Presentation on theme: "Learning Objectives Static and Dynamic Characteristics of Signals"— Presentation transcript:
1Learning Objectives Static and Dynamic Characteristics of Signals Signal DecompositionData Sampling and Acquisition
2Signals, Systems, DataA Signal is the function of one or more independent variables that carries some information to represent a physical phenomenon.A continuous-time signal, also called an analog signal, is defined along a continuum of time.Systems process input signals to produce output signals.Output signals are often converted to digital information with an analog to digital converter.Transfer FunctionHow the analog input signal relates to the analog or digital output signal. This can be represented as a graph or a calibration curve.
3Signal / Sensor Characteristics Static characteristic: Comparison between output signal and ideal output when the input is constant.Dynamic characteristics: Comparison between output signal and ideal output when the input changes.
4Instrument Static Characteristics AccuracyRelation of the instrument output to the true value.Typically shown as percent error relative to true value as determined through calibration.PrecisionThe repeatability of an instrument when reading the same input.High accuracy means that the mean is close to the true value, while high precision means that the standard deviation σ is small.Systematic error:High Precision, low accuracy.
5Static Characteristics Example : Two pressure gauges (pressure gauge A and B) have a full scale accuracy of ± 5%. Sensor A has a range of 0-1 bar and Sensor B 0-10 bar. Which gauge is more suitable to be used if the reading is 0.9 bar? Answer : Sensor A : Equipment max error = ± 5 x 1 bar = ± 0.05 bar 100 Equipment 0.9 bar ( in %) = ± 0.05 bar x 100 = ± 5.6% 0.9 bar Sensor B : Equipment max error = ± 5 x 10 bar = ± bar ( in %) = ± 0.5 bar x 100 = ± 55% Conclusion : Sensor A is more suitable to use at a reading of 0.9 bar because the error percentage (± 5.6%) is smaller compared to the percentage error of Sensor B (± 55%).Source: D. Veeman
6Instrument Static Characteristics RangeThe difference of reading between the minimum value and maximum value for the measurement of an instrument.BiasConstant error which occurs during the measurement of an instrument.This error is usually rectified through calibration.LinearityLargest deviation from linear relation between input and output.Shown as full scale percentage (% fs).SensitivityRatio of change in output towards the change in input at a steady state condition.ResolutionThe minimum detectable change in signal – (% fs).
7Instrument Static Characteristics Most sensitiveVariation of the physical variablesSource: D. Veeman
8Instrument Static Characteristics Dead Band - The range of input reading when there is no change in output (unresponsive system). Threshold - Minimum value before a response is observed. Hysteresis - Lag in sensor reading returning to previous value.OutputReading-+MeasuredVariablesDead BandSource: D. Veeman
9Dynamic Characteristics Behaviour of instruments when the input signal is changing.Characterized by standardized inputs –StepSudden change in inputTransient responseRampLinear changeRamp responseSine waveHarmonic inputFrequency responseInputResponseTime
10Dynamic Characteristics Response from a 2nd order instrument: Rise Time ( tr ) - Time taken for the output to rise from 10% to 90 % of the steady state value. Settling time (ts) - Time taken for output to reach a steady state value.Source: D. Veeman
11Classification of Signals Deterministic & Non Deterministic SignalsPeriodic & A periodic SignalsEven & Odd Signals
12Source: Dr. AJAY KUMAR, BCET Gurdaspur Elementary SignalsSinusoidal & Exponential SignalsSinusoids and exponential signals arise naturally in physical systems and mathematical representations.x(t) = A sin (2Пfot+ θ)= A sin (ωot+ θ)x(t) = Aeat Real Exponential= Aejω̥t = A[cos (ωot) +j sin (ωot)] Complex Exponentialθ = Phase of sinusoidal waveA = amplitude of a sinusoidal or exponential signalfo = fundamental cyclic frequency of sinusoidal signalωo = radian frequencySinusoidal signalSource: Dr. AJAY KUMAR, BCET Gurdaspur
13Time versus Frequency Domain Source: Data Communications and Networking:
14Composite periodic signal Periodic analog signals can be classified as simple or composite. A simple periodic analog signal, a sine wave, cannot be decomposed into simpler signals. A composite periodic analog signal is composed of multiple sine waves.According to Fourier analysis, any composite signal is a combination of simple sine waves with different frequencies, amplitudes, and phases.If the composite signal is periodic, the decomposition gives a series of signals with discrete frequencies;if the composite signal is nonperiodic, the decomposition gives a combination of sine waves with continuous frequencies.Source: Data Communications and Networking:
15Decomposition of a composite periodic signal in the time and frequency domains Source: Data Communications and Networking:
16Mathematical Modeling of Continuous Systems Most continuous time systems represent how continuous signals are transformed via differential equations.E.g. RC circuit:System indicating car velocity:Source: Dr. AJAY KUMAR, BCET Gurdaspur
17Discrete-Time Signals Sampling is the acquisition of the values of a continuous-time signal at discrete points in timex(t) is a continuous-time signal, x[n] is a discrete-time signalSource: Dr. AJAY KUMAR, BCET Gurdaspur
18Discrete Time Sinusoidal Signals Source: Dr. AJAY KUMAR, BCET Gurdaspur
19Mathematical Modeling of Discrete Time Systems Most discrete time systems represent how discrete signals are transformed via difference equationse.g. bank account, discrete car velocity systemSource: Dr. AJAY KUMAR, BCET Gurdaspur
20Discrete Time Exponential and Sinusoidal Signals DT signals can be defined in a manner analogous to their continuous-time counter partx[n] = A sin (2Пn/No+θ)= A sin (2ПFon+ θ)x[n] = ann = the discrete timeA = amplitudeθ = phase shifting radians,No = Discrete Period of the wave1/N0 = Fo = Ωo/2 П = Discrete FrequencyDiscrete Time Sinusoidal SignalDiscrete Time Exponential SignalSource: Dr. AJAY KUMAR, BCET Gurdaspur
21Source: D. Gheith Abandah - http://www.abandah.com/gheith/ Signal ProcessingSignal processing involves systems that process input signals to produce output signals.A system is combination of components that manipulate one or more signals to accomplish a function and produces some output.systemoutput signalinput signalSource: D. Gheith Abandah -
22Analog to Digital Conversion Most physical signals are analog.Analog signals are captured by sensors or transducers.Examples: temperature, sound, pressure, …Need to convert to digital signals to facilitate processing by the microcontroller.The device that does this is analog-to-digital converter (ADC).Source: D. Gheith Abandah -
23Analog v. Digital Signals Source: Data Communications and Networking:
24Analog vs. Digital Property Analog Digital Representation Continuous voltage or currentBinary NumberPrecisionInfinite range of valuesLimited by the number’s lengthResistance to DegradationWeakTolerant to signal degradationProcessingLimitedPowerfulStorageImpossiblePossibleSource: D. Gheith Abandah -
25Elements of a data acquisition system Source: D. Gheith Abandah -
26Elements of a data acquisition system Transducers: physical to electricalAmplify and offset circuitsThe input voltage should traverse as much of its input range as possibleVoltage level shifting may also be requiredFilter: get rid of unwanted signal componentsMultiplexer: select one of multiple inputsSampler: the conversion rate must be at least twice the highest signal frequency (Nyquist sampling criterion)ADCSource: D. Gheith Abandah -