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 u= @(n) (n >= 0) 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] = z[n]-x[-n]¸ 2 4. In a separate plot window, plot the even component [n] = a[n]+x[-n] 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(e) = x-xe[n]² of xe[n] and the total energy Ex(x) = -xo[n]² of xo[n]. 6. Compare the total energy of x[n] Ex(x) and Ex(xe) + Ex(xo).
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).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F072e444d-1bde-4899-b3c3-9f07885f3d58%2Fa15ba4ed-448b-4866-a50c-08cbba3ba269%2Fotvtkcu_processed.png&w=3840&q=75)
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Algorithm to Analyze Discrete-Time Signals:
Define the unit-step function
u[n]
and the unit-impulse functiondelta[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 signalsx1[n]
,x2[n]
,x3[n]
, andx[n]
, labeling each plot.Calculate the odd component
co[n]
as the difference betweenx[n]
and its time-reversed versionx[-n]
. Plotco[n]
.Calculate the even component
ce[n]
as the average ofx[n]
andx[-n]
. Plotce[n]
.Calculate the total energy for each signal:
Ex_x
is the total energy ofx[n]
Ex_e
is the total energy of the even componentce[n]
Ex_o
is the total energy of the odd componentco[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."
- If
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