A 10-bit analog-to-digital converter (ADC) has a sampling frequency of 1 MHz and a full scale voltage of 3.3 V. For an input sinusoidal signal with frequency 500 kHz, the maximum SNR (in dB, rounded off to two decimal places) and the data rate (in Mbps) at the output of the ADC are _________, respectively.

Question

Consider a real-valued random process \[ f(t) = \sum_{n=1}^{N} a_n p(t - nT), \] where \( T > 0 \) and \( N \) is a positive integer. Here, \( p(t) = 1 \) for \( t \in [0, 0.5T] \) and 0 otherwise. The coefficients \( a_n \) are pairwise independent, zero-mean unit-variance random variables. Read the following statements about the random process and choose the correct option.

(i) The mean of the process \( f(t) \) is independent of time \( t \).
(ii) The autocorrelation function \( E[f(t)f(t + \tau)] \) is independent of time \( t \) for all \( \tau \).

(Here, \( E[.] \) is the expectation operation.)

Answer 1

SNR Calculation. The maximum SNR for an ADC is given by the formula: \[ {SNR (dB)} = 6.02 \cdot N + 1.76, \] where \( N \) is the number of bits. For a 10-bit ADC: \[ {SNR} = 6.02 \cdot 10 + 1.76 = 61.96 \, {dB}. \] Step 2: Data Rate Calculation. The data rate of the ADC is given by: \[ {Data Rate} = {Sampling Frequency} \times {Number of Bits}. \] Given the sampling frequency is 1 MHz and the ADC has 10 bits: \[ {Data Rate} = 1 \, {MHz} \times 10 = 10 \, {Mbps}. \] Thus, the correct answer is (A).

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The Correct Option is A

Solution and Explanation

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