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What is the nyquist rate of the signal x(t)=3cos(50*pi*t)+10sin(300*pi*t)-cos(100*pi*t)?
  • a)
    50Hz
  • b)
    100Hz
  • c)
    200Hz
  • d)
    300Hz
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
What is the nyquist rate of the signal x(t)=3cos(50*pi*t)+10sin(300*pi...
Explanation:
The frequencies present in the given signal are:
F1=25Hz
F2=150Hz
F3=50Hz


Thus,
Fmax=150Hz
and from the sampling theorem,
Nyquist rate=2*Fmax
Therefore, Fs=2*150=300Hz.

Hence, the Correct Answer is Option D
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Most Upvoted Answer
What is the nyquist rate of the signal x(t)=3cos(50*pi*t)+10sin(300*pi...
Nyquist Rate:

The Nyquist rate is the minimum sampling rate required to accurately reconstruct a continuous-time signal from its discrete-time samples.

Given Signal:

The signal x(t)=3cos(50*pi*t) 10sin(300*pi*t)-cos(100*pi*t) has the following frequency components:

- A cosine wave with frequency 50*pi Hz
- A sine wave with frequency 300*pi Hz
- A cosine wave with frequency 100*pi Hz

Nyquist Rate Calculation:

The Nyquist rate for this signal can be calculated using the following formula:

Nyquist rate = 2 * maximum frequency component

In this case, the maximum frequency component is 300*pi Hz. Therefore, the Nyquist rate is:

Nyquist rate = 2 * 300*pi Hz = 600*pi Hz

Converting this to Hz, we get:

Nyquist rate = 600*pi / (2*pi) Hz = 300 Hz

Therefore, the correct answer is option D, i.e., 300 Hz.
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