A Is the system memoryless B is the system causal Please ex

Solution

The equation y(n)=log₂(x(n+2))+5 is memory system and noncausal .

For a memoryless system, changing the input at any instant can change the output only at that instant. If, in some case, a change in input signal at some instant changes the output at some other instant, we can be sure that the system has memory.Lets test our system when n=2, then y(n) becomes log₂(x(2+2))+5 ie log₂(x(4))+5 here evenif our instant is at n=2 the output depends on value of system at n=4 which necesitates the need for a memory

In a causal system, the value of the output signal at any instant depends only on \"past\" and \"present\" values of the input signal (i.e. only on values of the input signal at \"instants\" less than or equal to that \"instant\"). Such a system is often referred to as being non-anticipative, as the system output does not anticipate future values of the input. Here also we can check the system by giving the value . for eg. lets say n=2 as in previous case . We have already seen that output at n=2 depends on input at n=4 which is actually a future input as far as our selected instant is considered. Therefore the system is not causal