Introduction to engineering experimentation 3rd edition pdf free download

Introduction to engineering experimentation 3rd edition pdf free download

Introduction to Engineering Experimentation (3rd Edition),People also downloaded these free PDFs

Engineering experimentation, which in a general sense involves using the measure­ ment process to seek new information, ranges in scope from experiments to establish new concepts About Introduction To Engineering Experimentation 3rd Edition pdf Free Download An up-to-date, practical introduction to engineering experimentation. Introduction to [PDF] Files Introduction to Engineering Experimentation (3rd Edition) By Anthony J. Wheeler, Ahmad R. Ganji >> Fast Download Click Here KEY BENEFIT: An up-to-date, This book is a recommended must-read for the serious Introduction To Engineering Experimentation 3Rd Edition enthusiast. The book is jam-packed with the latest info, tips, Introduction To Engineering Experimentation 3Rd Edition PDF Book Details About the Author of Introduction To Engineering Experimentation 3Rd Edition PDF Free Download Book. ... read more

Many standards e. USB and Firewire are backward compatible such that a device based on the old standard recent standard, can be connected to a device or computer designed using the more · albeit with the speed limited to that of the old specification. In addition, most recent standards have a provision for delivering DC power to the connected device, eliminating the need for an external power source for devices requiring relatively low power. More recently, wireless connections between devices have become prevalent. The most common standards found in home networks are IEEE In addition, cellular networks are also allowing many devices to connect to a computer remotely via the Internet.

The length and speed of wireless connections depend greatly on the strength of signal between the host and receiver and generally are significantly slower than their hardwired counterpart. Wireless connections, however, allow for mobility such that a measurement system is not confined to a single location. For example, a technician may be able to travel to a remote site with a handheld device and upload the data to a central computer. Various "off-the-shelf'! For example, one may wish to mea­ sure the pressure and temperature of a fluid at several locations as it travels through a large and complex piping system.

A simple, but not very efficient, approach would be to have separate sensors and displays located at each station with the values manually checked periodically to ensure that things are operating smoothly. A more elegant and useful approach, however, would to be combine all of the signals together and display them on single screen. This is possible using commercial software packages such as National Instruments LabVIEW, which allows one to create a custom "virtual instru­ ment" designed for a particular application. These types of commercial software pack­ ages have become extremely sophisticated, allowing the user to take data, display it in real time, write the data to files, perform real-time data processing, conduct process control and perform safety checks, just to name a few functions.

TYpically, the software consists of a graphical user interface that allows the user to design a custom screen con­ sisting of various menus and icons connected to the various components in the system. With Ethernet connections, these components can even be spread across several states or countries. In the above scenario, the custom software may consist of an on-screen schematic of the piping system with the current pressure and temperature displayed at each measurement station. The interface may also allow for various settings to be changed, such as the closing or opening of a valve, by simply clicking on a button located near the valve in the schematic. The system may also be set up to take appro­ priate action, such as automatic shut down, in the event of a failure that might compro­ mise safety or cause property damage. Virtual instruments are recognized in contrast to measurement hardware that has a predefined function.

For example, a digital multimeter uses an AID converter and a digital display to read and display a voltage level. Other functions, such as measuring AC voltage amplitude are hard-wired into the device and new functions cannot be added as needed. A computer with an AID convertor and appropriate software can also perform the same functions, but provide additional flexibility and customizability by exploiting the capabilities of the computer to which it is attached. For example, one could build a program to not only indicate the amplitude of the AC signal but also dis­ play the signal on the screen and indicate the frequency and phase at which it is oscil­ lating. It would also be possible to display multiple signals on a single screen or perform mathematical operations on the signals. While this example would be straight­ forward to implement for even a lightly trained programmer, it would still take time and resources to implement and may be an overkill for certain tasks.

As such, the sys­ tem engineer must balance the function of the device with the cost. Figure 4. The signal is first amplified and then digitized using a spe­ cial AID convertor commonly referred to as a high-speed digitizer. High-speed digitiz­ ers are similar to conventional AID circuits except that they emphasize speed, or 96 Chapter 4 Computerized Data-Acquisition Systems High-speed digitzer AID Acquisition memory Micro­ processor Display memory Display FIGURE 4. sampling rate, over precision. Digitizers are available with speeds in the GHz range and typically have 8-bit precision. As the digitization occurs at speeds greater than that at which the signal can be processed and displayed, the digital output is immediately stored into memory. The stored signal is then sent to a microprocessor and a display unit, such as an LCD screen. The inclusion of a microprocessor into the system archi­ tecture allows for the inclusion of advanced data processing and triggering algorithms to be included as part of the function of the DSo.

For example, the scope can also be used to measure the signal frequency, amplitude, pulse width, and rise time, or set to trigger on a particular type of event, just to name a few of the functions commonly available. In addition, digital scopes are capable of acquiring and displaying multiple signals simultaneously on the same screen. Many DSOs, taking advantage of the digital nature of the device, are also outfit­ ted with components found in personal computers e. hard drive, DVD-ROMs, etc. and include an operating system allowing for the instrument to be integrated into more complex test environments and for the use of customized software. Similarly, high­ speed digitizers can be purchased separately and installed on a computer, allowing the computer to function as an oscilloscope. Regardless of whether the scope is analog, digital, or PC-based, there are a number of performance parameters that must be con­ sidered when selecting a scope for a particular measurement.

The first is the dB Le. the output is The bandwidth takes into account the frequency response of all elements of the oscilloscope prior to digitization e. amplifier, connec­ tion circuitry, etc. and is distinct from the sampling rate of the scope, which refers to the rate at which the digitizer samples the signal and is typically much greater than the bandwidth. More details about the limitations associated with bandwidth and 4. Additional parameters of importance are the record length, which is the number of points that can be acquired and stored for a given waveform, and the waveform capture rate, which is a measure of how quickly succes­ sive waveforms can be read and captured by the scope.

A general purpose data logger might be temporarily installed for a building air conditioning system in order to obtain diagnostic performance data over a period of time such as temperature, airflow, and fan operation. Some buildings are permanently instrumented using data loggers to obtain acceleration and other data if and when an earthquake occurs. The flight data recorder in a commercial aircraft is a specialized data logger and provides important information after accidents. Recent automobiles often include a data logger that records a small amount of speed and other data just before and after an accident may be part of the airbag system. Many sys­ tems are commercially available, so a suitable solution for a particular application should be readily available. To take a data sample, for example, the following instructions must be executed: 1. Instruct the multiplexer to select a channel. Instruct the AID converter to make a conversion.

Retrieve the result and store it in memory. In most applications, other instructions are also required, such as setting amplifier gain or causing a simultaneous sample-and-hold system to take data. The software required depends on the application. Using selections from various menus, the operator can configure the program for the particular application. These programs can be configured to take data from transducers at the times requested, display the data on the screen, and use the data to perform required control functions. These systems are often con­ figured by technicians rather than engineers or programmers, so it is important that the software setup be straightforward. For complicated processing or control func­ tions, it is possible to include instructions programmed in a higher-level language such as C.

There are a number of very sophisticated software packages now available for personal computer-based data-acquisition systems. These packages are very capable ­ they can take data, display it in real time, write the data to files for subsequent process­ ing by another program, and perform some control functions. The programs are configured for a particular application using menus or icons. They may allow for the incorporation of C program modules. These software packages are the best choice for the majority of experimental situations. Instrumentation for Process Measurement and Control, Chilton, Radnor, PA. Intelligent Instrumentation, Prentice Hall, Englewood Cliffs, NJ. Instrumentation Reference Book, 3rd ed. Lab VIEW 8 Student Edition. Prentice Hall, Englewood Cliffs, NJ. AND MCCONNELL, K. Instrumentation for Engineering Measure­ ments, 2d ed. Design with Operational Amplifiers and Analog Integrated Circuits, McGraw-Hill, New York. IEEE Std IEEE Standard for Local and Met­ ropolitan Area Networks: Overview and Architecture.

The Institute for Electrical and Electronic Engineers, Inc. IEEE IEEE Standard for a High-Perfor­ mance Serial Bus. The Handbook ofPersonal Computer Instrumenta­ tion, Intelligent Instrumentation, Thcson, AZ. Introduction to Labview: 6-Hour Hands-On Tutorial. National Instruments Corporation, Austin, TX. Board-level systems set the trend in data acquisition, Computer Design, Apr. Analog Digital Conversion Handbook, Prentice Hall, Engle­ wood Cliffs, NJ. Semiconductor IC Data Book , AID, DIA Converters, Sony Corp, Tokyo, Japan. Computer-Based Data Acquisition, Instrument Society of America, Research 'ftiangle Park, NC. XYZs of Oscilloscopes, Tektronix, Beaverton, OR. Instrumentation for Engineers, Springer-Verlag, New York. PROBLE M S 4. Convert the decimal number to 8-bit simple binary. Convert the decimal number 1 to bit simple binary. Convert the decimal number to bit simple binary. Find the bit 2's-complement binary equivalent of the decimal number The number is an 8-bit 2's-complement number.

What is its decimal value? How many bits are required for a digital device to represent the decimal number 27, in simple binary? How many bits for 2's-complement binary? How many bits are required for a digital device to represent the decimal number 12, in simple binary? How many bits are required to represent the number in 2's-complement binary? A bit AID converter has an input range of ±8 V, and the output code is offset binary. Find the output in decimal if the input is a b c d 4. Find the output in decimal if the input is 4. Find the output in decimal if the input is o v. Find the output in decimal if the input is a b c d 6. The output of the AID converter is in 2's-complement format. Find the output of the AID converter if the input to the amplifier is a 1.

A bit AID converter has an input range of ±1O V and an amplifier at the input with a gain of Find the output of the AID converter if the input to the amplifier is a 0. Estimate the quantization error as a percent of reading for an input of 1. Estimate the quantization error as a percent of reading for an input of 2. If the input is 8. Estimate the quantization error as a percentage of reading for an input An amplifier is connected to the input and has selectable gains of 10, , and Select the best value for the gain to minimize the quantizing error. What will be the quantizing error as a percentage of the reading when the transducer voltage is 3. Could you attenuate the signal before amplification to reduce the quantizing error?

The connected transducer has a maximum output of 7. Select the appropriate gain to minimize the quantization error, and com­ pute the quantization error as a percent of the maximum input voltage. The connected transducer has a maximum output of 10 mV. Estimate the analog voltage output if the input is simple binary and has the decimal value of Problems 4. Simulate the successive-approximations process to determine the simple binary output. Specify whether these errors are of bias or precision type. List the questions that you want to discuss with an application engineer working for a supplier.

D i screte Sa m p l i n g a n d CHAPTER Ana lys i s of Ti me-Va ryi n g Sig nals Unlike analog recording systems, which can record signals continuously in time, digital data-acquisition systems record signals at discrete times and record no information about the signal in between these times. Unless proper precautions are taken, this dis­ crete sampling can cause the experimenter to reach incorrect conclusions about the original analog signal. In this chapter we introduce restrictions that must be placed on the signal and the discrete sampling rate. In addition, techniques are introduced to determine the frequency components of time-varying signals spectral analysis , which can be used to specify and evaluate instruments and also determine the required sam­ pling rate and filtering.

For example, a reading sample may be taken every 0. The experimenter is then left with the problem of deducing the actual measurand behavior from selected samples. The rate at which measurements are made is known as the sampling rate, and incorrect selection of the sampling rate can lead to mis­ leading results. Figure 5. We are going to explore the output data of a discrete sampling system for which this continuous time­ dependent signal is an input. The important characteristic of the sampling system here is its sampling rate normally expressed in hertz. Figures 5. To infer the form of the original signal, the sample data points have been connected with straight-line segments. In examining the data in Figure 5. However, we know that the sampled signal is, in fact, a sine wave.

The amplitude of the sampled data is also 1 02 5. misleading -it depends on when the first sample was taken. This behavior a constant value of the output occurs if the wave is sampled at any rate that is an integer fraction of the base frequency fm e. The data in Figure 5. The frequency, 1 Hz, is the difference between the sampled-data frequency, 10 Hz, and the sampling rate, 11 Hz. The apparent frequency is 8 Hz, the difference between the sam­ pling rate and the signal frequency, and is again incorrect relative to the input fre­ quency. These incorrect frequencies that appear in the output data are known as aliases.

Aliases are false frequencies that appear in the output data, that are simply artifacts of the sampling process, and that do not in any manner occur in the origi­ nal data. It turns out that for any sampling rate greater than twice fm ' the lowest apparent frequency will be the same as the actual 1 04 Chapter 5 Discrete Sampling and Ana lysis of Time-Va rying Signals 1. This restriction on the sampling rate is known as the sampling-rate theo­ rem. This theorem simply states that the sampling rate must be greater than twice the highest-frequency component of the original signal in order to reconstruct the origi­ nal waveform correctly.

The theorem also specifies methods that can be used to reconstruct the original signal. The amplitude in Figure 5. The sampling-rate theorem has a well-established theoretical basis. There is some evidence that the concept dates back to the nineteenth-century mathematician Augustin Cauchy Marks, The theorem was formally introduced into modern technology by Nyquist and Shannon and is fundamental to communica­ tion theory. The theorem is often known by the names of the latter two scientists. A comprehensive but advanced discussion of the subject is given by Marks In the design of an experiment, to eliminate alias frequencies in the data sampled, it is neces­ sary to determine a sampling rate and appropriate signal filtering.

This process will be discussed in some detail later in the chapter. Even if the signal is correctly sampled i. For example, Figure 5. The sampled data are shown as the small squares. However, these data are not only consistent with a Hz sine wave but in this case, the data are also consistent with Actually, there are an infinite number of higher frequencies that are consistent with the data. If, however, the requirements of the sampling-rate theorem have been met perhaps with suitable filtering , there will be no frequencies less than half the sampling rate t�at are consistent with the data except the correct signal frequency. The higher frequencies can be eliminated from consideration since it is known that they don't exist. In some cases, the requirements of the sampling-rate theorem may not have been met, and it is desired to estimate the lowest alias frequency. The lowest is usually the most obvious in the sampled data. A simple method to estimate alias frequencies involves the folding diagram as shown in Figure 5.

This diagram enables one to predict the alias frequencies based on a knowledge of the signal fre­ quency and the sampling rate. To use this diagram, it is necessary to compute a fre­ quency iN called the folding frequency. iN is half the sampling rate, is. The use of this diagram is demonstrated in Example 5. Example 5. The lowest alias frequency is the difference between frequency. the sampling frequency and the signal frequency. In part b , the sampling frequency is less than the signal frequency. The folding diagram is the simplest method to determine the lowest alias frequency.

In part c , the requirement of the sampling-rate theorem has been met, and the alias frequency is in fact the signal frequency. We will always find a lowest frequency using the folding diagram, whether it is a cor­ rect frequency or a false alias. To know that the frequency is correct, we must insure that the sampling rate is at least twice the actual frequency, usually by using a filter to remove any frequency higher than half the sampling rate. How­ ever, the general time-varying signal does not have the form of a simple sine wave; Figure 5. As discussed below, complicated waveforms can be considered to be constructed of the sum of a set of sine or cosine waves of different fre­ quencies. The process of determining these component frequencies is called spectral analysis. There are two times in an experimental program when it may be necessary to perform spectral analysis on a waveform. The first time is in the planning stage and the second is in the final analysis of the measured data.

In planning experiments in which the data vary with time, it is necessary to know, at least approximately, the frequency characteristics of the measurand in order to specify the required frequency response of the transducers and other instruments and to determine the sampling rate required. While the actual signal from a planned experiment will not be known, data from simi­ lar experiments may be used to determine frequency specifications. In many time-varying experiments, the frequency spectrum of a signal is one of the primary results. In structural vibration experiments, for example, acceleration of the vibrating body may be a complicated function resulting from various resonant fre­ quencies of the system. The measurement system is thus designed to respond properly to the expected range of frequencies, and the resulting data are analyzed for the spe­ cific frequencies of interest.

To examine the methods of spectral analysis, we first look at a relatively simple waveform, a simple Hz sawtooth wave as shown in Figure 5. At first, one might think that this wave contains only a single frequency, Hz. However, it is much more complicated, containing all frequencies that are an odd-integer mUltiple of , such as , , and Hz. The method used to determine these component fre­ quencies is known as Fourier-series analysis. The lowest frequency, to, in the periodic wave shown in Figure 5. s disc�ssed by Den Hartog , Churchill , and Kamen , any penodlc functlon J t can be represented by the sum of a constant and a series of sine and cosine waves. Of course, Eq. Since J t can­ not, in general, be expressed in equation form, it is normal to evaluate Eqs.

If J t is even, it can be represented entirely with a series of cosine terms, which is known as a Fourier cosine series. If fit is odd, it can be represented entirely with a series of sine terms, which is known as a Fourier sine series. Many functions are neither even nor odd and require both sine and cosine terms. If Eqs. bb b3 , bs, and � are the amplitudes of the first, third, fifth, and seventh harmonics of the function f t. These have frequencies of , , , and Hz, respectively. It is useful to present the amplitudes of the har­ monics on a plot of amplitude versus frequency as shown in Figure 5. As can be 1 10 Chapter 5 Discrete Sa m p l i n g and Ana lysis of Ti me-Va ryi ng Signals 2 1. seen, harmonics beyond the fifth have a very low amplitude. Often, it is the energy con­ tent of a signal that is important, and since the energy is proportional to the amplitude squared, the higher harmonics contribute very little energy. As can be seen, the sum of the first and third harmonics does a fairly good job of representing the sawtooth wave.

The main problem is apparent as a rounding near the peak- a problem that would be reduced if the higher harmonics e. were included. Fourier analysis of this type can be very useful in specify­ ing the frequency response of instruments. If, for example, the experimenter considers the first-plus-third harmonics to be a satisfactory approximation to the sawtooth wave, the sensing instrument need only have an upper frequency limit of Hz. The · process of determining Fourier coefficients using numerical methods is demonstrated in Section A. t, Appendix A. Solution: The fundamental frequency for this wave is 10 Hz and the angular frequency, w is Also, by examination, we can conclude that it is an odd function and that the cosine terms will be zero and only the sine terms will be required. Using Eq. S , the first harmonic coefficient can be computed from 1 0 1°0 2 [ 1°.

os �[ rO. l Sawtooth wave. One problem associated with Fourier-series analysis is that it appears to only be useful for periodic signals. In fact, this is not the case and there is no requirement that f t be periodic to determine the Fourier coefficients for data sampled over a finite time. We could force a general function of time to be periodic simply by duplicating the function in time as shown in Figure 5. If we directly apply Eqs. However, if the resulting Fourier series were used to compute values off t outside the time interval O-T, it would result in values that would not necessarily and probably would not resemble the original signal. The analyst must be careful to select a large enough value of T so that all wanted effects can be represented by the resulting Fourier series. An alternative method of finding the spectral content of signals is that of the Fourier transform, discussed next.

The Fourier transform is a generalization of Fourier series. The Fourier transform can be applied to any practical function, does not require that the function be periodic, and for discrete data can be evaluated quickly using a modern computer technique called the Fast Fourier Transform. In presenting the Fourier transform, it is common to start with Fourier series, but in a different form than Eq. This form is called the complex exponential form. These relationships can be used to transform Eq. L cn ejnwot n - oo 5. In Section 5. If a longer value of T is selected, the lowest frequency will be reduced. This concept can be extended to make T approach infinity and the lowest frequency approach zero. In this case, frequency becomes a continuous function. It is this approach that leads to the concept of the Fourier transform. The Fourier transform of a function. Once a Fourier transform has been deter­ mined, the original function.

Such a signal is not well suited to analysis by the continuous Fourier transform. The increment of f, Af, is equal to lIT, and the increment of time the sampling period At is equal to TIN. The Fs are complex coefficients of a series of sinusoids with frequencies of 0, Af, 2Af, 3Af,. The amplitude of F for a given frequency represents the relative contribution of that frequency to the original signal. Only the coefficients for the sinusoids with frequencies between 0 and N 12 - 1 Af are used in the analysis of signal. The coefficients of the remaining frequencies provide redundant information and have a special meaning, as discussed by Bracewell The requirements of the Shannon sampling-rate theorem also prevent the use of any 1 14 Chapter 5 Discrete Sa m p l i ng a n d Ana lysis of Ti me-Varying Signals frequencies above NI2!

f ej 21Tkt f nt A sophisticated algorithm called the Fast Fourier Transform FFf has been developed to compute discrete Fourier transforms much more rapidly. This algorithm requires a time proportional to N log2 N to complete the computations, much less than the time for direct integration. The only restriction is that the value of N be a power of 2: for example, , , , and so on. Programs to perform fast Fourier transforms are widely available and are included in major spreadsheet programs. The fast Fourier transform algorithm is also built into devices called spectral analyzers, which can discretize an analog signal and use the FFf to determine the frequencies. It is useful to examine some of the characteristics of the discrete Fourier transform. If we discretize one second of the signal into samples and perform an FFf we used a spreadsheet program as demonstrated in Section A. f I , versus the frequency, k! As expected, the magnitudes of F at f 10 and f 15 are dominant.

However, there are some adjacent frequencies showing appreciable magnitudes. number of points used to discretize the signal. It can be noticed that the magnitude of I F I for the 10 Hz is different in Figures 5. This is a consequence of the definition of the discrete Fourier transform and the FFf algorithm. To get the correct amplitude of the input sine wave, I F I should be multiplied by 21N. In Figure 5. Similarly for Figure 5. In many cases finding a natural frequency for example , only the relative amplitudes of the Fourier compo­ nents are important so this conversion step is not necessary.

For Figure 5. The actual maximum frequency is Hz. For the FFTs shown in Figures 5. In general, the experimenter will not know the spectral composition of the signal and will not be able to select a sampling time T such that there will be an integral number of cycles of any frequency in the signal. This complicates the process of Fourier decomposition. To demonstrate this point, we will modify Eq. Although 15 complete cycles of the Hz components are sampled, The results of the DFT are shown in Figure 5. The first thing we notice is that the Fourier coefficient for It should be recognized that without a priori knowledge, the user would not be able to deduce whether the signal had separate lO-Hz and Hz components or just a single component at 1O. An unexpected result is the fact that the entire spectrum outside of 10, 11, and Hz has also been altered, yielding significant coefficients at frequencies not present in the original signal. This effect is called leakage and is caused by the fact that there are a non-integral number of cycles of the 1O.

Since one does not � 50 Frequency Hz FIGURE 5. The actual cause is that the sampled value of a particular frequency component at the start of the sampling interval is different from the value at the end. A common method to work around this problem is the use of a windowing function to attenuate the signal at the beginning and the end of the sampling interval. A windowing function is a waveform that is applied to the sampled data. This equa­ tion is plotted in Figure 5. The sampled data is multiplied by this window function producing a new set of data with smoother edges. The Hann function is superimposed on top of the data with the sinusoidal shape apparent. The central portion of the signal is unaffected while the amplitude at the edges is gradually reduced to create a smoother transition. Compared to Fig 5. This should not come as a surprise as the windowing function clearly suppresses the average amplitude of the original signal. This tradeoff between frequency resolution and amplitude is inherent for all window types.

Windows that present good resolution in frequency but poor determination of amplitude are often referred to as being of high resolution with low dynamic range. A variety of window functions and their char­ acteristics have been defined in the literature. Each type of window has its own unique characteristics, with the proper choice depending on the application and preferences of the user. Some common window functions are rectangular, Hamming, Hann, cosine, Lanczos, Bartlett, triangular, Gauss, Bartlett-Hann, Blackman, Kaiser, Blackman­ Harris, and Blackman-Nutall. See Engelberg , Lyons , Oppenheim et. FIGURE 5. b Modified data. An additional consideration in spectral analysis is the types of plots used to dis­ play the data.

In the previous figures, a linear scale has been used both for the ampli­ tude and frequency. It is common, however, to plot one or both axes on a logarithmic scale. In the case of amplitude, it is common to plot the spectral power density, which is typically represented in units of decibels dB. The majority of signals encountered in practice will have record lengths much longer than the examples presented here. Consider a microphone measurement sampled at 40 kHz over a s period of time. The record length in this case would 5. In this case, the apparent frequency resolution, tlf, of the FFT would be 0. As already seen, spectral leakage is likely to limit the resolution to much higher values and it is unlikely that this level of resolution would practically be needed. Rather, it is more common to use methods such as Bartlett's or Welch's methods. In these methods, the sampled signal is divided into equal length segments with a window function applied to each segment.

An FFT is then computed for each segment and then aver­ aged together to produce a single FFT for the entire signal. For example, if one were to take the example above, it could be divided into approximately segments with values in each segment. The FFT of each segment would have a frequency resolution The major advantage to this form of analysis is that any uncertainty in the Fourier coefficients is reduced through the averaging of multiple FFT coefficients. This typically yields a much smoother curve than a single FFT. See Lyons and Oppenheim, et. In most cases the experimenter can deter­ mine the maximum signal frequency of interest, which we shall call fe. However, the signal frequently contains significant energy at frequencies higher than fe. If the signal is to be recorded with an analog device, such as an analog tape recorder, these higher frequencies are usually of no concern. They will either be recorded accurately or attenuated by the recording device.

If, however, the signal is to be recorded only at discrete values of time, the potential exists for the generation of false, alias signals in the recording. The sampling-rate theorem does not state that to avoid aliasing, the sampling rate must be twice the maximum frequency of interest but that the sampling rate must be greater than twice the maximum frequency in the signal, here denoted by fm ' As an example, consider a signal that has Fourier sine components of 90, , , and Hz. If we are only interested in frequencies below Hz, we might set the sampling rate at Hz. In our sampled output, however, we will see frequencies of Hz and 40 Hz, which are aliases caused by the and Hz components of the signal.

Section 5. twice fm, w� s�ould not only avoid aliasing but also be able to recover at least theoretically the ongm? l wave­ form. In the foregoing example, in which fm is Hz, we would select a samplIng rate, fs, greater than Hz. The first term after the summation, fe n aT}, represents the discretely sampled values of the function, n is an integer cor­ responding to each sample, and aT is the sampling period, 1Ifs. One important charac­ teristic of this equation is that it assumes an infmite set of sampled data and is hence an infinite series. Real sets of sampled data are finite.

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[PDF] Files Introduction to Engineering Experimentation (3rd Edition) By Anthony J. Wheeler, Ahmad R. Ganji >> Fast Download Click Here KEY BENEFIT: An up-to-date, 17/06/ · Introduction To Engineering Experimentation 3rd Edition Solution Manualpdf.. introduction to engineering experimentationsolution manual pdf download, the plaintiffs Introduction to Engineering Experimentation. 3rd Edition. Edit: I found it. Press J to jump to the feed. Press question mark to learn the rest of the keyboard shortcuts Wheeler, A. J. and About Introduction To Engineering Experimentation 3rd Edition pdf Free Download An up-to-date, practical introduction to engineering experimentation. Introduction to 18/01/ · Introduction to Engineering Experimentation 3rd Edition by Wheeler Solutions Manual 2. a) From Eq. , G R R R R R R 1 1 99 2 1 2 1 2 1 Since R1 and R2 This book is a recommended must-read for the serious Introduction To Engineering Experimentation 3Rd Edition enthusiast. The book is jam-packed with the latest info, tips, ... read more

To assist the reader in developing capabilities in both unit systems, both SI and British units systems are used in example problems in this book. For the central limit theorem to apply, the sample size n must be large. Based on the nomenclature of Figure 6. t Although it is normally desirable to select such a sampling rate, it is possible to relax this in some cases. Montgomery, George C.

National Instruments Corporation, Austin, TX. PDF Engineering Graphics Essentials Fifth Edition By Kirstie Plantenberg P. Of course, Eq. The probability of success introduction to engineering experimentation 3rd edition pdf free download constant throughout the experiment. In the sections that follow, we discuss the determination of these uncertainty intervals. The first major source of systematic error is that resulting from calibration of the measurement system. Often, professional engineering organizations such as the American Society of Mechanical Engineers ASMEthe Institute of Electrical and Electronic Engineers IEEEand the International Society of Automation ISA have established detailed procedures for performance testing.