Static and dynamic characteristics of signals
- 1. STATIC AND DYNAMIC CHARACTERISTICS OF SIGNALS CHAPTER # 02 THEORY AND DESIGN FOR MECHANICAL MEASUREMENTS – 5TH EDITION FIGLIOLA – BEASELY ASST. PROF. SALMAN ABUBAKAR BUGVI MED - UOL
- 2. INTRODUCTION A measurement system takes an input quantity and transforms it into an output quantity that can be observed or recorded. The corresponding lecture discusses characteristics of both the input signals to a measurement system and the resulting output signals. The shape and form of a signal are often referred to as its waveform.
- 5. SIGNAL CONCEPTS Two important tasks engineers face in the measurement of physical variables are (1) Selecting a measurement system (2) Interpreting the output from a measurement system. Input range of car tire 275 kPa Input range of bicycle tire 700 kPa Idea of input of range of instrument Some basic understanding of nature of input signal (magnitude) Necessary for selecting a measurement system
- 6. SIGNAL CONCEPTS Will the tire gauge work for measuring the pressure change inside an automobile cylinder? A much more difficult task especially when time and spatial behavior of input is not known. Pressure in cylinder varies with time. Select a measurement system to determine the time varying pressure. Information of pressure changes inside cylinder would be necessary. From thermodynamics and speed range of engine magnitude of pressures expected may be estimated along with their rate of change.
- 8. DEFINITION OF SIGNAL Associate signal with transmission of information. A signal is the physical variation about the measured variable being transmitted between process and measurement system, between stages of measurement system or as output. Many measurement systems exhibit similar responses under variety of conditions. Performance and capabilities of measurement system may be described in a generalized way. Generalized behavior of measurement system can be examined by possible forms of input and output signals.
- 9. WAVEFORM CLASSIFICATION Analog Signals Discrete Time Signals Digital Signals
- 12. SIGNAL WAVEFORMS A static signal does not vary with time. Example is diameter of shaft. Many physical variables change very slowly with respect to time and are considered static. Example the voltage difference across battery terminal is considered static in time over the useful life. When we are interested in how measured value changes with respect to time we study dynamic signals. Dynamic signal is time dependent signal.
- 13. CLASSIFICATION OF DYNAMIC SIGNALS A deterministic signal varies in time in a predictable manner, such as a sine wave, a step function or a ramp function. A non deterministic signal that has no discernible pattern of repetition. It cannot be prescribed before it occurs, although certain characteristics may be known in advance. Transmission of data files from one computer to another. Rate of data transmission – possible range of signal magnitude, are known for any signal Not possible to predict future signal characteristics based on existing information in such a signal.
- 14. FUNCTIONS OF DETERMINISTIC VARIABLES STEP FUNCTION RAMP FUNCTION SINE FUNCTION Aperiodic Periodic
- 15. PERIODIC AND APERIODIC WAVEFORMS A signal is steady periodic if the variation of the magnitude of the signal repeats at regular intervals in time. Motion of an ideal pendulum, the temperature variations of an IC engine under steady operating conditions. A simple periodic waveform contains only one frequency. A complex periodic waveform contains multiple frequencies and is represented as superposition of multiple simple periodic waveforms. Aperiodic is the term used to describe deterministic signals that do not repeat at regular intervals.
- 17. SIGNAL ANALYSIS A measurement system produces a signal that may be analog, discrete time or digital. An analog signal is continuous with time and has a magnitude analogous to the physical variable being measured. Mean or average value of signal is found by DC OFFSET
- 18. SIGNAL ANALYSIS The mean value does not provide any indication of the amount of variation in the dynamic portion of the signal. The characterization of the dynamic portion or AC component of the signal can be done by signal root mean square value.
- 20. SUBTRACTING DC OFFSET • When AC component is of primary interest the DC component can be removed. • Procedure allows change of scale or plotting of signal such that fluctuations which were small percentage of DC signal can be more clearly observed without superposition of large DC component.
- 21. SOLVED EXAMPLE - 2.1 Spend 5 minutes in reading and following the solved example 2.1 Theory and Design for Mechanical Measurements 5th Edition Figliola - Beasely
- 22. SIGNAL AMPLITUDE AND FREQUENCY A key factor in measurement system behavior is the nature of input signal to the system. A means is needed to classify waveforms for both input and resulting output signal relative to their magnitude and frequency. A very complex signal even one that is non deterministic in nature can be approximated as an infinite series of sine and cosine functions This method is called Fourier Analysis.
- 23. FOURIER ANALYSIS Combining a number of different pure tones can generate rich musical sound. Another example is separation of white light through a prism. Complex waveform represented by white light is broken into simpler components represented by colors of spectrum. Fourier Analysis is roughly the equivalent of a prism. It yields a representation of complex signal in terms of simple periodic functions. This allows measurement system response to be reasonably well defined by examining output resulting from few specific input waveforms.
- 24. FOURIER ANALYSIS
- 25. STUDY THE 3 PAGES OF HANDOUT PROVIDED CHAPTER #19 – VIBRATIONS PERIODIC SIGNALS VECTOR MECHANICS FOR ENGINEERS (DYNAMICS) 5TH EDITION BEER - JOHNSTON
- 26. Chapter 2. Characteristics of Signal Signal Amplitude and Frequency ② A trigonometric series is given by A0 + A1 cos t + B1 sin t + A2 cos 2t + B2 sin 2t +…+ An cos nt + Bn sin nt Where An and Bn are the coefficients of the series
- 27. Chapter 2. Characteristics of Signal Fourier Coefficients A periodic y(t) with T = 2π y(t) = A0 + (An cos nt + Bn sin nt) with y(t) known, the coeffs. An and Bn are to be determined
- 28. Chapter 2. Characteristics of Signal Fourier Coefficients (n=m non zero)
- 29. Chapter 2. Characteristics of Signal Fourier Coefficients Similarly, Euler formula
- 30. Chapter 2. Characteristics of Signal Fourier Coeffs. for fns. having Arbitrary Periods Euler formulas : The coeffs. of a trigonometric series representing a fn. of freq. of W
- 31. Chapter 2. Characteristics of Signal Fourier Coefficients When n=1, the corresponding terms in the Fourier series are called fundamental The fundamental freq. is w = 2n/T Freq. Corresponding to n=2, 3, 4 are known as harmonics
- 32. Chapter 2. Characteristics of Signal Fourier Coefficients Where
- 33. Chapter 2. Characteristics of Signal Even and Odd Functions A fn. g(t) is even if g(-t) = g(t) cos nt : even A fn. h(t) is odd if h(-t) = - h(t) sin nt : odd
- 34. Chapter 2. Characteristics of Signal Fourier Cosine Series If y(t) is even, its Fourier series contains only cosine terms :
- 35. Chapter 2. Characteristics of Signal Fourier Sine Series If y(t) is odd, its Fourier series contains only sine terms :
- 36. STUDY AND FOLLOW THE SOLVED EXAMPLES 2.3 – 2.4 – 2.5 THEORY AND DESIGN FOR MECHANICAL MEASUREMENTS 5th EDITION FIGLIOLA - BEASELY
- 37. ASSIGNMENT # 02 EXERCISE PROBLEMS CHAPTER #2 THEORY AND DESIGN FOR MECHANICAL MEASUREMENTS 5TH EDITION FIGLIOLA – BEASELY PROBLEMS # 2.1-2.2-2.3-2.4-2.7-2.9-2.10-2.11- 2.12-2.13-2.14-2.15-2.16-2.21