PLEASE DO F AND I and/or homogeneous. Justify your answers by p erty if it holds

Question

PLEASE DO F AND I

and/or homogeneous. Justify your answers by p erty if it holds or a counterexample if it does not. Inlrin-21, x[n-1]0 t[n-1] = 0 x(t) L dr .30. Determine if each of the following systems is invertible. If it is, construct the invere system. If it is not, find two input signals to the system that have the same output. (a) y(t) = x(t-4) (e) y[n] = nx[n] (b) y(t) cos(x(t)] rn-1]. nl 0, In]. (d) y(t) = 1.. x(r)dr (f) y[n]=x[n]x(n-1] (h) y(t) = ft, e-(t-r)x(T)dr (e) y[n] = n=0 ns-1 (j) y(t) = dx(t) (1) y(t) = x(2) (n) y[n]=|x(n/2], in + 1 rln). -1 (m) y[n] [2n] n even n odd

Explanation / Answer

As we know that signal is invertible if and only if the output is different for the different inputs.

F) if y[n]=x[n]x[n-1]

Let x[n]=n then

y1[n]=n×x[n-1]

Let x[n]= -n then

y2[-n]=-n × x[n-1]

hence this signal is invertible signal

To construct Inverse system for this,inverse of this output has to give input then that is inverse system

Then in the output signal

Let n=x[n]/n then

y3[n]=x[n]x[n-1] which is the input we get hence the inverse of the signal is y[n]=x[n]/n x[n-1] and y[-n]=x[n]/-n x[n-1]

Similarly do the same thing for all...

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