P-2.8 Suppose that MATLAB is used to plot a sinusoidal signal. The following MATLAB code generates the signal and makes the plot. Derive a formula for the signal; then without running the program, draw a sketch of the plot that will be done by MATLAB. dt = 1/1000; tt = -0.15 : dt: 0.15; Fo = 7; zz = 15*exp(j* (2*pi*Fo* (tt + 0.875))); xx = real( zz ); plot ( tt, xx ), grid on title('SECTION xlabel ('TIME of a SINUSOID' ) (s)/ )
P-2.8 Suppose that MATLAB is used to plot a sinusoidal signal. The following MATLAB code generates the signal and makes the plot. Derive a formula for the signal; then without running the program, draw a sketch of the plot that will be done by MATLAB. dt = 1/1000; tt = -0.15 : dt: 0.15; Fo = 7; zz = 15*exp(j* (2*pi*Fo* (tt + 0.875))); xx = real( zz ); plot ( tt, xx ), grid on title('SECTION xlabel ('TIME of a SINUSOID' ) (s)/ )
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Please assist with question P-2.8. With details on how to do it. Thank you.
Transcribed Image Text:### Complex Numbers and MATLAB
#### P-2.7 Simplify the following expressions:
(a) \( 3e^{j\pi/3} + 4e^{-j\pi/6} \)
(b) \( (\sqrt{3} - j3)^{10} \)
(c) \( (\sqrt{3} - j3)^{-1} \)
(d) \( (\sqrt{3} - j3)^{1/3} \)
(e) \( \Re \left\{ je^{-j\pi/3} \right\} \)
**Instructions**: Give the answers in both Cartesian form (\( x + jy \)) and polar form (\( re^{j\theta} \)).
#### P-2.8 MATLAB Plotting a Sinusoidal Signal
**Scenario**: Suppose that MATLAB is used to plot a sinusoidal signal. The following MATLAB code generates the signal and makes the plot. Derive a formula for the signal; then without running the program, draw a sketch of the plot that will be done by MATLAB.
```matlab
dt = 1/1000;
tt = -0.15 : dt : 0.15;
Fo = 7;
zz = 15*exp(j*(2*pi*Fo*(tt + 0.875)));
xx = real( zz );
plot( tt, xx ), grid on
title('SECTION of a SINUSOID')
xlabel('TIME (s)')
```
**Explanation**: This code snippet generates a section of a sinusoidal wave. Let’s break down the code to derive the formula for the signal and sketch the plot.
1. **Line 1**:
```matlab
dt = 1/1000;
```
This sets the time step \( dt \) to 0.001 seconds.
2. **Line 2**:
```matlab
tt = -0.15 : dt : 0.15;
```
This creates a time vector \( tt \) from -0.15 to 0.15 seconds in increments of \( dt \).
3. **Line 3**:
```matlab
Fo = 7;
```
This sets the frequency \( F_o \) to 7 Hz.
4. **Line 4**:
```matlab
zz = 15*exp(j*(2*pi*Fo
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