$s(t)$ is a multi-level (-1, 0, +1, +2) signal representing a long sequence of random symbols from the above source which is generating $10^4$ symbols per second.
Which of the following options is the correct value of equivalent Nyquist bandwidth of $s(t)$?
Nyquist Bandwidth Calculation for Digital Source
The problem asks for the equivalent Nyquist bandwidth of a signal $s(t)$ generated by a discrete memoryless source.
Key information provided:
- Source alphabet size: 4 symbols.
- Signal levels: {-1, 0, +1, +2}.
- Source symbol generation rate: $R_s = 10^4$ symbols per second.
Nyquist Bandwidth Concept
The Nyquist bandwidth is the minimum theoretical bandwidth required to transmit a digital signal without inter-symbol interference (ISI). It is directly related to the symbol rate ($R_s$) of the source.
The formula relating Nyquist bandwidth ($B_{Nyquist}$) and symbol rate ($R_s$) is:
$B_{Nyquist} = \frac{R_s}{2}$This formula indicates that the required bandwidth is half the symbol rate.
Bandwidth Calculation
Given the symbol rate $R_s = 10^4$ symbols/sec:
- Substitute the value of $R_s$ into the formula: $B_{Nyquist} = \frac{10^4 \text{ symbols/sec}}{2}$
- Calculate the result: $B_{Nyquist} = 5 \times 10^3 \text{ Hz}$
- Convert the bandwidth to kilohertz (kHz): $B_{Nyquist} = 5 \text{ kHz}$
The equivalent Nyquist bandwidth of the signal $s(t)$ is 5 kHz.
Conclusion
Comparing the calculated bandwidth with the given options:
- Option 1: 10 kHz
- Option 2: 64 kHz
- Option 3: 5 kHz
- Option 4: 20 kHz
The calculated value of 5 kHz matches Option 3.
Important Questions from Information Theory
- Match items in List – I with items in List – II and select the correct answer from the code given below :
List – I List – II a. The Screening Hypothesis 1. George A. Akerlof b. Job Market Signalling 2. K.J. Arrow c. The problem of moral hazard in the case of medical insurance 3. M. Spencer d. The market for lemons 4. Paul W. Miller and Paul A. Volcker
Codes : A source transmits symbols from an alphabet of size 16. The value of maximum achievable entropy (in bits) is _______
An analog baseband signal, bandlimited to 100 Hz, is sampled at the Nyquist rate. The samples are quantized into four message symbols that occur independently with probabilities $p_1 = p_4 = 0.125$ and $p_2 = p_3$. The information rate (bits/sec) of the message source is ____________
The random variable $X$ takes values in $\{-1, 0, 1\}$ with probabilities $P(X = -1) = P(X = 1)$ and $\alpha$ and $P(X = 0) = 1 - 2\alpha$, where $0 < \alpha < \frac{1}{2}$. Let $g(\alpha)$ denote the entropy of $X$ (in bits), parameterized by $\alpha$. Which of the following statements is/are TRUE?
An information system uses the following daily workflow. Each function can start only after the input it explicitly requires has been produced. Arrange the functions in execution order.
(A) Process and validate the day’s sales transactions.
(B) Update the inventory master file using the validated transactions.
(C) Process managers’ enquiries using the figures in the completed daily report.
(D) Generate the daily report from the updated inventory master file.
(E) Run interactive decision-support scenarios using the results returned by those enquiries.
Choose the correct answer from the options below.
