---
title: "Classification of measurement signals"
subject: "Instrumentation and Measurement"
chapter: 2
key: "semester_4/instrumentation_and_measurement:classification-of-measurement-signals"
source: https://www.bctengineer.com/q/semester_4/instrumentation_and_measurement/classification-of-measurement-signals
site: BCT Engineering
---

# Classification of measurement signals

Instrumentation and Measurement · Chapter 2: Time Dependent Properties of Signal

- Asked in: year not given, 5 marks
- Video: [Classification of Signals Explained | Types of Signals in Communication](https://www.youtube.com/watch?v=E4E1GftPD1M) — ALL ABOUT ELECTRONICS
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/instrumentation_and_measurement/classification-of-measurement-signals
- Whole chapter: https://www.bctengineer.com/md/semester_4/instrumentation_and_measurement/chapter-2

## Question

Write short notes on the classification of measurement signals: static and dynamic, deterministic and random, periodic, aperiodic and transient. Give one example of each.

## Short answer

Static signals are time-invariant (weight); dynamic vary with time (vibration). Deterministic signals follow a mathematical function (sinusoid); random signals are unpredictable (turbulent noise). Periodic signals repeat (50 Hz mains); aperiodic signals never exactly repeat (incommensurate frequencies); transients are short-lived (impulse).

## Answer

A measurement signal is the physical or electrical quantity carrying information about the measurand. Signals are classified in several ways.

#### Static and dynamic
- **Static signal:** does not change with time, or changes very slowly. Example: the weight of an object on a scale, dead-load pressure.
- **Dynamic signal:** varies with time. It may be steady-periodic, aperiodic or transient. Example: engine vibration, pressure in a cylinder.

#### Deterministic and random
- **Deterministic:** can be described by a mathematical function of time and predicted exactly. Example: $x(t) = A\sin\omega t$.
- **Random (nondeterministic):** cannot be predicted; it can only be described statistically by its mean, variance and probability density. Example: turbulent wind velocity, noise.

#### Periodic signals
- **Simple periodic (harmonic):** a single sine or cosine at one frequency, $x = A\sin(\omega t + \phi)$. Example: the 50 Hz mains voltage.
- **Complex periodic:** repeats after a period $T$ but contains many harmonics, $x(t) = x(t+T)$. Example: a square wave from a rotating machine, which has a Fourier series.

#### Aperiodic and transient
- **Almost periodic:** a sum of harmonics whose frequency ratios are not rational, so the signal never exactly repeats. Example: $x(t) = \sin t + \sin\sqrt{2}\,t$, such as the vibration of a machine driven by two shafts at unrelated speeds.
- **Transient:** exists for a short time and then dies away. Example: a step input, the impulse from a hammer blow, decaying vibration after an impact.

```text
 Signals
  |-- Static
  |-- Dynamic
        |-- Deterministic
        |     |-- Periodic (simple, complex)
        |     |-- Aperiodic (almost periodic, transient)
        |-- Random (stationary, non-stationary)
```

## Check yourself

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

1. How does a random signal differ from a deterministic one?
   A. It is described only statistically and cannot be predicted exactly
   B. It is always periodic
   C. It can be written as A sin(wt)
   D. It does not vary with time
   Answer: A. Deterministic signals follow a mathematical function; random signals need mean, variance and probability density. (Key point: Deterministic vs random)

2. What is a complex periodic signal?
   A. A single sine wave at one frequency
   B. A signal that exists briefly and dies away
   C. A signal repeating every T that contains many harmonics
   D. A signal whose harmonics have irrational frequency ratios
   Answer: C. It satisfies x(t) = x(t+T) and has a Fourier series with many harmonics, e.g. a square wave. (Key point: Complex periodic)

3. Why does an almost periodic signal never exactly repeat?
   A. It is random in nature
   B. Its harmonic frequency ratios are not rational
   C. It decays with time
   D. It has a single frequency
   Answer: B. It is a sum of harmonics whose frequency ratios are not rational, so no common period exists. (Key point: Almost periodic)

4. Which is a transient signal?
   A. Decaying vibration after a hammer blow
   B. A steady 50 Hz sine
   C. Weight on a scale
   D. Turbulent wind velocity
   Answer: A. A transient exists for a short time then dies away, like the impulse or decaying vibration after impact. (Key point: Transient example)

## Related in Instrumentation and Measurement

- [Dynamic characteristics: rise time, delay, response](https://www.bctengineer.com/question.md?key=semester_4%2Finstrumentation_and_measurement%3Adynamic-characteristics-rise-time-delay) — Instrumentation and Measurement, chapter 4
- [Classification of transducers with examples](https://www.bctengineer.com/question.md?key=semester_4%2Finstrumentation_and_measurement%3Aclassification-of-transducers) — Instrumentation and Measurement, chapter 5
- [Limiting error in calculated power](https://www.bctengineer.com/question.md?key=semester_4%2Finstrumentation_and_measurement%3Apower-error-limiting-error) — Instrumentation and Measurement, chapter 1
- [Models of zero, first and second order systems](https://www.bctengineer.com/question.md?key=semester_4%2Finstrumentation_and_measurement%3Azero-first-second-order-models) — Instrumentation and Measurement, chapter 4

## Related in other subjects

- [Sum of periodic signals can be aperiodic](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Asum-periodic-signals-aperiodic) — Signals and Systems, chapter 1
- [Periodic and aperiodic signals](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Aperiodic-aperiodic-examples) — Signals and Systems, chapter 1
- [Deterministic and random signals](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Adeterministic-random-signals) — Data Communication, chapter 2, asked 2×
- [Parseval's theorem for CT aperiodic signals](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Act-parseval-aperiodic) — Signals and Systems, chapter 3, asked 5×