Question

Theorem/law and its corresponding specified quality are given in the table below. Match List-I with List-II

• A. A - I, B - II, C - III, D - IV
• B. A - IV, B - III, C - II, D - I
• C. A - I, B - II, C - IV, D - III
• D. A - IV, B - II, C - III, D - I

Hint:

Create strong associations: - Shannon Source Coding \(\leftrightarrow\) Entropy/Code Length - Shannon-Hartley \(\leftrightarrow\) Channel Capacity - Wiener-Kintchine \(\leftrightarrow\) Power Spectrum \& Autocorrelation - Dimensionality \(\leftrightarrow\) Time-Bandwidth Product (Signal Space)

Answer 1

The Correct Option is D

Step 1: Match each theorem/law with its corresponding concept.

(A) Shannon Source Theorem: This is a fundamental theorem of data compression, also known as the noiseless coding theorem. It states that the minimum average number of bits per symbol required to represent a source is equal to its entropy. It defines the (IV) Optimum code length.
(B) Dimensionality Theorem: This theorem relates the time-bandwidth product of a signal to its degrees of freedom or dimensionality. It essentially describes the (II) Storage space of a signal. A signal of duration T and bandwidth W can be represented by 2WT samples.
(C) Wiener-Kintchine Theorem: This theorem states that the (III) Power spectral density of a wide-sense-stationary random process is the Fourier transform of its autocorrelation function.
(D) Shannon-Hartley Law: This famous law gives the upper bound for the data rate of a communication channel. It defines the (I) Channel capacity (C) in terms of bandwidth (B) and signal-to-noise ratio (S/N): \(C = B \log_2(1 + S/N)\).

Step 2: Combine the matches. The correct matching is: A-IV, B-II, C-III, D-I. This corresponds to option (D).