The Periodic Table of Oscilloscope Tools: Math

Figure 1: DSP-based
Math functions can
reveal deep insights
hidden in waveforms

The usefulness of oscilloscopes skyrocketed once digital signal processing began to be applied to acquired waveforms. By applying DSP, oscilloscopes could now perform complex processing in the time, frequency, statistical, and other domains, all while imposing no restrictions on acquisition length. Here at Teledyne LeCroy, we collectively refer to these DSP-based processes as Math functions. We've presented those functions, along with all of the other functions our instruments perform, in chart form in our Periodic Table of Oscilloscope Tools.

Our oscilloscopes' Math functions delve deeply into the rich information that a waveform conveys to reveal a great deal of hidden insight. Not only do the functions themselves expose this information, but they can be chained in an intuitive visual editor or created from scratch as custom Math functions.

The Fourth Step: Math

The Periodic Table divides Math functions into plain functions and more advanced processes. We'll begin by looking at the first grouping:

• Fast Fourier Transforms may be calculated on full acquisition memories. At up to 256 Mpts, we enhance calculation speed by means of Intel performance primitives; for longer records, enhancement comes through proprietary techniques. The benefits of using long acquisition memory for FFT calculation is that FFT frequency resolution increases inversely with acquisition time, and FFT span increases sample rate. Long memory FFTs permit both long span and high resolution in the FFT calculation. The FFT tool supports seven different output types, five windows and two different calculation algorithms. 
• Tracks/Trends: Tracks provide an intuitive display of the changes in a measurement parameter value versus time, with the Track remaining time-correlated to the originally acquired waveforms from which the measurement parameters were derived. Tracks may utilize standard Teledyne LeCroy measurement parameters, parameters created through Parameter Math, or Custom Measure (see below). Tracks may be further processed by additional math functions to obtain other information, such as a jitter spectrum. Trends provide a means to display a series of measurement parameter values as acquired over a long period of time asynchronous to the acquisition window for real-time acquired waveforms, much like a conventional chart recorder or data logger would provide.
• The Demodulation math function operates on analog Frequency Modulated (FM), Phase Modulated (PM), Amplitude Modulated (AM), Wide-band AM, Time, and Real/Imaginary signal modulations. Users may define the carrier frequency. Decimation is permitted so that the high-frequency modulated signal can be appropriately sampled, but the recovered signal, which does not need as high a sampling rate, can be decimated to allow for faster processing time. A low-pass FIR filter may be applied for baseband signal recovery, with complete user control of rolloff via tap settings.

The second Math grouping of Advanced Functions takes things even further:

• Digital Filters: Users may create a variety of Infinite Impulse Response (IIR) and Finite Impulse Response (FIR) filters with low-pass, high-pass, band-pass, band-stop, raised-cosine, raised-root cosine, Gaussian, or custom characteristics. Boxcar filtering lets you create a local running average filter of specified length. Enhanced resolution (ERES) filters perform simple noise reduction and smoothing, and simple Sinx/x filters may be applied to provide increased sample points through interpolation. Some of the filters are available as a post-processing step directly in the Channel setup dialog, making application simple and intuitive.
• The Teledyne LeCroy Processing Web is a graphical programming interface in which math and measurements are wired together in a flow diagram. It permits graphical processor-block view of the post-acquisition processing and setup of analytics performed on the acquired waveforms. Math, Measure, and other processing blocks may be dragged and dropped to place and link them together in the graphical user interface. Using the Processing Web removes GUI-related constraints on the number of math or measurement processing steps, enabling deployment of complex processing setups.
• Users can create Custom Math functions using MATLAB, MathCad, C++, VBScript, Jscript (JavaScript), or Excel. The Custom Math capability in Teledyne LeCroy oscilloscopes provides for complete integration of the calculation within the oscilloscope program. It uses ActiveDSO to send acquired data to the third-party program and accept a result back for native display within the oscilloscope. The data is then available for further processing, just like any other standard oscilloscope math function. Furthermore, Automation commands may be embedded within the Custom Math setup to further invoke other oscilloscope operations or to invoke a third-party program.

Our next post on the topic of the Periodic Table of Oscilloscope Tools will begin covering the broad array of Analysis tools.