All parts and include the MATLAB code. Three discrete-time signals are defined as x₁ [n] = n(u[n] - u[n − 5]), x₂[n] = 4(u[n- 5] - u[n-11])and x3[n] = -28 [n-8]. Let x[n] be the discrete-time signal defined as x[n] = x₁ [n] + x₂ [n] + x3[n].In MATLAB do the following:1. define the unit-step function u[n] as an anonymous function in MATLAB as@(n) (n >= 0)u =and the unit-impulse function as an anonymous function in MATLAB asdelta@(n) (n = 0)2. Using subplot, plot x₁ [n], x2 [n], x3[n] and x[n] in a 2-by-2 plot window. Note that for discretesignals, stem() is used instead of plot(). Make sure to label your plots.3. In a separate plot window, plot the odd component xo[n] = [n]-x[-n]24. In a separate plot window, plot the even component re[n] = x[n]+x[-n]22=-∞05. Use the MATLAB defined function sum() to calculate the total energy Ex(x) = x - x[n]|²of x[n], the total energy Ex(x) = Σn-xe[n]|² of xe[n] and the total energy Ex(xo)- xo[n]² of xo[n].6. Compare the total energy of x[n] Ex(x) and Ex(xe) + Ex(xo).

Algorithm to Analyze Discrete-Time Signals:Define the unit-step function u[n] and the unit-impulse…

Answered: Three discrete-time signals are defined…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

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All parts and include the MATLAB code.

Three discrete-time signals are defined as x₁ [n] = n(u[n] - u[n − 5]), x₂[n] = 4(u[n- 5] - u[n-11])
and x3[n] = -28 [n-8]. Let x[n] be the discrete-time signal defined as x[n] = x₁ [n] + x₂ [n] + x3[n].
In MATLAB do the following:
1. define the unit-step function u[n] as an anonymous function in MATLAB as
@(n) (n >= 0)
u =
and the unit-impulse function as an anonymous function in MATLAB as
delta
@(n) (n = 0)
2. Using subplot, plot x₁ [n], x2 [n], x3[n] and x[n] in a 2-by-2 plot window. Note that for discrete
signals, stem() is used instead of plot(). Make sure to label your plots.
3. In a separate plot window, plot the odd component xo[n] = [n]-x[-n]
2
4. In a separate plot window, plot the even component re[n] = x[n]+x[-n]
2
2=-∞0
5. Use the MATLAB defined function sum() to calculate the total energy Ex(x) = x - x[n]|²
of x[n], the total energy Ex(x) = Σn-xe[n]|² of xe[n] and the total energy Ex(xo)
- xo[n]² of xo[n].
6. Compare the total energy of x[n] Ex(x) and Ex(xe) + Ex(xo).

Expert Solution

Step 1: Algorithm of the Source Code:

Algorithm to Analyze Discrete-Time Signals:

Define the unit-step function u[n] and the unit-impulse function delta[n] as anonymous functions:
- u(n) = (n >= 0)
- delta(n) = (n == 0)
Define the range of n over which you want to analyze the signals:
- n = -10:20
Define the three discrete-time signals:
- x1[n] = n * (u[n] - u[n-5])
- x2[n] = 4 * (u[n-5] - u[n-1])
- x3[n] = -28 * (n - 8)
- x[n] = delta[n] + x2[n] + x3[n]
Create a 2-by-2 plot window and use the stem() function to plot the four signals x1[n], x2[n], x3[n], and x[n], labeling each plot.
Calculate the odd component co[n] as the difference between x[n] and its time-reversed version x[-n]. Plot co[n].
Calculate the even component ce[n] as the average of x[n] and x[-n]. Plot ce[n].
Calculate the total energy for each signal:
- Ex_x is the total energy of x[n]
- Ex_e is the total energy of the even component ce[n]
- Ex_o is the total energy of the odd component co[n]
Compare the total energy of x[n] with the sum of energies of the even and odd components (Ex_e + Ex_o):
- If |Ex_x - (Ex_e + Ex_o)| < 1e-6, then print "The total energy of x[n] is approximately equal to Ex_e + Ex_o."
- Otherwise, print "The total energy of x[n] is not equal to Ex_e + Ex_o."

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