2. Consider the system defined by the relation y[n] = x[n] +2x[n− 1] + x[n-2]
(a) Obtain an expression for the frequency response of the system
(b) Graph the system frequency response (magnitude and phase) using the freqz command in MATLAB (attach code listing and output)
(c) Determine the output when the input is the signal x[n] = 10+4 cos(0.5πn+π/4)
(d) Determine the output with the input is the unit impulse function x[n] = δ [n].
(e) Determine the output with the input is the unit step function z[n] = u[n].
(more…)![Find the convolution of the two sequences 𝑥[𝑛] = [2 1 — 2 3 — 4] and h[n]=[3 1 2 1 4]](https://electricalstudent.com/wp-content/uploads/2023/07/20ea49c5-663e-4cfd-b479-2f043fce85ec-4844-000006f16d904655_file-1024x122.jpg)
![Find the convolution of the two sequences 𝑥[𝑛] = [2 1 — 2 3 — 4] and h[n]=[3 1 2 1 4]](https://i0.wp.com/electricalstudent.com/wp-content/uploads/2023/07/20ea49c5-663e-4cfd-b479-2f043fce85ec-4844-000006f16d904655_file.jpg?resize=1024%2C122&ssl=1 "Find the convolution of the two sequences 𝑥[𝑛] = [2 1 — 2 3 — 4] and h[n]=[3 1 2 1 4]")
![Using the FSMA method, find the output 𝑦[𝑛] of the system described by theimpulse response given by ℎ[𝑛] = 𝛿[𝑛] — 𝛿[𝑛— 1] + 2𝛿[𝑛— 2] — 𝛿[𝑛— 3] +𝛿[𝑛-4] if the input is 𝑥[𝑛] = 𝑢[𝑛 + 1]](https://electricalstudent.com/wp-content/uploads/2023/07/3811bfb0-bd67-4784-9086-4933f5d5f5bc-4844-000006f0a7a24226_file-1024x158.jpg)
![Using the FSMA method, find the output 𝑦[𝑛] of the system described by theimpulse response given by ℎ[𝑛] = 𝛿[𝑛] — 𝛿[𝑛— 1] + 2𝛿[𝑛— 2] — 𝛿[𝑛— 3] +𝛿[𝑛-4] if the input is 𝑥[𝑛] = 𝑢[𝑛 + 1]](https://i0.wp.com/electricalstudent.com/wp-content/uploads/2023/07/3811bfb0-bd67-4784-9086-4933f5d5f5bc-4844-000006f0a7a24226_file.jpg?resize=1024%2C158&ssl=1 "Using the FSMA method, find the output 𝑦[𝑛] of the system described by theimpulse response given by ℎ[𝑛] = 𝛿[𝑛] — 𝛿[𝑛— 1] + 2𝛿[𝑛— 2] — 𝛿[𝑛— 3] +𝛿[𝑛-4] if the input is 𝑥[𝑛] = 𝑢[𝑛 + 1]")
![3. A system is described by the impulse response given by:h[n]=(3/4)^nu(n+2) compute the output of the system at times n=-5,n=5&n=10 when the input is x[n]=u[n+1]](https://electricalstudent.com/wp-content/uploads/2023/07/a3ec126f-912c-4ae2-a911-927fe03a78f3-4844-000006f007ecd726_file-1024x288.jpg)
![3. A system is described by the impulse response given by:h[n]=(3/4)^nu(n+2) compute the output of the system at times n=-5,n=5&n=10 when the input is x[n]=u[n+1]](https://i0.wp.com/electricalstudent.com/wp-content/uploads/2023/07/a3ec126f-912c-4ae2-a911-927fe03a78f3-4844-000006f007ecd726_file.jpg?resize=1024%2C288&ssl=1 "3. A system is described by the impulse response given by:h[n]=(3/4)^nu(n+2) compute the output of the system at times n=-5,n=5&n=10 when the input is x[n]=u[n+1]")
![2.A system is described by the impulse response given by:ℎ[𝑛] = 2𝛿[𝑛] — 3𝛿[𝑛 — 1] + 2𝛿[𝑛 — 2]Find its output 𝑦[𝑛] when the input to this system is:](https://electricalstudent.com/wp-content/uploads/2023/07/bf182fc2-8cf5-48bb-b61f-5ea582ee8d5b-4844-000006ef11080c27_file-1024x499.jpg)
![2.A system is described by the impulse response given by:ℎ[𝑛] = 2𝛿[𝑛] — 3𝛿[𝑛 — 1] + 2𝛿[𝑛 — 2]Find its output 𝑦[𝑛] when the input to this system is:](https://i0.wp.com/electricalstudent.com/wp-content/uploads/2023/07/bf182fc2-8cf5-48bb-b61f-5ea582ee8d5b-4844-000006ef11080c27_file.jpg?resize=1024%2C499&ssl=1 "2.A system is described by the impulse response given by:ℎ[𝑛] = 2𝛿[𝑛] — 3𝛿[𝑛 — 1] + 2𝛿[𝑛 — 2]Find its output 𝑦[𝑛] when the input to this system is:")
![Let the impulse response ℎ[𝑛] of a system be:ℎ[𝑛] = 2𝛿[𝑛] + 𝛿[𝑛 — 2] — 2𝛿[𝑛 — 3] Find the output 𝑦[𝑛] of this system if the input is given by:𝑥[𝑛] = 3𝛿[𝑛] + 2 𝛿[𝑛 — 2] + 𝛿[𝑛 — 3]](https://electricalstudent.com/wp-content/uploads/2023/07/4eeee0ed-e26e-4bc5-b21b-405813c7301c-4844-000006ede1698142_file-1024x389.jpg)
![Let the impulse response ℎ[𝑛] of a system be:ℎ[𝑛] = 2𝛿[𝑛] + 𝛿[𝑛 — 2] — 2𝛿[𝑛 — 3] Find the output 𝑦[𝑛] of this system if the input is given by:𝑥[𝑛] = 3𝛿[𝑛] + 2 𝛿[𝑛 — 2] + 𝛿[𝑛 — 3]](https://i0.wp.com/electricalstudent.com/wp-content/uploads/2023/07/4eeee0ed-e26e-4bc5-b21b-405813c7301c-4844-000006ede1698142_file.jpg?resize=1024%2C389&ssl=1 "Let the impulse response ℎ[𝑛] of a system be:ℎ[𝑛] = 2𝛿[𝑛] + 𝛿[𝑛 — 2] — 2𝛿[𝑛 — 3] Find the output 𝑦[𝑛] of this system if the input is given by:𝑥[𝑛] = 3𝛿[𝑛] + 2 𝛿[𝑛 — 2] + 𝛿[𝑛 — 3]")