Step 1: Match the following theorems/laws with their corresponding concepts.
(A) Shannon Source Theorem: This theorem, central to data compression and also known as the noiseless coding theorem, posits that the minimum average bits per symbol needed to represent a source equals its entropy. It defines the (IV) Optimum code length. (B) Dimensionality Theorem: This theorem links a signal's time-bandwidth product to its dimensionality or degrees of freedom, essentially describing the (II) Storage space of a signal. Specifically, a signal with duration T and bandwidth W can be represented by 2WT samples. (C) Wiener-Kintchine Theorem: This theorem establishes 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 law provides the upper limit on the data rate of a communication channel. It defines the (I) Channel capacity (C) based on bandwidth (B) and signal-to-noise ratio (S/N), expressed as: \(C = B \log_2(1 + S/N)\).
