Signal types. Signal characteristics: RMS, power, db Probability Density Function (PDF). Analogue-to-Digital Conversion (ADC).

Transcription

1 Signal types. Signal characteristics:, power, db Probability Density Function (PDF). Analogue-to-Digital Conversion (ADC).

2 Signal types Stationary (average properties don t vary with time) Deterministic Instantaneous value is predictable at all points in time Random Only statistical properties are predictable Spectrum is continuous Non-stationary Continuous - eg speech Transient eg shock

3 Signal characteristics?

4 Power of a signal Electric Power Vi Measured quantity ( units) V units sensitivity Power units Transducer V R V units sensitivity Power R R sensitivity Power units R Signal Conditioning (amplifier) V transducer sensitivity i R i=v/r Voltage across a resistor (recording device)

5 Instantaneous power In signal analysis the instantaneous sample squared is referred to as POWER It s is simply the instantaneous quantity squared, eg.5 (m/s )

6 Mean power of vibration and Root Mean Squares () Mean power of a sampled vibration signal (mean squares) N Mean power 0.3 N i 1 g i Mean level that produces the same power as the signal 1 or Root Mean Squares () N g i N N 1 i1 g i g N i 1 Standard deviation

7 of a signal stored in vector g rms=sqrt(mean(g.^)) Average Power Average Power

8 Mean power of harmonic signal A cos x over the period of (analytical solution) A cos A A x dx x 1 4 sin x 0 of a harmonic signal A A A

9 db scale (decibel) db scale is a relative logarithmic scale db db Since 10 log Power 10 log Power Power ref ref 0 db corresponds to? the reference level 0 log ref

10 db scale In air acoustics in which the sound pressure level is measured, the reference for the db scale is the average lowest threshold of audibility, by convention taken as 0 Pa ( x 10-5 Pa ) This 0 Pa is the of the reference signal In other applications, however, the db scale is used to compare the levels of two signals and the choice of reference level is arbitrary

11 db - example The level increases from the reference level (0 db) to 40 db in increments of 10 db. What is the corresponding factor by which the level and power increase? db P 10 0log db Power ref 0dB 1 1 db 0 10 ref 10dB db 0dB Pref 30dB dB

12 Dynamic range of ADC Dynamic range (in db), ref.=1 bi-polar ADC Dynamic range = 0 log (^resolution /) Eg. 0 log (^1 /) = 0 log 4096/ = 66 db 0 log (^16 /) = 0 log 65536/ = 90 db uni-polar ADC Dynamic range = 0 log (^resolution ) Eg. 0 log (^1 ) = 0 log 4096= 7 db

13 Probability Density pdfexample.m 4 random-gaussian 4 Probability Density Function Units Time (s) Normally distributed (Gaussian) random signal White noise

14 Probability Density Function - PDF random-gaussian 3 Probability Density Function pdf ( bin) In MATLAB: ti T binwidth 1 1 [ p, bins] hist( g, nbins); Units 0 0 p p / length( g) / diff ( bins(1: )); plot( bins, p) % or bar( bins, p) -1 - t 1 t -1 - xlabel('signal g (units)') ylabel(' PDF (1/unit') Time (s) x PDF estimate the fraction of total time the signal is within a particular bin, normalised (divided) by the bin width. The same as the number of points of data within a bin divided by the bin width Histogram of frequency of occurrence

15 Exercise Calculate the 3-phase mains voltage in Australia.

16 ADC parameters Analogue-to-Digital Converter Sample rate or frequency (Hz) Sampling interval (s, ms, s) Sample interval Sample 1 frequency Resolution the ability of ADC to distinguish the voltage Gain

17 Resolution of ADC Expressed in bits, eg. 1 bit resolution from 0 to states bit resolution states from 0 to 65535

18 Gain Internal amplification in the ADC Input voltage is amplified the gain times and supplied to the AD converter Why bother? Gain is used to improve the resolution of ADC conversion for lower voltage signals Example Voltage of V measured with the gain of 4 would appear to the ADC as 8V Low level ADC boards with the high gain (eg 500) are used for low sensitivity transducers such as thermocouples (eg full range +/-10V/500 = 0mV)

19 ADC - Voltage range (span) Bi-polar, eg. +/-10V Uni-polar, eg. 0-5V The range is divided into the resolution number of states, eg 1 = 4096 Bi-polar +/-10V, 1 bit resolution

20 Offset binary coded ADC The lowest voltage of the range is mapped to 0 by the ADC The highest voltage is mapped to bit_ resolution 10V 4096 = 1 0V V Voltage 0 Digital values

21 Example offset binary coding A bi-polar ADC with the voltage range of +/-10V, 1 bit resolution and the gain of one returns a digital value (DV) of 500. What is the voltage? Voltage span is 0 V (from 10V to 10V) Number of states is 4096 ( 1 ) -10V correspond to the DV of zero 10V correspond to the DV of V corresponds to 048 (4096/) Voltage Voltage DV V

22 Conversion of DV to voltage Various forms of conversion Voltage Voltage Voltage Voltage DV or 048 Specific cases 0 DV 10 or 4096 Span DV lowest voltage resolution Span DV lowest voltage resolution gain