---
title: "What is sampling"
subject: "Signals and Systems"
chapter: 4
key: "semester_4/signals_and_systems:what-is-sampling"
source: https://www.bctengineer.com/q/semester_4/signals_and_systems/what-is-sampling
site: BCT Engineering
---

# What is sampling

Signals and Systems · Chapter 4: Sampling

- Asked in: 2072 Magh, 2 marks
- Video: [Sampling Signals](https://www.youtube.com/watch?v=AcuQnIXiZ2A) — Iain Explains Signals, Systems, and Digital Comms
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/signals_and_systems/what-is-sampling
- Whole chapter: https://www.bctengineer.com/md/semester_4/signals_and_systems/chapter-4

## Question

What do you mean by sampling? Explain.

## Short answer

Sampling is the process of converting a continuous-time signal x(t) into a discrete-time sequence by measuring its value at equally spaced instants t=nT, yielding x[n]=x(nT). It is modeled mathematically as multiplying x(t) by an impulse train. Sampling must satisfy the Nyquist criterion (f_s > 2f_max) to enable exact recovery and avoid aliasing.

## Answer

**Sampling** is the process of converting a continuous-time signal $x(t)$ into a discrete-time signal by measuring its value at equally spaced instants $t = nT$:
$$
x[n] = x(nT), \qquad n = 0, \pm1, \pm2, \dots
$$
Here $T$ is the sampling period and $f_s = 1/T$ is the sampling rate. Mathematically it is modelled as multiplying $x(t)$ by an impulse train $p(t)=\sum_n \delta(t-nT)$. Sampling is the first step in analog-to-digital conversion and lets continuous signals be processed by digital systems. A band-limited signal can be rebuilt from its samples only if $f_s > 2f_M$ (sampling theorem); otherwise aliasing occurs.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Sampling is
   A. Measuring x(t) at equally spaced instants t = nT
   B. Quantizing amplitude levels
   C. Encoding bits
   D. Filtering high frequencies
   Answer: A. x[n] = x(nT). (Key point: Definition)

2. Sampling is modelled mathematically as
   A. Convolution with a step
   B. Multiplication by an impulse train
   C. Integration
   D. Addition of an impulse train
   Answer: B. p(t) = sum δ(t - nT). (Key point: Model)

3. A band-limited signal can be rebuilt only if
   A. fs < fM
   B. fs = 0
   C. fs > 2fM
   D. fs < 2fM
   Answer: C. Else aliasing. (Key point: Condition)

## Related in Signals and Systems

- [Impulse train sampling and reconstruction](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Aimpulse-train-sampling-reconstruction) — Signals and Systems, chapter 4
- [Sampling requirement; Nyquist of product](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Asampling-requirement-nyquist-product) — Signals and Systems, chapter 4
- [Impulse train sampling, aliasing, reconstruction](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Aimpulse-train-aliasing-reconstruction) — Signals and Systems, chapter 4
- [Aliasing via impulse-train sampling](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Aaliasing-impulse-train-frequency) — Signals and Systems, chapter 4

## Related in other subjects

- [Sampling distribution of mean; standard error](https://www.bctengineer.com/question.md?key=semester_5%2Fprobability_and_statistics%3Asampling-distribution-mean-se-finite) — Probability and Statistics, chapter 4, asked 2×
- [Sampling distribution of proportion; parameter vs statistic](https://www.bctengineer.com/question.md?key=semester_5%2Fprobability_and_statistics%3Aparameter-vs-statistic-sampling-proportion) — Probability and Statistics, chapter 4
- [Sub-sampling; sampling sinc(5πt) at 10 Hz](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Asubsampling-sinc5pit-10hz) — Communication Systems, chapter 4
- [Aperture effect correction; bandpass sampling 80–115 kHz](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aaperture-correction-bandpass-80-115) — Communication Systems, chapter 4