Inlab report 1 find the roots for polynomials shown above

Question

MATLAB Session on Signals, Systems

MATLAB Session

-Continuous Time System Analysis

• Learn to find "roots" for "Characteristic Functions" in MATLAB.
• Find "Zero Input Response" from "Differential Equation" in CT system and plot the result w.r.t. time.
• Find "Zero State Response" from "Differential Equation" in CT system and plot the result w.r.t. time.

• Discrete Time System Analysis

• Learn to find and plot DT signals, impulse, response.
• Find "Zero State Response" using filter function from "DifferenCE Equation" in DT system and plot the result w.r.t. time sequence.
• Write MATLAB code to plot Zero State Response (Convolution), y(t), for given signal and impulse response using conv function.

Finding Roots for Characteristic Functions -

INLAB Report (1):

• Find the roots for polynomials shown above using MATLAB.
• Can you guess a function which finds "roots" for polynomials in MATLAB?
• Use help in MATLAB to find the syntax for function.

Finding Zero Input Response and Zero State Response in CT System -

INLAB Report (2):

• Find the Zero Input Response using MATLAB.
• Consider using "dsolve" function.
• Use help in MATLAB to find the syntax for function.

INLAB Report (3):

• Add following results to your previous C2.2 results.
• Plot your result, y_zi(t), w.r.t. time.
• Use "linspace" function to define time from 0[sec] to 3[sec] with 100[samples].
• Use "y_zi = eval(vectorize(y));" to convert function into a vector.
• Display between 0 ~ 3[sec] in x-axis, 0 ~ 6 in y-axis.
• Use help in MATLAB to find the syntax for function.

INLAB Report (4):

• Find the Zero State Response using MATLAB.
• Plot your result, y_zs(t), w.r.t. time.
• Use "linspace" function to define time from 0[sec] to 3[sec] with 100[samples].
• Display between 0 ~ 3[sec] in x-axis, 0 ~ 6 in y-axis.

Finding Impulse Response (h(n)) for a DT system -

INLAB Report (5):

Generate DT unit step function x[n] = u[n]

• Define time sequence n from 0 to 19.
• Use "ones" function to generate unit step function.
• Use help in MATLAB to find the syntax for function.

Plot your result, x[n], w.r.t. time sequence n using "stem" function.

• Display result from -1 to 19 in x-axis and -2 to 2 in y-axis

INLAB Report (6):

Generate DT unit ramp function x[n] = r[n] = t x u[n]

• Define time sequence n from 0 to 19.
• Use "ones" function to generate unit step function.
• Use help in MATLAB to find the syntax for function.

Plot your result, x[n], w.r.t. time sequence n using "stem" function.

• Display result from -1 to 19 in x-axis and -2 to 20 in y-axis.

INLAB Report (7):

Generate DT unit impulse function x[n] = d[n]

• Define time sequence n from 0 to 19.
• Use "zeros" function to generate unit step function.
• Use help in MATLAB to find the syntax for function.

Plot your result, x[n], w.r.t. time sequence n using "stem" function.

• Display result from -1 to 19 in x-axis and -2 to 2 in y-axis

INLAB Report (8):

Find the Impulse Response for a DT system below using MATLAB.

y[n+2] - 0.6y[n+1] - 0.16y[n] = 5x[n=2]

Plot your result, h[n], w.r.t. time sequence n using "stem" function.

Use "filter" function to describe the difference equation.

a = [1 -0.6 -0.16];

b = [5 0 0];

h = filter(b, a, x);

Think about your input x[n]... Use time sequence n from 0 to 19.

Finding Zero State Response for a DT system -

INLAB Report (9):

For the same DT system below,

y[n+2] - 0.6y[n+1] - 0.16y[n] = 5x[n+2]

Apply DT unit step input x[n] = u[n] to the system. Use time sequence n from 0 to 19.

Plot your results, x[n] (input), y[n] (output), w.r.t. time sequence n using "stem" function.

INLAB Report (10):

For the same DT system below,

y[n+2] - 0.6y[n+1] - 0.16y[n] = 5x[n+2]

Apply DT unit ramp input x[n] = r[n] to the system. Use time sequence n from 0 to 19.

Plot your results, x[n] (input), y[n] (output), w.r.t. time sequence n using "stem" function.

INLAB Report (11):

For the same DT system below,

y[n+2] - 1.5y[n+1] + y[n] = 2x[n]

Apply DT input x[n] = 4^-nu[n] to the system.

• Use time sequence n from 0 to 19.
• Use "stp_fn(n)" to generate input.

Plot your results, x[n] (input), y[n] (output), w.r.t. time sequence n using "stem" function.

Finding and plotting Convolution Integral -

INLAB Report (12):

Write MATLAB code to plot Discrete Time Zero State Response (Convolution), y(t), for below signal, x[n] ,and impulse response, h[n].

• Use "conv" function to find convolution.
• Plot your results (x[n], h[n], y[n] )

Explain your code. (Provide line-by-line description on the code)

INLAB Report (13):

Write MATLAB code to plot Continuous Time Zero State Response (Convolution), y(t), for the same signal, x( t ) ,and impulse response, h(t).

-Convert your DT signals to CT signals (Use 100 sample points between 1 discrete sequences to be considered as "continuous")

• x[n] → x(t)
• h[n] → h(t)

-Use "conv" function to find convolution.

-Think about spacing between integers (number of sample points between 1 discrete sequences), you will have to normalize your result.

-Plot your results (x(t), h(t), y(t))

Explain your code. (provide line-by-line description on the code)

Attachment:- Matlab Assignment.rar