# Waveform determination

## Waveform determination

The definition of a waveform, which describes the variation of a quantity with respect to time. The necessary measurements are normally carried out and presented in one of two ways: the amplitude may be presented as a function of time (time domain), or an analysis may be given of the relative amplitudes and phases of the frequency components (frequency domain). Although the simplest instruments measure and display the information in the same domain, it is possible to convert the data in either direction by mathematical processing.

Waveforms may be divided into two classes, depending on whether the signal is repeated at regular intervals or represents a unique event. The former signal is defined as a periodic or continuous wave, the latter as an aperiodic signal or transient.

The oscilloscope is an example of an instrument that measures and displays directly in the time domain, by deflecting an electron beam in a vertical direction in accordance with the signal while scanning at a uniform rate in the horizontal direction. The position of the beam is revealed by a fluorescent screen. See Oscilloscope

Several methods may be used to obtain the spectral content of a waveform. In the simplest, the signal is applied to a filter that is manually tuned in turn to each frequency that is expected to be present. In order to automate the measurement, the tuning of a filter may be varied by a linear, logarithmic, or other sweep and the resulting output displayed. However, there are important restrictions that limit the technique to continuous waveforms. A fleeting appearance of a signal at a frequency away from that to which the filter happens to be tuned at the instant will be completely missed. In order to provide high resolution, the tuned circuit must have high selectivity, or high Q. Its response to changes in amplitude is therefore slow, and the rate of sweeping has to be limited. By using this technique, it is possible to construct instruments that cover extremely wide frequency ranges.

In order to overcome the limitations of the swept filter, an array of separate fixed tuned filters may be used, each adjusted to respond to a slightly different frequency. The amplitude of the signal in each filter is sampled in turn and displayed, giving a histogram of the frequency components of the waveform. The number of filters and their selectivities depend on the resolution required. Though simple in concept, such instruments are inclined to be bulky if high resolution is needed. They have the great advantage that all frequency components are taken into account throughout the measurement and their amplitudes can be examined continuously. Such instruments are useful for the analysis of music and speech.

Since the purpose of such instruments is to display the frequency components of the signal, they are often called spectrum or harmonic analyzers.

Many modern instruments use techniques in which the signal to be measured is sampled and digitized. In sampling oscilloscopes a sufficiently large number of samples is taken to define the waveform. The sampling rate is not necessarily high; where the waveform is repetitive, the Nyquist requirement that more than two samples should be available per cycle of the highest frequency of interest can be satisfied by obtaining the samples over a large number of periods of the signal. Each sample is digitized and stored. The waveform is then displayed by plotting the data on a cathode-ray tube or similar display in the correct order. As the data can be read out of digital storage at any convenient speed, this process can be relatively slow and low bandwidth display circuits are adequate.

Once the data have been collected in digital form, they can be processed in many different ways. The application of a discrete Fourier transformation (DFT) to the amplitude data enables the information to be presented in the frequency domain. In this way, harmonic distortion which was invisible on a directly displayed waveform can be made obvious.

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