Written by Grant Maloy Smith, the data acquisition expert

Signal processing involves converting or transforming data in a way that allows us to see things in it that are not possible via direct observation. Signal processing allows engineers and scientists to analyze, optimize, and correct signals, including scientific data, audio streams, images, and video.

In this article you will learn about signal processing with enough detail that you will:

  • Understand what signal processing is at the top level
  • Learn how signal processing is performed
  • See how signal processing is applied in DAQ (data acquisition) applications

Displaying vibration data in both time and frrequency axes simultaneously
Displaying vibration data in both the time and frequency axes simultaneously

Companies spend millions of dollars every year buying test equipment so that their engineers and technicians can record test data. This investment in equipment and manpower to conduct tests is for one purpose: to understand how their products will work in the real world. This understanding can only come from capturing and analyzing high-quality, objective data.

But the data itself is only step one. To understand what the data means, we need to analyze it. Analysis has several components, including:

  • Making observations - by recorded data and then reviewing it
  • Making comparisons - one of the fundamental elements of analysis is comparing A versus B, e.g., “how much torque does the drive shaft increase when we increase the speed from 100 to 200?” or “how does the current change with respect to voltage?”

The above methods are direct observations. We apply sensors of many kinds and then operate the machine or process while recording their responses. Then we look at the data and compare parameters during different phases of operation. But there’s another data analysis tool that we can use:

Signal processing - transforming data in a way that allows us to see things that are not possible by direct observation or comparison.

  • Signal processing (aka digital signal processing), takes several forms depending on the application. In the data acquisition (DAQ) world, we use signal processing in order to analyze measured data. 

How is Signal Processing Done?

Historically, signal processing was performed entirely in the analog domain. For example, signal filters were built using discrete components like resistors, capacitors, and inductors. This is still done, of course, but since the late 20th century, data of all types have become increasingly digitized. As a result, signal processing has necessarily transitioned from the analog to the digital domain.

Today, digital signal processing is done primarily in software. Signal processing software can run on the processor or graphics card of a desktop computer, or in a smart device. For more demanding applications it runs on dedicated DSPs (Digital Signal Processors), ASICs (Applications Specific Integrated Circuits), or FPGAs (Field Programmable Gate Arrays), and on powerful computer mainframes.

Analog Devices A-DSP-21363 with SHARC coreAnalog Devices A-DSP-21363 with SHARC core, Pedant01, CC BY-SA 3.0, via Wikimedia Commons

The original DSP chips were developed in the 1960s, and used for improving RADAR and SONAR in military applications. They were later applied to geophysical applications like oil exploration, space applications like data compression, and for medical imaging applications like CAT or “C.T.” (computed tomography) and MRI (magnetic resonance imaging) human body scanning.

Today, the power of even notebook computers is far greater than the biggest mainframes from the past, and a huge array of signal processing functions can be performed both in real-time and post-processing by PC-based DAQ systems.

Many systems employ a combination of host computer processing and DSP processing to perform signal processing functions. DSP hardware is very fast and can be dedicated to common functions. For example, DSPs are used in analog to digital converters (ADCs) for filtering, combining digital bit streams, and more. They can handle a lot of data very quickly. 

Signal Processing Applications

Signal processing is applied across numerous industries and applications, including:

  • Audio compression and signal processing
  • Data acquisition and signal processing
  • Digital image and graphics processing
  • Video compression and signal processing
  • Speech recognition and processing
  • RADAR, SONAR, and LiDAR signal processing and signal optimization
  • Seismic studies and data analysis
  • Geophysical applications, including oil exploration
  • Data transmission, including error detection and error correction
  • Economic modeling and analysis
  • Medical applications, especially imagery (CAT and MRI)
  • Weather forecasting
  • Oceanography, including undersea acoustic performance predictions

Signal processing operates on both linear and nonlinear systems, however, most systems fall into the nonlinear camp, i.e., those whose values change over time, often in unpredictable ways, where a change in output is not linearly proportional to a change in the input. 

Nonlinear signal processing can be implemented in several domains, including:

  • The Time domain, i.e., amplitude points plotted against time
  • The Frequency domain, i.e., frequencies plotted against their magnitudes
  • Spatio-temporal domain, i.e., across both space and time. For example, monitoring the routes of hundreds of aircraft all around the world, or thousands of satellites orbiting the Earth

Types of Signal Processing

Filtering

Filtering is one of the most basic and important signal processing techniques. It has been used since the very beginning of the analog recording, to enhance our ability to see the true signal by suppressing “noise” and other interferences. Filtering was (and is) used for applications from adjusting the bass and treble response of your music player to adjusting the channel frequency of a radio, and improving sound quality on telephone lines. 

A low-pass filter is used to remove unwanted high frequency noise on a signalA low-pass filter is used to remove unwanted high frequency “noise” on a signal

In DAQ systems, analog filters were used to attenuate signal content higher or lower than a certain frequency, to reduce “noise” in the signal. These filters were normally part of the DAQ system’s signal conditioners or preamplifiers.

The four basic filter types include:

The four basic filter typesThe four basic filter types

Filters are also defined by how many poles they have. The more poles, the steeper the roll-off they are capable of performing on the signal. This roll-off or slope simply means how many decibels of the signal can be rolled off per octave. The specification of the filter in question will typically give the maximum roll-off in dB/Q.

Filter Prototypes

No filter is perfect. They can impose phase delays, ripple, ringing, and other distortions within the passband. The trick is to choose the correct filter prototype that works best for the type of signals being processed. You will hear of filter prototypes such as Bessel, Butterworth, Elliptic, and Chebyshev, to name a few. Over the years, engineers have developed numerous filtering prototypes in order to provide the best possible results for various applications:

Prototype Roll-off Ripple or Distortion Other Factors
Butterworth Good No ripple, but square waves cause distortion (hysteresis) Moderate phase distortion
Chebyshev Steeper Ripples in the pass-band Poor transient response
Bessel Good No ringing or overshoot from non-sinus waveforms Increased phase delay
Elliptic Steepest Ripples in the pass-band Nonlinear phase response

What’s Better, Analog or Digital Filtering?

In applications that require a simple, unchanging filter in the analog domain, it can be cheaper and easier to use an analog filter design. However, if it is required to have filters that are adaptable to a variety of applications, or to run in the digital domain, the digital approach is far less expensive and occupies a lot less space. Digital filtering can also be more accurate since it eliminates the tolerances of discrete components in the analog domain (resistors, capacitors, etc). 

In the DAQ world, filtering used to be done exclusively inside the system’s signal conditioning front-end. But this shifted when DAQ systems became digital in the 1980s. Today it is common for the signal conditioners to offer no filtering at all, except in a few cases where it is necessary to filter certain frequencies before the digitization process. There are two notable examples of this:

High-pass filtering of accelerometers, especially when the signal will be integrated or double-integrated. 

Anti-aliasing filtering. The primary stage of anti-aliasing filtering must be done in the analog domain. An alias is a “false” signal caused by sampling too slow compared to the frequency content of the signal. Once this alias has been digitized, there is no way to recreate the true signal.

Digital Filtering

Digital filtering can be performed in computer software, or in a dedicated DSP (digital signal processor). High-end applications sometimes employ custom ASICs or FPGAs to perform filtering functions.

Filter design screen from DewesoftX softwareFilter design screen from DewesoftX software

IIR versus FIR Filtering

IIR and FIR are two basic approaches to digital filtering. Each has its advantages and disadvantages:

FIR (Finite Impulse Response) filters are calculated with many coefficients and are well-known for having essentially zero phase shift within the passband. This is critical when signals will be compared on the time axis. FIR filtering is very calculation-intensive.

FIR filter setup screen shows zero phase shift and distortion within the passband FIR filter setup screen shows zero phase shift (green line) and distortion (red line) within the passband (vertical gray line)

IIR (Infinite Impulse Response) filters are calculated with far fewer coefficients than FIR filters, so they are less processing intensive. They are a direct equivalent to the classic analog filters. For example, with IIR filters we can achieve the exact theoretical low pass, high pass, sound weighting, and other standard filters found in analog circuits.

Phase shift comparison of IIR and FIR filtersPhase shift comparison of IIR and FIR filters

In the phase comparison graph above, the green curve is the original sine wave.

The red curve is the response calculated with an IIR filter. The phase delay of the output is very obvious and quite large.

The blue curve is calculated with an FIR filter. Note that there is zero phase shift. In many applications, it is very important that the signals are not delayed by the filters, since phase comparisons are being made. In these applications, FIR filters are very important.

FFT Analysis

Converting a signal from the time domain to the frequency domain allows us to see things in it that are not possible via direct observation. In the complex AC waveform shown below, the signal is composed of numerous frequencies:

A recording of a complex waveformA recording of a complex waveform

It is difficult to know which frequencies are contained within the signal from this time vs. history graph. The solution is to use the fast Fourier transform (FFT) to capture short “windows” of time and convert them to the frequency domain. The FFT makes it easy to see what the largest magnitude frequencies are, as shown below:

The same signal shown in the frequency domainThe same signal is shown in the frequency domain (frequency vs. magnitude)

Using FFT signal processing we can see our measured data on the frequency axis as opposed to the more familiar time axis.

Modal Analysis

Modal tests and analysis are indispensable tools to determine natural frequencies, damping ratios, and mode shapes of any structure. You “excite” a structure with an impact hammer or one or more multiple modal shakers, then measure the responses using accelerometers mounted on it.

When you strike a structure with an impact (impulse) hammer, you excite a broad range of frequencies within the structure. Impulse hammers have an accelerometer built into them so that we know the exact force that has been applied.

Modal shakers operate at one frequency at a time. They can “run-up” and “run down” from one frequency to another in series, according to the test. It is also possible to use multiple shakers at the same time.


Overview of SIMO, MIMO, and ODS Modal Testing

Modal analysis is heavily used in civil engineering and industries such as aerospace and automotive, across a vast range of applications, including:

  • Ensuring that resonances are separated from excitation frequencies
  • Prediction of the dynamic behavior of components and assembled structures
  • Optimization of the structure’s dynamic properties (mass, stiffness, damping)
  • Prediction of the responses due to complex excitation
  • Inclusion of damping in Finite Element Models
  • Damage detection and assessment

Important implementations of modal testing include Modal Testing itself, Sine Reduction Test (COLA), Shock Response Spectrum (SRS), Fatigue Analysis, and more. 

Mathematics

Math functions available in DewesoftX software

Because data is digital in today’s DAQ systems, there are a host of mathematical processes that can be performed on it. It is well beyond the scope of this article to cover them all, but here is just a short summary of some of the more popular math functions available in popular DAQ software programs:

  • Statistics: RMS, average, min, max, standard deviation, variance, classification, counting, array statistics, etc.
  • Time-domain analysis: delay channel, integral, derivative, latch value math, scope math, time-to-vector transform
  • Frequency domain analysis: cepstrum, correlation, exact frequency, Fourier transform, full-spectrum, octave analysis, short-time Fourier transform (SFFT)
  • FIltering: FIR, IIR, FFR, integration, derivation
  • Machinery diagnostics: angle sensor math, combustion noise, envelope detection, sine processing (COLA), tracking filter
  • Counting procedures
  • Acoustics: including weighting filters
  • Strain and stress: strain rosette calculations
  • Constants: vectors, matrix constant
  • Basic operators: addition, subtraction, division, multiplication, mod, power
  • Functions: square, square root, absolute, truncate, random, logarithm (base2), logarithm (base10), natural logarithm, exponent, if condition, min, max
  • Trigonometry: sin, cos, tan, asin, acos, atan, Pi
  • Logic: less than, equal, more than, less than or equal, more than or equal, not equal, not, and, or, xor
  • Signals: number of samples acquired, sample rate, the time elapsed, sine wave, square wave, triangular wave, noise
  • Measure: pulse width, stopwatch

Signal Processing Tools

There are a number of signal processing tools available to engineers and scientists today. Here is a shortlist of some of the better known and popular ones:

Product Company Comments
MatLab The MathWorks Very powerful and extensible software system
GNU Octave GNU Open-source version of MatLab
SciPly SciPly Open source Python library
DewesoftX Dewesoft, d.o.o. DAQ software with extensive filtering, FFT, modal and mathematical capabilities

Summary

Signal processing is applied across many industries and sectors, including acoustics, modal testing of structures, video processing, geophysics, automotive engineering, aerospace engineering, energy, medical imaging, RADAR, SONAR, LIDAR, and more. Each one applies the signal processing methods that are most germane to their particular requirements.