(Solved): 2. IIR versus FIR systems A significant difference between IIR and FIR discrete-time systems is st ...

2. IIR versus FIR systems A significant difference between IIR and FIR discrete-time systems is stability. Consider an IIR filter with the difference equation $${?}_1[n]=x[n]?0.5y_1[n?1]$$ where $$x[n]$$ is the input and $$y_1[n]$$ is the output. Then consider an FIR filter $${?}_2?n]=x[n]+0.5x[n?1]+3x[n?2]+x[n?5]$$ where $$x[n]$$ is the input and $$y_2[n]$$ is the output. (a) Since to check the stability of these filters we need their impulse responses, find the impulse responses $$h_1?n?$$ corresponding to the IIR filter by recursion, and $$h_2[n?$$ corresponding to the FIR fiter. (b) Use the impulse response $$h_1?n?$$ to check the stability of the IIR filter. (c) Use the impulse response $$h_2[n]$$ to check the stability of the FIR filter. (d) Since the impulse response of a FIR filter has a finite number of nonzero terms, would it be correct to say that FIR filters are always stable? Explain.