.

now i want to apply this on the given system how can i do?
Let t1= (n+1)*T and see if your definition applies.
 
it has memory.
right?
 
angel23 said:
it has memory.
right?
Yes, since Y[t1] depends on T[t1-T].
 
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