Determine if the following systems are time-invariant, linear, causal, and/or memoryless. dy(t) a) + 5y(t) =...

 

Transcribed Image Text:

Determine if the following systems are time-invariant, linear, causal, and/or memoryless. dy(t) a) + 5y(t) = 4x(t) dt dy(t) b) dt c) y[n] + 2y[n- 3] = x[n + 1] d) y(t) = 3sin (x(t)) + 4ty(t) = x(t) Solve the following difference equations using recursion first by hand (for n=0 to n=4), then using MATLAB (for n=0 to n=30). Plot the output computed by MATLAB on a stem plot. a) y[n] + 2y[n-1] = 2x[n-1]; x[n] = 8[n], y[-1] = 0 b) y[n] +1.2y[n-1] + 0.32y[n-2] = x[n]-x[n-1]; x[n] = u[n], y[-2] = 1, y[-1]=2 Determine if the following systems are time-invariant, linear, causal, and/or memoryless. dy(t) a) + 5y(t) = 4x(t) dt dy(t) b) dt c) y[n] + 2y[n- 3] = x[n + 1] d) y(t) = 3sin (x(t)) + 4ty(t) = x(t) Solve the following difference equations using recursion first by hand (for n=0 to n=4), then using MATLAB (for n=0 to n=30). Plot the output computed by MATLAB on a stem plot. a) y[n] + 2y[n-1] = 2x[n-1]; x[n] = 8[n], y[-1] = 0 b) y[n] +1.2y[n-1] + 0.32y[n-2] = x[n]-x[n-1]; x[n] = u[n], y[-2] = 1, y[-1]=2