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A 4 kHz sinusoidal message signal having amplitude 4 V is fed to a delta modulator (DM) operating at a sampling rate of 32 kHz. The minimum step size required to avoid slope overload noise in the DM (rounded off to two decimal places) is _______ V.
Correct answer is '3.14'. Can you explain this answer?
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A 4 kHz sinusoidal message signal having amplitude 4 V is fed to a del...
Given information:
- Message signal frequency (f) = 4 kHz
- Message signal amplitude (A) = 4 V
- Sampling rate (fs) = 32 kHz
Explanation:
Delta modulation (DM):
Delta modulation is a simple form of analog-to-digital conversion technique used to convert analog signals into digital signals. It is a type of differential pulse code modulation (DPCM) where the difference between consecutive samples is quantized and transmitted.
Step size and slope overload noise:
In delta modulation, the step size determines the resolution of the quantizer and the accuracy of the digital representation of the analog signal. If the step size is too large, it can cause slope overload noise. Slope overload noise occurs when the slope of the input analog signal exceeds the maximum slope that can be tracked by the delta modulator.
Calculating the minimum step size:
To calculate the minimum step size required to avoid slope overload noise, we need to consider the maximum frequency of the input signal and the sampling rate.
Maximum frequency:
The maximum frequency of the input signal can be determined using the Nyquist-Shannon sampling theorem, which states that the sampling rate should be at least twice the maximum frequency of the signal.
Maximum frequency (fmax) = (fs/2)
= (32 kHz/2)
= 16 kHz
Step size calculation:
The step size can be calculated using the formula:
Step size = (maximum amplitude of the input signal) / (maximum slope of the input signal)
Maximum amplitude:
The maximum amplitude of the input signal is given as 4 V.
Maximum slope:
The maximum slope of a sinusoidal signal can be calculated using the formula:
Maximum slope = (2 * π * f * A)
Substituting the values:
Maximum slope = (2 * π * 4 kHz * 4 V)
= 32 * π kV/s
Now, substituting the values in the step size formula:
Step size = (4 V) / (32 * π kV/s)
Calculating the step size:
Step size ≈ 0.03979 kV/s
Rounding off to two decimal places, we get:
Step size ≈ 0.04 kV/s
≈ 40 V/s
Therefore, the minimum step size required to avoid slope overload noise in the delta modulator is approximately 0.04 V or 40 mV.
- Message signal frequency (f) = 4 kHz
- Message signal amplitude (A) = 4 V
- Sampling rate (fs) = 32 kHz
Explanation:
Delta modulation (DM):
Delta modulation is a simple form of analog-to-digital conversion technique used to convert analog signals into digital signals. It is a type of differential pulse code modulation (DPCM) where the difference between consecutive samples is quantized and transmitted.
Step size and slope overload noise:
In delta modulation, the step size determines the resolution of the quantizer and the accuracy of the digital representation of the analog signal. If the step size is too large, it can cause slope overload noise. Slope overload noise occurs when the slope of the input analog signal exceeds the maximum slope that can be tracked by the delta modulator.
Calculating the minimum step size:
To calculate the minimum step size required to avoid slope overload noise, we need to consider the maximum frequency of the input signal and the sampling rate.
Maximum frequency:
The maximum frequency of the input signal can be determined using the Nyquist-Shannon sampling theorem, which states that the sampling rate should be at least twice the maximum frequency of the signal.
Maximum frequency (fmax) = (fs/2)
= (32 kHz/2)
= 16 kHz
Step size calculation:
The step size can be calculated using the formula:
Step size = (maximum amplitude of the input signal) / (maximum slope of the input signal)
Maximum amplitude:
The maximum amplitude of the input signal is given as 4 V.
Maximum slope:
The maximum slope of a sinusoidal signal can be calculated using the formula:
Maximum slope = (2 * π * f * A)
Substituting the values:
Maximum slope = (2 * π * 4 kHz * 4 V)
= 32 * π kV/s
Now, substituting the values in the step size formula:
Step size = (4 V) / (32 * π kV/s)
Calculating the step size:
Step size ≈ 0.03979 kV/s
Rounding off to two decimal places, we get:
Step size ≈ 0.04 kV/s
≈ 40 V/s
Therefore, the minimum step size required to avoid slope overload noise in the delta modulator is approximately 0.04 V or 40 mV.
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Community Answer
A 4 kHz sinusoidal message signal having amplitude 4 V is fed to a del...
Given : Message signal frequency, fm = 4kHz
Message signal amplitude, Am = 4V
Sampling rate, fs = 32kHz
Assume message signal, m(t) = Am cos 2π fmt
To avoid slope overload distortion,
So, minimum value of step size s is,
Hence, the minimum step size required to avoid slope overload is 3.14 V.
Question_Type: 4
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A 4 kHz sinusoidal message signal having amplitude 4 V is fed to a delta modulator (DM) operating at a sampling rate of 32 kHz. The minimum step size required to avoid slope overload noise in the DM (rounded off to two decimal places) is _______ V.Correct answer is '3.14'. Can you explain this answer?
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