Inlab report 1 find the roots for polynomials shown above


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, yzi(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, yzs(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

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