Question

In delta modulation (DM) system, the granular noise occurs when the modulating signal

• A. Increases rapidly
• B. Decreases rapidly
• C. Remains constant
• D. Has high frequency components

Hint:

Delta Modulation (DM) uses a 1-bit quantizer and a fixed step size \(\Delta\).
\textbf{Slope Overload:} Input signal changes too fast (\( |dm(t)/dt|_{max}>\Delta/T_s \)).
\textbf{Granular Noise:} Input signal changes too slowly or is constant (staircase oscillates around the signal).
Adaptive Delta Modulation (ADM) varies the step size to reduce both types of noise.

Answer 1

The Correct Option is C

Delta Modulation (DM) is a technique where the analog input signal is approximated by a staircase waveform. At each sampling instant, the DM system transmits a single bit indicating whether the staircase approximation should increase or decrease by a fixed step size (\(\Delta\)). There are two main types of distortion in DM: 1. Slope Overload Distortion: Occurs when the input analog signal changes too rapidly (steep slope) for the staircase approximation to follow. The step size \(\Delta\) is too small to keep up with the signal's rate of change. This happens when the signal "increases rapidly" (option a) or "decreases rapidly" (option b). 2. Granular Noise (or Idling Noise): Occurs when the input analog signal is relatively constant or changes very slowly. The staircase approximation "hunts" or oscillates around the flat input signal, stepping up and down by \(\Delta\). This causes a granular or noisy appearance in the reconstructed signal. This happens when the signal "remains constant" (option c) or changes slower than \(\Delta/T_s\). Option (d) "Has high frequency components" can lead to slope overload if the amplitude is also large, as high frequency implies rapid changes. Therefore, granular noise occurs when the modulating signal remains constant or changes slowly relative to the step size. \[ \boxed{\text{Remains constant}} \]