Consider a system with the input/output relationship y(t) = x(t)cos(15πt). (a) Is this system (i) linear,...

Consider a system with the input/output relationship y(t) = x(t)cos(15πt).
(a) Is this system (i) linear, (ii) causal, (iii) stable, (iv) memoryless, (v) time-invariant, and (vi) invertible. Justify each answer with a clear mathematical argument. (b) Find the Fourier Transform Y (f) of y(t) in terms of the transform X(f) of x(t).

Repeat problem (2) for the system with the input-output relationship y(t) =R1 τ=0(1−τ)2x(t−τ)dτ.

Expert Solution

Colby Messinger answered 2 years ago

x[n] is the input of a system and y[n] is the output of the system. The...

x[n] is the input of a system and y[n] is the output of the system. The relationship between the input and output is the following: y[n] = x[n]u[n+1] a) Is the system memoryless? Just yes or no is sufficient. b) Is this system causal? Just yes or no is sufficient. c) Is the system linear? Just yes or no is sufficient. d) Is the system time invariant? Justify. e) Is the system BIBO stable? Justify. f) Is the system invertible?...

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