16.9 Signal Analyzers and Display Devices

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Vibration signal analysis may employ both analog and digital procedures. Since signal analysis results in

extracting various useful bits of information from the signal, it is appropriate to consider the topic within

the present context of signal modification as well. Here, we will introduce digital signal analyzers.

Signal display devices also make use of at least some signal processing. This may involve filtering and

change of the signal level and format. More sophisticated signal display devices, particularly digital

oscilloscopes, can carry out more complex signal analysis functions such as those normally available with

digital signal analyzers. Oscilloscopes as well are introduced in the present section, though they may be

treated under vibration instrumentation.

Signal-recording equipment commonly employed in vibration practice includes digital storage devices

such as hard drives, floppy disks, and CD-ROMs, analog devices like tape recorders, strip-chart recorders

and X – Y plotters, and digital printers. Tape recorders are used to record vibration data (transducer

outputs) that are subsequently reproduced for processing or examination. Often, tape-recorded

waveforms are also used to generate (by replay) signals that drive vibration test exciters (shakers). Tape

recorders use tapes made of a plastic material that has a thin coating of a specially treated ferromagnetic

substance. During the recording process, magnetic flux proportional to the recorded signal is produced

by the recording head (essentially an electromagnet), which magnetizes the tape surface in proportion to

the signal variation. Reproduction is the reverse process, whereby an electrical signal is generated at the

reproduction head by electromagnetic induction in accordance with the magnetic flux of the magnetized

(recorded) tape. Several signal-conditioning circuitries are involved in the recording and reproducing

stages. Recording by FM is very common in vibration testing.

Strip-chart recorders are usually employed to plot time histories (that is, quantities that vary with

time), although they also may be used to plot such data as frequency-response functions and

response spectra. In these recorders, a paper roll unwinds at a constant linear speed, and the writing head

moves across the paper (perpendicular to the paper motion) proportionally to the signal level. There are

many kinds of strip-chart recorders, which are grouped according to the type of writing head that is

employed. Graphic-level recorders, which use ordinary paper, employ such heads as ink pens or brushes,

fiber pens, and sapphire styli. Visicoders are simple oscilloscopes that are capable of producing

permanent records; they employ light-sensitive paper for this. Several channels of input data can be

incorporated with a visicoder. Obviously, graphic-level recorders are generally limited by the number of

writing heads possible (typically, one or two), but visicoders can have many more input channels

(typically, 24). Performance specifications of these devices include paper speed, frequency range of

operation, dynamic range, and power requirements.

In vibration experimentation, X – Y plotters are generally employed to plot frequency data (for example,

PSD, frequency-response functions, response spectra, transmissibility curves), although they also can be

used to plot time-history data. Many types of X – Y plotter are available, most of them using ink pens and

ordinary paper. There are also hard-copy units that use heat-sensitive paper in conjunction with a heating

element as the writing head. The writing head in an X – Y plotter is moved in the X and Y directions on the

paper by two input signals that form the coordinates for the plot. In this manner, a trace is made on

stationary plotting paper. Performance specifications of X – Y plotters are governed by such factors as

paper size; writing speed (in./sec, cm/sec); dead band (expressed as a percentage of the full scale), which

measures the resolution of the plotter head; linearity (expressed as a percentage of the full scale), which

measures the accuracy of the plot; minimum trace separation (in., cm) for multiple plots on the same

axes; dynamic range; input impedance; and maximum input (mV/in., mV/cm).

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Today, the most widespread signal recording device is in fact the digital computer (memory, storage)

and printer combination. This and the other (analog) devices used in signal recording and display make

use of some signal modification to accomplish their functions. However, we will not discuss these devices

in the present section.

16.9.1 Signal Analyzers

Modern signal analyzers employ digital techniques of signal analysis to extract useful information that is

carried by the signal. Digital Fourier analysis using FFT is perhaps the single common procedure that is

used in the vast majority of signal analyzers. As we have noted before, Fourier analysis will produce the

frequency spectrum of a time signal. It should be clear, therefore, why the terms digital signal analyzer,

FFT analyzer, frequency analyzer, spectrum analyzer, and digital Fourier analyzer are to some extent

synonymous as used in the commercial instrumentation literature.

A signal analyzer typically has two (dual) or more (multiple) input signal channels. To generate results

such as frequency response (transfer) functions, cross spectra, coherence functions, and cross-correlation

functions, we need at least two data signals and hence a dual-channel analyzer.

In hardware analyzers, digital circuitry rather than software is used to carry out the mathematical

operations. Clearly, these are very fast but less flexible (in terms of programmability and functional

capability) for this reason. Digital signal analyzers, regardless of whether they use the hardware or the

software approach, employ some basic operations. These operations, carried out in sequence, are:

1. Antialias filtering (analog)

2. Analog-to-digital conversion (i.e., single sampling)

3. Truncation of a block of data and multiplication by a window function

4. FFT analysis of the block of data

We have noted the following facts. If the sampling period of the ADC is DT (i.e., the sampling

frequency is 1=DT) then the Nyquist frequency fc ¼ 1=2DT: This Nyquist frequency is the upper limit of

the useful frequency content of the sampled signal. The cutoff frequency of the antialiasing filter should

be set at fc or less. If there are N data samples in the block of data that is used in the FFT analysis, the

corresponding record length is T ¼ N·DT: Then, the spectral lines in the FFT results are separated at a

frequency spacing of DF ¼ 1=T: In view of the Nyquist frequency limit, there will be only N=2 useful

spectral lines of FFT result.

Strictly speaking, a real-time signal analyzer should analyze a signal instantaneously and continuously

as the signal is received by the analyzer. This is usually the case with an analog signal analyzer. However, in

digital signal analyzers, which are usually based on digital Fourier analysis, a block of data (i.e., N samples

of record length T) is analyzed together to produce N=2 useful spectral lines (at frequency spacing 1=T).

This is, then, not a truly real-time analysis. For practical purposes, if the speed of analysis is sufficiently

fast, the analyzer may be considered real time, which is usually the case with hardware analyzers and also

modern, high-speed software analyzers.

The bandwidth B of a digital signal analyzer is a measure of its speed of signal processing. Specifically,

for an analyzer that uses N data samples in each block of signal analysis, the associated processing time

may be given by

Tc ¼

N

B ð16:108Þ

Note that the larger the B; the smaller the Tc: The analyzer is considered real-time if the analysis time ðTcÞ

of the data record is less than the generation time ðT ¼ N·DTÞ of the data record. Hence, we need

Tc , T

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or

N

B

, T

or

N

B

, N·DT

or

1

DT

, B ð16:109Þ

In other words, a real-time analyzer has a bandwidth greater than its sampling rate.

A multichannel digital signal analyzer can analyze one or more signals simultaneously and generate

(and display) results such as Fourier spectra, power spectral densities, cross spectral densities, frequencyresponse

functions, coherence functions, autocorrelations, and cross correlations. They are able to

perform high-resolution analysis on a small segment of the frequency spectrum of a signal. This is termed

zoom analysis. Essentially, in this case, the spectral line spacing, DF; is decreased while keeping the

number of lines (N), and hence the number of time data samples, the same. That means the record length

ðT ¼ 1=DFÞ has to be increased in proportion, for zoom analysis.

16.9.2 Oscilloscopes

An oscilloscope is used to observe one or two signals separately or simultaneously. Amplitude, frequency,

and phase information of the signals can be obtained using an oscilloscope. In this sense, the oscilloscope

is a signal modification as well as a measurement (monitoring) and display device. Both analog and

digital oscilloscopes are available. A typical application of an oscilloscope is to observe (monitor)

experimental data such as vibration signals of machinery as obtained from transducers. They are also

useful in observing and examining vibration test results, such as frequency-response plots, PSD curves,

and response spectra. Typically, only temporary records are available on an analog oscilloscope screen.

The main component of an analog oscilloscope is the cathode-ray tube (CRT), which consists of an

electron gun (cathode) that deflects an electron ray according to the input-signal level. The oscilloscope

screen has a coating of electron-sensitive material, so that the electron ray that impinges on the screen

leaves a temporary trace on it. The electron ray sweeps across the screen horizontally, so that waveform

traces can be recorded and observed. Usually, two input channels are available. Each input may be

observed separately, or the variations in one input may be observed against those of the other. In this

manner, signal phasing can be examined. Several sensitivity settings for the input-signal-amplitude scale

(in the vertical direction) and sweep-speed selections are available on the panel.

16.9.2.1 Triggering

The voltage level of the input signal deflects the electron gun proportionally in the vertical (y-axis)

direction on the CRT screen. This alone will not show the time evolution of the signal. The true time

variation of the signal is achieved by means of a sawtooth signal that is generated internally in the

oscilloscope and used to move the electron gun in the horizontal (x-axis) direction. As the name implies,

the sawtooth signal increases linearly in amplitude until a threshold value then suddenly drops to zero,

and then repeats this cycle again. In this manner, the observed signal is repetitively swept across the screen

and a trace of it can be observed as a result of the temporary retention of the illumination of the electron

gun on the fluorescent screen. The sawtooth signal may be controlled (triggered) in several ways. For

example, the external trigger mode uses an external signal from another channel (not the observed

channel) to generate and synchronize the sawtooth signal. In the line trigger mode, the sawtooth signal is

synchronized with the AC line supply (60 or 50 Hz). In the internal trigger mode, the observed signal

(which is used to deflect the electron beam in the y direction) itself is used to generate (synchronize) the

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sawtooth signal. Since the frequency and the phase of the observed signal and the trigger signal are

perfectly synchronized in the last case, the trace on the oscilloscope screen will appear stationary. Careful

observation of a signal can be made in this manner.

16.9.2.2 Lissajous Patterns

Suppose that two signals, x and y; are provided to the two channels of an oscilloscope. If they are used to

deflect the electron beam in the horizontal and the vertical directions, respectively, a pattern known as

Lissajous pattern will be observed on the oscilloscope screen. Useful information about the amplitude

and phasing of the two signals may be observed by means of these patterns. Consider sine waves x and y:

Several special cases of Lissajous patterns are given below.

1. Same frequency, same phase: Here,

x ¼ xo sinðvt þ fÞ

y ¼ yo sinðvt þ fÞ

Then we have

x

xo ¼

y

yo

which gives a straight-line trace with a positive slope, as shown in Figure 16.29(a).

(a) (b)

x

y

x

y

(c) (d)

x

y

x

y

(e)

x

y

x

y

yo

yintercept

x

y

1

2

=

1

3

=

2

3

=

wy

wx

wy

wx

wy

wx

FIGURE 16.29 Some Lissajous patterns: (a) equal frequency and in-phase; (b) equal frequency and 908 out-ofphase;

(c) equal frequency and 1808 out-of-phase; (d) equal frequency and u out-of-phase; (e) integral frequency ratio.

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2. Same frequency, 908 out-of-phase: Here,

x ¼ xo sinðvt þ fÞ

y ¼ yo sinðvt þ f þ p=2Þ ¼ yo cosðvt þ fÞ

Then we have

x

xo

􀀏 􀀐2

þ

y

yo

􀀏 􀀐2

¼ 1

which gives an ellipse, as shown in Figure 16.29(b).

3. Same frequency, 1808 out-of-phase: Here,

x ¼ xo sinðvt þ fÞ

y ¼ yo sinðvt þ f þ pÞ ¼ 2yo sinðvt þ fÞ

Hence,

x

xo þ

y

yo ¼ 0

which corresponds to a straight line with a negative slope, as shown in Figure 16.29(c).

4. Same frequency, u out-of-phase:

x ¼ xo sinðvt þ fÞ

y ¼ yo sinðvt þ f þ uÞ

When vt þ f ¼ 0; y ¼ yintercept ¼ yo sin u:

Hence,

sin u ¼

yintercept

yo

In this case, we obtain a tilted ellipse as shown in Figure 16.29(d). The phase difference u is obtained

from the Lissajous pattern.

5. Integral frequency ratio:

vy

vx ¼

Number of y-peaks

Number of x-peaks

Three examples are shown in Figure 16.29(e).

vy

vx ¼

2

1

;

vy

vx ¼

3

1

;

vy

vx ¼

3

2

Note: The above observations are true for narrowband signals as well. Broadband random signals produce

scattered (irregular) Lissajous patterns.

16.9.2.3 Digital Oscilloscopes

The basic uses of a digital oscilloscope are quite similar to those of a traditional analog oscilloscope.

The main differences stem from the manner in which information is represented and processed

“internally” within the oscilloscope. Specifically, a digital oscilloscope first samples a signal that arrives

at one of its input channels and stores the resulting digital data within a memory segment. This is

essentially a typical ADC operation. This digital data may be processed to extract and display the

necessary information. The sampled data and the processed information may be stored on a floppy

disk, if needed, for further processing using a digital computer. Also, some digital oscilloscopes have the

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communication capability so that the information may be displayed on a video monitor or printed to

provide a hard copy.

A typical digital oscilloscope has four channels so that four different signals may be acquired (sampled)

into the oscilloscope and displayed. Also, it has various triggering options so that the acquisition of a

signal may be initiated and synchronized by means of either an internal or an external trigger. Apart from

the typical capabilities that are possible with an analog oscilloscope, a digital oscilloscope can

automatically provide other useful features such as the following:

1. Automatic scaling of the acquired signal

2. Computation of signal features such as frequency, period, amplitude, mean, root-mean-square

(rms) value, and rise time

3. Zooming into regions of interest of a signal record

4. Averaging of multiple signal records

5. Enveloping of multiple signal records

6. FFT capability, with various window options and antialiasing

These various functions are menu selectable. Typically, first a channel of the incoming data (signal) is

selected and then an appropriate operation on the data is chosen from the menu (through menu

buttons).

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