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- Homework Statement
- Determine whether the system is (a) linear, (b) time-invariant:

- Relevant Equations
- y[n] = T{x[n]} = x(t)

y(t) = cos(3t)x(t)

A system is linear if it satisfies the properties of superposition and homogeneity.

Superposition: adding the inputs of two systems results in the addition of the two outputs.

Ex) x

Homogeneity: multiplying the input by some scalar value is equal to the output multiplied by that same value.

Ex) ax

After doing some internet searching, I also found this equation for superposition: f(a+b) = f(a) + f(b)

However, I don't know how to apply these rules to determine whether my equations are linear or not.

My attempt for determining SP:

y

If my attempt at SP is correct, what is the next step? If it is wrong, what is the right way to write it, and then what is the next step?

Superposition: adding the inputs of two systems results in the addition of the two outputs.

Ex) x

_{1}(t) + x_{2}(t) = y_{1}(t) + y_{2}(t)Homogeneity: multiplying the input by some scalar value is equal to the output multiplied by that same value.

Ex) ax

_{1}(t) = ay_{2}(t)After doing some internet searching, I also found this equation for superposition: f(a+b) = f(a) + f(b)

However, I don't know how to apply these rules to determine whether my equations are linear or not.

My attempt for determining SP:

y

_{1}[n] + y_{2}[n] = T{x_{1}[n] + x_{2}[n]} = n(x_{1}[n] + x_{2}[n])If my attempt at SP is correct, what is the next step? If it is wrong, what is the right way to write it, and then what is the next step?