Question

1) Linearity: In order for a system to be linear it must satisfy the following equation: In other words, the response of a linear system to an input that is a linear combination of two signals is the linear combination of the responses of the system to each one of these signals. Let xi)- u(t) -u(t-1) and x2t) u- u(t-2) be input signals to the systems described by the i/o relationships ylt) 2x() and yt)-). Determine if the linearity property holds for these two systems. To examine if the systems are linear, we use the scalars a1 2 and a2- 3. The time interval considered is -3ts3 Show if both systems are linear or non-linear mathmatically and using matlab software (hint: plot the left side of the equation above and then plot the equation of the right side and compare the two graphs). Note: in order to plot u(t)-u(t-1) use matlab built-in function “heaviside". x1sheaviside(t)-heaviside(t_1); 2) Time-Invariant and Time-Variant Systems Suppose that the response of a system S to an input signal x()is y) te x(t). Determine if this system is time invariant by using the input signal x(t)u)-u( 5 In order to determine if the system is time invariant, first compute and plot the system response y(t) to the given input signal x(t) =u(t)-u(t-5). Next the computed output y(t) is shifted by x units i.e. 3 to the right to represent the signal y1(t)-y(t-3). This process corresponds to the left side of the above equation. As to the right side of the equation, first the input signal x(t) is shifted 3 units to the right in order to represent the signal x(t-3). Next system response y2(t) Sx(t-3)) is computed and plotted. If the output is equal, the system is considered to be time-invariant. 3) Stable and unstable systems Suppose that an input signal x(f)- cos (2mt) is applied to two systems described by the i/o relationships y) t) and y2(t)-tx) Determine if these two systems are stable Show if both systems are stable/unstable mathmatically and using matlab software

need solution and code for this signal and system problem

Answer 1

.11'3 і」 Nan.요.near.

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