Question

A message signal $m(t)$ is defined as, $\begin{cases} 1, & -2 \le t < -1, \\ -t, & -1 \le t < 0 \\ t, & 0 \le t < 1, \\ 1, & 1 \le t < 2 \\ 0 & others \end{cases}$ The unit for the time in above equation is second. The carrier is given as $c(t) = A_ccos(2\pi f_ct)$ where $A_c = 1$ and $f_c = 10Hz$. 1. Sketch the waveform of the FM and PM modulations. 2. Identify the amplitude for the most significant seven frequency components for FM modulation signal where $m(t) = A_mcos(2\pi f_mt)$ and $A_m = 1.5v, f_m = 1.5Hz$ and $k_f = 2.5Hz/v$. Use the function of stem to plot the spectrum.

          A message signal $m(t)$ is defined as,
$\begin{cases}
1, & -2 \le t < -1, \\
-t, & -1 \le t < 0 \\
t, & 0 \le t < 1, \\
1, & 1 \le t < 2 \\
0 & others
\end{cases}$
The unit for the time in above equation is second. The carrier is given as $c(t) = A_ccos(2\pi f_ct)$ where $A_c = 1$ and $f_c = 10Hz$.
1. Sketch the waveform of the FM and PM modulations.
2. Identify the amplitude for the most significant seven frequency components for FM modulation signal where $m(t) = A_mcos(2\pi f_mt)$ and $A_m = 1.5v, f_m = 1.5Hz$ and
$k_f = 2.5Hz/v$. Use the function of stem to plot the spectrum.

A message signal m(t) is defined as,
1, -2 ≤ t < -1,

-t, -1 ≤ t < 0

t, 0 ≤ t < 1,

1, 1 ≤ t < 2

0 others
The unit for the time in above equation is second. The carrier is given as c(t) = Accos(2π fct) where Ac = 1 and fc = 10Hz.
1. Sketch the waveform of the FM and PM modulations.
2. Identify the amplitude for the most significant seven frequency components for FM modulation signal where m(t) = Amcos(2π fmt) and Am = 1.5v, fm = 1.5Hz and
kf = 2.5Hz/v. Use the function of stem to plot the spectrum.

Added by Celia C.

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