Question

The process of converting a continuous-time signal into a discrete-time signal is called

• A. Quantization
• B. Sampling
• C. Encoding
• D. Aliasing

Hint:

- Sampling: Discretizes the Time axis of a signal. - Quantization: Discretizes the Amplitude axis of a signal.

Answer 1

The Correct Option is B

Concept: Signals can be categorized based on how they behave over time. A continuous-time signal is defined continuously across an uninterrupted time interval, meaning it has an analog value at every single moment. In contrast, a discrete-time signal is only defined at specific, distinct points in time. The process of converting a continuous-time signal into a discrete-time signal is called sampling. Let's look at how sampling works step-by-step:
• A continuous-time analog signal, represented mathematically as \(x(t)\), is measured or captured at uniform time intervals called the sampling period, \(T_s\).
• This conversion can be modeled as multiplying the analog signal by a periodic train of ideal Dirac delta impulses: \[ x_{\delta}(t) = x(t) \cdot \sum_{n=-\infty}^{\infty} \delta(t - nT_s) \]
• This operation results in a sequence of discrete data samples, denoted as \(x[n]\), where each index corresponds to a specific point in time: \[ x[n] = x(nT_s) \] To see why the other options are incorrect, let's look at what they mean:
• Quantization: The process of converting a continuous *amplitude* value into a discrete, mapped amplitude level. It limits the precision of the signal's value rather than discretizing time.
• Encoding: The step where quantized values are translated into specific binary code words (such as 0s and 1s) for digital processing.
• Aliasing: An unwanted distortion effect that occurs if the signal is sampled too slowly (below the Nyquist rate), causing overlapping and misidentification of high-frequency components. Thus, the specific process that converts the time domain from continuous to discrete is sampling.