Expected GATE-2022 Geophysics Solution (9)

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 $T_{Ni}=\frac{1}{2\times f_{max}}$

$T_{Ni}=\frac{1}{300}$

$T_{Ni}=0.0033 s$

$T_{Ni}=3.3 ms$

GEOPHYSICS