MECH 430 Notes 2, Spring 2014

Instrumentation & Measurements MECH 430 MECH 430 Slide 1 Introduction Chapter 2 Static and Dynamic Characteristics of Signals 2.2 Signals and Waveforms • A signal is used to transmit information • In the context of measurement systems, both the input and the output have a waveform, which can be represented as a signal. • Signals may be classified as: – Analog signals – Discrete signals – Digital signals • A Discrete Signal results from the sampling of an analog signal at repeated finite time intervals. We estimate the value of the signal in between discrete values by assuming it is equal to the last available value (Sample and Hold). • The magnitude of a Digital Signal are also discrete by the effect of Quantization. MECH 430 Introduction Slide 2 2.2 Signals and Waveforms • Three types of signals: MECH 430 Introduction Slide 3 2.2 Signals and Waveforms • Signals may also be characterized as static or dynamic. • A static signal does not vary with time, Example, the diameter of a shaft. Voltage of a battery, outdoor temperature? • A Dynamic signal is a time dependent signal. They can be deterministic or non-deterministic. They can be simple periodic, complex periodic or aperiodic. MECH 430 Introduction Slide 4 2.2 Signals and Waveforms MECH 430 Introduction Slide 5 2.2 Signals and Waveforms MECH 430 Introduction Slide 6 2.3 Signal Analysis • Signal Mean or DC-Component MECH 430 Introduction Slide 7 Analog Discrete 2.3 Signal Analysis • The root-mean-square (rms) is another measure that is related to the energy in an oscillating signal. • If we have a sinusoidal current, the rms value is a constant current that would produce the same energy dissipation in a resistor. MECH 430 Introduction Slide 8 Analog Discrete 2.3 Signal Analysis • Root Mean Square MECH 430 Introduction Slide 9 2.4 Signal Amplitude and Freq MECH 430 Introduction Slide 10 Radial Fourier Series • In many cases, signals do not have a clearly defined trigonometric form. • We can represent such signal as a weighted sum of sinusoidal signals (sines and cosines). • This decomposition into an infinite number of sines and cosines is called a Fourier series. MECH 430 Introduction Slide 11 Fourier Series MECH 430 Introduction Slide 12 Fourier Series MECH 430 Introduction Slide 13 Frequency content of white light MECH 430 Introduction Slide 14 Example MECH 430 Introduction Slide 15 - Example • This is an odd function then the DC component is zero and the cosine coefficients are all zeros. • The sine coefficients MECH 430 Introduction Slide 16 Example • Use tools to compute integrals • Take a look at http://www.wolframalpha.com MECH 430 Introduction Slide 17 Example MECH 430 Introduction Slide 18 Note that the yellow line represents the sum of the first three terms - Example MECH 430 Introduction Slide 19 Example MECH 430 Introduction Slide 20 Example MECH 430 Introduction Slide 21