Calculate the Nyquist rate and Nyquist interval from the given signal,
x(t)=5cos50\pi
t+20sin300\pi t+5cos100\pi t
Solution:
x(t)=5cos50\pi
t+20sin300\pi t+5cos100\pi t
This
is like below equation
x(t)=5cos\omega_1
t+20sin\omega_2 t+5cos\omega_3 t
\omega_1=50\pi
\omega_2=300\pi
\omega_3=100\pi
To
calculate the maximum frequency from above values is
\omega=2\pi
f
Therefore,
f_1=25Hz
f_2=150Hz
f_3=50Hz
Maximum frequency is nothing but highest frequency in a given signal
maximum
frequency f_{max}=150Hz
To
calculate the Nyquist rate or sampling rate
f_{Nr}=2f_{max}
f_{Nr}=2\times
150
f_{Nr}=300
Hz
To calculate the Nyquist interval, T_{Ni} is
T_{Ni}=\frac{1}{f_{Nr}}
or T_{Ni}=\frac{1}{2\times f_{max}}
T_{Ni}=\frac{1}{300}
T_{Ni}=0.0033
s
T_{Ni}=3.3 ms
Reference material
ReplyDeletehttps://electronicspost.com/what-is-nyquist-rate-and-nyquist-interval/
Deletehttps://ccsuniversity.ac.in/bridge-library/pdf/ENGG-EI-4th-sem-Signal-and-Systems-Code-BT-403-the-Sampling-theorem-and-its-implications.pdf
Delete