Digital Signal Processing Guide
What do we mean by signal processing?
Signal processing involves the mathematical representation of a signal and the algorithmic operations carried out on it to extract or enhance the information contained in the signal of interest.
Why use digital signal processing?
Limitations of analogue techniques
- Time drift
- Temperature drift
- Loading effects between stages of a circuit
- Analogue techniques are sensitive to component tolerances (some components such as capacitors have large tolerances)
- Post processing limitations - difficult to store an analogue signal for a long time without loss of information
Advantages of digital techniques
- No time and temperature drift (but clocks used in DSP hardware are analogue components and have time and temperature drift)
- No loading effects between stages
- No sensitivity to component tolerance (but DSP is sensitive to coefficient quantisation noise)
- Easy to adapt/update/reconfigure the system (flexibility)
- Long-term storage for future reference without loss of information
- Bandwidth utilisation for signal transmission by using time division multiplexing
Disadvantages of digital techniques
- Still need analogue circuitry (and this circuitry limits the performance)
- Limited range of frequencies available for processing (sampling theorem)]
- The digital circuitry requires large space in an integrated circuit and has large power consumption
- Loss of information due to quantisation
- Reliability (there is no widely acceptable definition of DSP software reliability)
Why it's important to measurement scientists
Signal processing, particularly digital signal processing (DSP), is ubiquitous in modern measurement science. Almost all physical events of interest to scientists are ultimately converted (or transduced) to an electrical signal which is then sampled, digitised and downloaded into a computer. In addition, much modern data acquisition and analysis software contains built-in functions for processes such as windowing, filtering and transforming signals that can be treated as "black boxes" by the user.
Digital signal conditioning and processing underpins almost all electrically-based measurements and new developments in Information and Communications Technology in the UK economy. Digitised measurements are omnipresent throughout technology; in any measurement or control application where it is necessary to obtain a correct measurement of the parameters of complex (real-world rather than simplified ideal-world) waveforms, digitisation and DSP are required within an uncertainties framework.
The challenges that DSP presents to measurement scientists
As a result of uninformed use of the highly sophisticated measurement software that is available today, there is a potential to introduce artefacts and additional sources of uncertainty into the results of measurements if the scientist using these tools is not aware of the limitations of the applied methods. Choice of hardware and firmware introduces further complications, so that the effects of resolution, sampling synchronization and sampling jitter require analysis. Finally, many sensors with frequency-dependent properties are calibrated by deriving their impulse response from comparisons of output and input signals using convolution and deconvolution methods. Such methods need care if one requires a reliable determination of the amplitude and phase response of the sensor in question.
How NPL's mathematicians and software specialists help solve signal processing problems
We advocate a software engineering approach to signal processing that emphasises the need for a clear definition of the problem, good choice of algorithms and of numerical methods, and rigorous testing. We recognise that uncertainties that arise from the choice and implementation of signal processing techniques are often not studied systematically and uncertainty budgets may omit contributions arising from these sources. We aim to provide support, good practice guidance and signal processing tools that will ensure that good practice can be adopted by metrologists in an easily-implementable manner, which can allow them to concentrate on their measurements results with the confidence that the uncertainties arising from their chosen signal processing techniques have been accurately quantified.
Learning more about signal processing in measurement science
We are developing resources and identifying sources of information that can be used by measurement scientists, industrial scientists and engineers, teachers and other interested individuals to learn about signal processing, to help select appropriate signal processing methods that will be suitable for specific measurement tasks and to support informed selection of hardware and software. This web-based set of resources and links aims to meet these requirements. The good-practice resources are mainly concerned with one-dimensional signals such as those that are a function of time, but much of the material is also relevant to two-dimensional signals, including images. Topics covered include:
- Uncertainty evaluation when using DSP.
- The use of analogue signal conditioning techniques, including amplification, noise reduction and filtering.
- The advantages and disadvantages of analogue techniques, as compared with digital methods.
- Limitations of equipment, especially those with on-board digitisation facilities.
- The effects of digitisation.
- Validation of DSP software, including testing its numerical adequacy the estimation of uncertainties associated with the measurement of complex quantities (real and imaginary, or amplitude and phase).