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Expected GATE-2022 Geophysics Solution (9)

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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

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  1. Replies
    1. https://electronicspost.com/what-is-nyquist-rate-and-nyquist-interval/

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    2. https://ccsuniversity.ac.in/bridge-library/pdf/ENGG-EI-4th-sem-Signal-and-Systems-Code-BT-403-the-Sampling-theorem-and-its-implications.pdf

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