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COMMENT Fourier analysis and the examination of a signal’s frequency content have myriads
of applications. In this example, we demonstrated through frequency analysis a clear reason why
clarinets and trumpets sound quite different. The presence of only odd harmonics, or both even and
odd harmonics, is a very recognizable difference, easily perceived by the human ear.
2.6 SUMMARY
This chapter has provided a fundamental basis for the description of signals. The capabilities of a
measurement system can be properly specified when the nature of the input signal is known. The
descriptions of general classes of input signals will be seen in Chapter 3 to allow universal
descriptions of measurement system dynamic behavior.
Any signal can be represented by a static magnitude and a series of varying frequencies and
amplitudes. As such, measurement system selection and design must consider the frequency content
of the input signals the system is intended to measure. Fourier analysis was introduced to allow a
precise definition of the frequencies and the phase relationships among various frequency components within a particular signal. In Chapter 7, it will be shown as a tool for the accurate interpretation
of discrete signals.
Signal characteristics form an important basis for the selection of measurement systems and the
interpretation of measurement system output. In Chapter 3 these ideas are combined with the
concept of a generalized set of measurement system behaviors. The combination of generalized
measurement system behavior and generalized descriptions of input waveforms provides for an
understanding of a wide range of instruments and measurement systems.
REFERENCES
1. Monforte, J., The digital reproduction of sound, Scientific American, 251(6): 78, 1984.
2. Bracewell, R. N., The Fourier Transform and Its Applications, 3d ed., rev., McGraw Hill, New
York, 1999.
3. Champeney, D. C., Fourier Transforms and Their Physical Applications, Academic, London,
1973.
4. Bracewell, R. N., The Fourier transform, Scientific American, 260(6): 86, 1989.
5. Cooley, J. W., and J. W. Tukey, An Algorithm for the Machine Calculation of Complex Fourier
Series, Mathematics of Computation 19: 207, April 1965 (see also Special Issue on the fast
Fourier transform, IEEE Transactions on Audio and Electroacoustics AU-2, June 1967).
6. Bendat, J. S.,and A. G. Piersol, Random Data: Analysis and Measurement Procedures, 3rd ed.,
Wiley, New York, 2000 (see also Bendat, J. S., and A. G. Piersol, Engineering Applications of
Correlation and Spectral Analysis, 2nd ed., Wiley, New York, 1993).
7. Cochran, W. T., et al. What is the fast Fourier transform?, Proceedings of the IEEE 55(10):
1664, 1967.
SUGGESTED READING
Halliday, D.,and R. Resnick, Fundamentals of Physics, 6th ed., Wiley, New York, 2000.
Kreyszig, E., Advanced Engineering Mathematics, 9th ed., Wiley, New York, 2005.
Suggested Reading 71
13:35:20 Page 71
COMMENT Fourier analysis and the examination of a signal’s frequency content have myriads
of applications. In this example, we demonstrated through frequency analysis a clear reason why
clarinets and trumpets sound quite different. The presence of only odd harmonics, or both even and
odd harmonics, is a very recognizable difference, easily perceived by the human ear.
2.6 SUMMARY
This chapter has provided a fundamental basis for the description of signals. The capabilities of a
measurement system can be properly specified when the nature of the input signal is known. The
descriptions of general classes of input signals will be seen in Chapter 3 to allow universal
descriptions of measurement system dynamic behavior.
Any signal can be represented by a static magnitude and a series of varying frequencies and
amplitudes. As such, measurement system selection and design must consider the frequency content
of the input signals the system is intended to measure. Fourier analysis was introduced to allow a
precise definition of the frequencies and the phase relationships among various frequency components within a particular signal. In Chapter 7, it will be shown as a tool for the accurate interpretation
of discrete signals.
Signal characteristics form an important basis for the selection of measurement systems and the
interpretation of measurement system output. In Chapter 3 these ideas are combined with the
concept of a generalized set of measurement system behaviors. The combination of generalized
measurement system behavior and generalized descriptions of input waveforms provides for an
understanding of a wide range of instruments and measurement systems.
REFERENCES
1. Monforte, J., The digital reproduction of sound, Scientific American, 251(6): 78, 1984.
2. Bracewell, R. N., The Fourier Transform and Its Applications, 3d ed., rev., McGraw Hill, New
York, 1999.
3. Champeney, D. C., Fourier Transforms and Their Physical Applications, Academic, London,
1973.
4. Bracewell, R. N., The Fourier transform, Scientific American, 260(6): 86, 1989.
5. Cooley, J. W., and J. W. Tukey, An Algorithm for the Machine Calculation of Complex Fourier
Series, Mathematics of Computation 19: 207, April 1965 (see also Special Issue on the fast
Fourier transform, IEEE Transactions on Audio and Electroacoustics AU-2, June 1967).
6. Bendat, J. S.,and A. G. Piersol, Random Data: Analysis and Measurement Procedures, 3rd ed.,
Wiley, New York, 2000 (see also Bendat, J. S., and A. G. Piersol, Engineering Applications of
Correlation and Spectral Analysis, 2nd ed., Wiley, New York, 1993).
7. Cochran, W. T., et al. What is the fast Fourier transform?, Proceedings of the IEEE 55(10):
1664, 1967.
SUGGESTED READING
Halliday, D.,and R. Resnick, Fundamentals of Physics, 6th ed., Wiley, New York, 2000.
Kreyszig, E., Advanced Engineering Mathematics, 9th ed., Wiley, New York, 2005.
Suggested Reading 71