--- title: "Types of sampling operations compared" subject: "Digital Control System" chapter: 1 key: "semester_6/digital_control_system:compare-sampling-operations" source: https://www.bctengineer.com/q/semester_6/digital_control_system/compare-sampling-operations site: BCT Engineering --- # Types of sampling operations compared Digital Control System · Chapter 1: Introduction to Discrete Time Control System - Asked in: 2081 Chaitra, 4 marks; 2074 Bhadra, 4 marks; 2068 Magh, 6 marks (asked 3 times) - Video: [L4 Sampling and reconstruction](https://www.youtube.com/watch?v=rSvlk9Hg9qs) — Aniket Khandekar - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/digital_control_system/compare-sampling-operations - Whole chapter: https://www.bctengineer.com/md/semester_6/digital_control_system/chapter-1 ## Question Compare different types of sampling operations used for sampling of continuous time signal. ## Short answer Periodic sampling uses equal intervals and is easiest to analyze with the z-transform. Multiple-order sampling has a repeating pattern with unequal spacing within the pattern. Multiple-rate sampling uses different periods for different control loops. Random sampling occurs at irregular instants and is hard to analyze. Periodic flat-top sampling is most common in digital control. ## Answer **Sampling** converts a continuous-time signal into a sequence of values (pulses) taken at certain instants. Sampling operations are classified by how the sampling instants are chosen. #### Types 1. **Periodic (conventional) sampling:** samples are taken at equal intervals, $t = kT$. This is the most common type; it gives simple difference equations and allows use of the z-transform. 2. **Multiple-order sampling:** the pattern of sampling instants repeats periodically, i.e. $t_{k+r} - t_k$ is constant, but the spacing within a pattern is not equal. 3. **Multiple-rate sampling:** different loops or signals are sampled at different periods, e.g. a fast inner current loop and a slow outer speed loop. 4. **Random sampling:** the instants are random, e.g. in event-driven systems or networked control with random delays. It is hard to analyse. #### Comparison | Feature | Periodic | Multiple-order | Multiple-rate | Random | |---|---|---|---|---| | Sampling instants | $kT$, equal spacing | Pattern repeats with period | Different $T$ for different signals | Random | | Analysis tool | z-transform | Modified methods | Multirate z-transform | Statistical | | Hardware | Simple, one clock | Moderate | Several clocks | Event logic | | Use | Most digital controllers | Special systems | Cascade loops with fast and slow parts | Networks, events | | Ease of design | Easiest | Harder | Harder | Hardest | #### Sampling by pulse shape | Ideal (impulse) sampling | Natural sampling | Flat-top sampling | |---|---|---| | Train of impulses of strength $x(kT)$ | Pulses of width $\tau$ follow the signal shape | Pulses of width $\tau$ with constant height $x(kT)$ | | Mathematical model | Switch closed for $\tau$ | Practical S/H output | In digital control, periodic flat-top sampling (S/H) is used in practice, and it is modelled as ideal impulse sampling followed by a zero order hold. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Which sampling type takes samples at equal intervals t = kT and is the most common in digital controllers? A. Random sampling B. Multiple-rate sampling C. Periodic (conventional) sampling D. Multiple-order sampling Answer: C. Periodic sampling gives simple difference equations and the z-transform. (Key point: Periodic sampling) 2. What describes multiple-rate sampling? A. Different loops or signals are sampled at different periods, such as a fast inner loop and a slow outer loop B. Samples are taken at random times C. All signals sampled at the same period D. Samples taken only on events Answer: A. Cascade loops with fast and slow parts use different sampling periods. (Key point: Multiple-rate sampling) 3. Why is random sampling the hardest to design for? A. It needs the z-transform only B. It needs several clocks C. Instants are random, so it needs statistical analysis D. It has equal spacing Answer: C. Random instants (event-driven or networked systems) call for statistical analysis and are hard to analyse. (Key point: Random sampling) 4. Which pulse-shape sampling gives pulses of width τ with constant height x(kT) and is the practical S/H output? A. Ideal impulse sampling B. Natural sampling C. Flat-top sampling D. Random sampling Answer: C. Flat-top sampling holds the height constant; it is modelled as impulse sampling followed by a ZOH. (Key point: Flat-top sampling) ## Related in Digital Control System - [Sampling operations and DCS advantages](https://www.bctengineer.com/question.md?key=semester_6%2Fdigital_control_system%3Asampling-operations-advantages) — Digital Control System, chapter 1 - [Z-transform of ramp-and-hold continuous signal](https://www.bctengineer.com/question.md?key=semester_6%2Fdigital_control_system%3Awaveform-ramp-to-1-at-6) — Digital Control System, chapter 2 - [Z-transform of ramp-and-hold signal (T = 1 s)](https://www.bctengineer.com/question.md?key=semester_6%2Fdigital_control_system%3Awaveform-ramp-to-1-at-4) — Digital Control System, chapter 2 ## Related in other subjects - [Discrete vs continuous signal; convert (25.25)₁₀](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Adiscrete-continuous-convert-25-25) — Digital Logic, chapter 1 - [Why band-limit a signal before sampling](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Asampling-bandlimit) — Data Communication, chapter 5 - [Continuous-time vs discrete-time signals](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Act-vs-dt-signals) — Signals and Systems, chapter 1, asked 3× - [Properties of continuous time systems](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Act-system-properties) — Signals and Systems, chapter 5, asked 2×