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The Nyquist sampling interval, for the signal sinc(700t) + sinc(500t) is:
- a)(1/350)sec
- b)(π/350)sec
- c)(1/700)sec
- d)(π/175)sec
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The Nyquist sampling interval, for the signal sinc(700t) + sinc(500t) ...
Understanding the Nyquist Sampling Theorem
The Nyquist sampling theorem states that to accurately sample a signal without losing information, the sampling frequency must be at least twice the highest frequency present in the signal.
Signal Analysis
The given signal is:
- sinc(700t) + sinc(500t)
This consists of two sinc functions, where the sinc function is defined as sinc(x) = sin(πx)/(πx). The argument of the sinc function indicates the frequency.
Identifying Frequencies
- The first term, sinc(700t), has a frequency component of 700 Hz.
- The second term, sinc(500t), has a frequency component of 500 Hz.
Determining the Maximum Frequency
To find the Nyquist sampling interval, we first identify the highest frequency in the signal:
- Maximum frequency, f_max = max(700 Hz, 500 Hz) = 700 Hz
Calculating the Nyquist Rate
According to the Nyquist theorem, the Nyquist rate is twice the maximum frequency:
- Nyquist rate = 2 * f_max = 2 * 700 Hz = 1400 Hz
Finding the Nyquist Sampling Interval
The Nyquist sampling interval (T) is the inverse of the Nyquist rate:
- T = 1 / (Nyquist rate) = 1 / 1400 sec
Final Calculation
To simplify:
- T = 1 / 1400 sec = 1 / (2 * 700) sec = 1 / 700 sec
Thus, the Nyquist sampling interval for the signal sinc(700t) + sinc(500t) is:
- (1/700) sec
Hence, the correct answer is option 'C'.
The Nyquist sampling theorem states that to accurately sample a signal without losing information, the sampling frequency must be at least twice the highest frequency present in the signal.
Signal Analysis
The given signal is:
- sinc(700t) + sinc(500t)
This consists of two sinc functions, where the sinc function is defined as sinc(x) = sin(πx)/(πx). The argument of the sinc function indicates the frequency.
Identifying Frequencies
- The first term, sinc(700t), has a frequency component of 700 Hz.
- The second term, sinc(500t), has a frequency component of 500 Hz.
Determining the Maximum Frequency
To find the Nyquist sampling interval, we first identify the highest frequency in the signal:
- Maximum frequency, f_max = max(700 Hz, 500 Hz) = 700 Hz
Calculating the Nyquist Rate
According to the Nyquist theorem, the Nyquist rate is twice the maximum frequency:
- Nyquist rate = 2 * f_max = 2 * 700 Hz = 1400 Hz
Finding the Nyquist Sampling Interval
The Nyquist sampling interval (T) is the inverse of the Nyquist rate:
- T = 1 / (Nyquist rate) = 1 / 1400 sec
Final Calculation
To simplify:
- T = 1 / 1400 sec = 1 / (2 * 700) sec = 1 / 700 sec
Thus, the Nyquist sampling interval for the signal sinc(700t) + sinc(500t) is:
- (1/700) sec
Hence, the correct answer is option 'C'.
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Community Answer
The Nyquist sampling interval, for the signal sinc(700t) + sinc(500t) ...
Concept:
Nyquist rate: The minimum sampling rate is often called the Nyquist rate. The Nyquist sampling rate is two times the highest frequency of the input or message signal.
fs = 2fm
Where,
fs is the minimum sampling frequency or Nyquist rate
fm is the highest frequency of the input or message signal.
Calculation:
sinc(700t) + sinc(500t)
f1 = 700π/2π = 350 Hz
f2 = 500π/2π = 250 Hz
fm = max (f1, f2) = max (350, 250) = 350 Hz
Sampling frequency,
fs = 2fm = 2 × 350 = 700 Hz
Sampling time period = 1/700 sec
Nyquist rate: The minimum sampling rate is often called the Nyquist rate. The Nyquist sampling rate is two times the highest frequency of the input or message signal.
fs = 2fm
Where,
fs is the minimum sampling frequency or Nyquist rate
fm is the highest frequency of the input or message signal.
Calculation:
sinc(700t) + sinc(500t)
f1 = 700π/2π = 350 Hz
f2 = 500π/2π = 250 Hz
fm = max (f1, f2) = max (350, 250) = 350 Hz
Sampling frequency,
fs = 2fm = 2 × 350 = 700 Hz
Sampling time period = 1/700 sec
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