1

Signal Analyzer, the software

support for education of signal

processing and measurements

Jiří Tůma Faculty of Mechanical Engineering

Department of Control Systems and Instrumentation

VŠB Technical University of Ostrava

17. listopadu 15, Ostrava Poruba

Czech Republic

2

Outline

Signal processing branches

Requirements for education software

Basic principle of handing with Signal Analyzer

Input signals and instruments

Output plots

Teaching support

Research work

Conclusion

3

Signal Processing Branches

Overall data analysis (A-, B-, C-type filtration, Lin)

Fourier Transform, Hilbert Transform

Spectral analysis, averaging in the frequency domain

Spectral maps evaluation, auto- and cross- correlation analysis

Frequency responses evaluation

Envelope analysis and phase demodulation

Rotational speed evaluation from an impulse signal

Data resampling, averaging in the time domain

Order analysis based on FFT or Vold-Kalman filter

Filtration in the time and frequency domain, FIR filtering, wavelets

Quadrature mixing for envelope and phase analysis

Kalman filter for estimating a random constant

Eigenanalysis (Pisarenko’s and MUSIC methods)

Spectral analysis based on AR modeling

Statistics (histograms, rain-flow analysis, fatigue evaluation)

4

Requirements for Education Software

Windows based handling

Data and instrument setups encapsulation enabling capture of both data and setups in project files

User interface in English

Simulation of professional signal analyzers (averaging process, multispectra evaluation)

Replaying signals using a PC sound card

Plots based on Microsoft Graph component

Importing data from data files, clipboard or sound cards

Exporting graphs by Copy and Paste methods into Word documents

5

Main Window Arranged as a Multiple

Document Interface

Notepad Notepad Organisers Organisers

Program Icon Program Icon

6

Main Menu & Context Menu

Main Menu Main Menu

Submenu Submenu

Context Menus Context Menus

Input Signal

Presentation

Input Signal

Presentation

7

Organizers in the Form of Tree Structures Measurement Organiser (Root)

- Measurements

- Individual Signals

Instrument Organiser (Root)

-Instruments

- Input Signals

8

Data Source Description

Binary Data arranged in

Columns 16 bits data in binary file

ScopeWin binary W-Files Binary data generated by ScopeWin

ASCII Data from Clipboard ASCII data from clipboard

ASCII Data from Text File ASCII data text file (arbitrary format, UFF)

Waveform File Wave files (8, 16 and 24 bits)

Waveform Audio Input

Device and IO Device

Data recorded directly from sound cards

(mono/stereo, 8/16 bits) and NI USB-6009

BK 2032 Time, BK 3550,

PULSE LabShop

Binary & ASCII data from BK 2034/32 and

PULSE signal analyzers

Signal Generator Data generated manually or automatically

Type of Data Sources

9

Signal Generator

Sum of components consisting of

• up to 4 harmonic signals differing in frequency, amplitude and initial phase (amplitude and phase of 2 of them can be modulated)

• and/or rectangle

• and/or swept sine

• and/or white and pink noise

10

FIR Filter Design

Ideal Filters • Lowpass/Highpass FIR filter

• Lowpass differentiator FIR filter

• Lowpass Hilbert transformer FIR filter

• Bandpass FIR filter

Filters with Kaiser window • Lowpass/Highpass FIR filter

• Lowpass FIR differentiator

• Lowpass FIR Hilbert trasformer

• Bandpass FIR filter

11

Fast 1/fα Noise Generation

Flicker Noise : Signal (Alpha 1, Filter Number 8)

-0,6

-0,4-0,2

0,0

0,2

0,40,6

0,8

0,0 0,2 0,4 0,6 0,8 1,0

Time [s]

α = 0, Filtered White Noise

0 < α < 2, Filtered 1/fα Noise

α = 2, Random Walk

12

Processing of Raw Time Histories

ZOOM, Cursor

Individual sample editing

Inserting signal segments into Measurement Organizer

13

BK Signal Analyzers as a Source

of Time History Data

BK 2034/2032

ABF Files

BK 3550

Time History

Files

LabShop PULSE

Time History

ASCII Data LabShop PULSE

Time Capture

Instrument

LabShop PULSE

Wave Files

Signal Analyzer

Binary files Text files & Clipboard Data

Brüel & Kjær

14

Direct Recording Waveform Data

Sample Frequency Sample Frequency

Mono / Stereo Mono / Stereo

Bits per Sample Bits per Sample

Right Channel Right Channel

Data

MM Control MM Control

Insert into the tree Insert into the tree

Left Channel Data Left Channel Data

15

Multifunction I/O Devices

NI USB-6009:

14-Bit, 48 kS/s Low-Cost Multifunction DAQ

NI DAQCard-6036E (for PCMCIA):

200 kS/s, 16-Bit, 16 Analog Input Multifunction DAQ

NI USB-4432

102.4 kS/s, 100 dB, 0.8 Hz AC/DC Coupled, 5-Input

Sound and Vibration Device

16

Signal Analyzer Instruments 1

Instrument Description

Hilbert transform, filtration in the frequency domain,

amplitude and phase demodulation (full spectrum)

FFT, filtration in the frequency domain (full

spectrum)

Averaged 1/1-octave and 1/3-octave frequency

spectrum

Averaged autospectrum (full spectrum)

Averaged cross-spectrum

Averaged frequency response

FFT

CPB

Autospectrum

Cross-Spectrum

FRF`

Time

Instruments based on the Fast Fourier Transform Fourier Hilbert

17

Signal Analyzer Instruments 2

Instrument Description

Overall level of the high passed signal in RMS or

PWR

RPM evaluated from an impulse tachosignal

Resampling of signal

2nd Resampling of signal and time delay

Auto and cross correlation

Two FIR Filters, Hilbert transform, quadrature

mixing

FIR filter FRF including filter zeros

Overall

Tachometer

Resampling

2nd Resampling

Correlation

FIR Filters

FIR Filter FRF

18

Signal Analyser Instruments 3

Instrument Description

Vold-Kalman order tracking filter

Kalman Filter for Estimating a Random Constant

Histogram, Cumulative Histogram, Empirical

distribution function, Expected values of normally

distributed data

Autoregressive model coefficients evaluation

Frequency spectrum based on autoregressive

model including filter poles

Kalman Filter

Statistics

AR Spectrum

Vold-Kalman

AR Model

19

Signal Analyzer Instruments 4

Instrument Description

Linear combiner, Prediction, AR Process

Eigenanalysis of correlation matrix, Pisarenko’s

method, Music pseudospectrum

Weighted difference of two signals

Detrend of a signal

Unit is only for testing response of the 2-order

system

Programming language for signals

Eigenanalysis

Difference

Detrend

Test Unit

Linear Combiner

Script

20

Saving Output Data

ASCII Files

Waveform Files (16 bits)

ME’scope spreadsheet files for Operational Deflection Shapes &

Modal Analysis

Binary files for INOVA loading stands

Format of output data files

ASCII Files (extension *.sga)

Binary Files (extension *.sgb)

Files containing projects including signals and instrument setting

*.gif files

*.jpeg files

Export charts in the graphic format

21

Inserting Signals into Instrument Input

Signal Group

Context Menu Context Menu

Drag & Drop Drag & Drop

Main Menu Main Menu

22

Plot & Data Editing

Microsoft Graph Microsoft Graph

Environment

Data Sheet Data Sheet

23

Output Plot 1 Time History : DRIVEBY : Signal

-200

-100

0

100

200

0,0 0,2 0,4 0,6 0,8 1,0

Time [s]

[-]

Scatter with Line Plot Scatter with Line Plot

3-D Surface Plot 3-D Surface Plot Microsoft Graph Microsoft Graph

Environment

24

Output Plot 2

Surface (Top View) Plot Surface (Top View) Plot

3-D Clustered Bar Plot 3-D Clustered Bar Plot

Microsoft Graph Microsoft Graph

Environment

25

Plot Export into a Word Document

Click Copy button Click Copy button Click Paste button Click Paste button

Here doubleclick to edit Here doubleclick to edit

Select this form Select this form

26

Setup 1 for Data Processing

27

Setup 2 for Data Processing

28

Signal Processing and Machine

Diagnostics Teaching Support

Demo-projects based on both simulated signals and real signals from

a research work for industry (http://homel.vsb.cz/~tum52/Projekty/)

Help file and e-book support (76 pages in Czech)

Textbook on signals and signal processing methods (126 pages in

Czech)

Student’s homework support

29

Running Autospectra 0

115

231

346

461

577

692

807

922

1038

1153

1268

1384

1499

1614

1730

1845

1960

2076

2191

2306

2421

989

1117

1196

1290

1397

1503

1607

1703

1808

1897

2000

RM

S

[U]

Frequency [Hz]

Autospectrum 1 : VPM11A : Misto 1 hluk dB(A)

0,35-0,4

0,3-0,35

0,25-0,3

0,2-0,25

0,15-0,2

0,1-0,15

0,05-0,1

0-0,05

Frequency

RPM

Color:

Noise

RMS

Noise excited by run-up of a 8-cylinder and 4-stoke Diesel engine

30

Full Multispectrum of Signal x(t) + j y(t)

Two-side spectrum for journal bearing diagnostics -1

00

-90

-80

-70

-60

-50

-40

-30

-20

-10 0 10 20 30 40 50 60 70 80 90

10

0

1693

1935

2183

2378

2406

2212

1975

1727

0

1020

30

40

50

60

70

RMS

μm

Frequency [Hz]

RPM

Autospectrum : X + jY

60-70

50-60

40-50

30-40

20-30

10-20

0-10

0.475 ord 1.0 ord 2.0 ord

y(t)

x(t)

31

Test Unit

Test Unit : Generator 4 : Col 1

-100

-50

0

50

100

150

0,0 0,2 0,4 0,6 0,8

Time [s]

Time : Generator 4 : Col 1

0

100

200

300

400

500

600

0,0 0,2 0,4 0,6 0,8 1,0

Time [s]

-50-40-30-20-10

0102030

0 100 200 300 400

Frequency [Hz]

FR

F [

dB

]

Output Output Input Input

Frequency Response Function with Resonance & Anti-resonance

32

CPB, Autospectra and Frequency

Response Functions Ride comfort, truck seat frequency response functions

Frequency Weighting

33

Sound

Lin (no weighting), A-Type, B-Type, and C-Type

Vibrations

ISO, SAE J1490

Characteristics Frequency range Mezinárodní norma

Total vibration

Vertical direction (V-ISO 2631-1) 0,5 až 80 Hz ISO 2631-1 : 1997

Horizontal direction (H-ISO 2631-1) 0,5 až 80 Hz ISO 2631-1 : 1997

Building, all directions (Bu-ISO 2631-1) 1 až 80 Hz ISO 2631-2 : 1989

Vertical direction, motion sickness

(TV-ISO 2631-1)

0,1 až 0,5 Hz ISO 2631-1 : 1997

Z-SAE J1490 SAE J1490

X-SAE J1490 SAE J1490

Hands

All directions 8 až 1000 Hz ISO 5349 : 1986

34

Filtration in the Frequency Domain

Time 3 : Expanded Time(Encoder1) ; Expanded Time(Encoder2)

-2

0

2

4

6

0,0000 0,0005 0,0010 0,0015 0,0020 0,0025 0,0030 0,0035

Time [s]

V

Timer : Time: Real (Expanded Time(Encoder1)) ; Time 2: Real (Expanded Time(Encoder2))

-4

-2

0

2

4

0,0000 0,0005 0,0010 0,0015 0,0020 0,0025 0,0030 0,0035

Time [s]

Autospectrum

40

60

80

100

120

140

0 10000 20000

Frequency [Hz]

dB

/re

f 1

E-6

Conversion the frequency modulated impulse signal to a harmonic signal

Band Pass

0

1

0,0 0,5 1,0 1,5 2,0 2,5 3,0

Frequency

H(f)

Band Stop

0

1

0,0 0,5 1,0 1,5 2,0 2,5 3,0

Frequency

H(f)

Comb Band Pass

0

1

0,0 1,5 3,0 4,5 6,0 7,5 9,0

Frequency

H(f)

Comb Band Stop

0

1

0,0 1,5 3,0 4,5 6,0 7,5 9,0

Frequency

H(f)

Autospectrum

-80

-60

-40

-20

0

20

0 10000 20000Frequency [Hz]

dB

/re

f 1

V

35

FFT Convolution

0

2000

4000

0 8 16 24

- 200

0

200

0 2 4 6

200

- 200

0

200

0 2 4 6

0

2000

4000

0 8 16 24 0

2000

4000

0 8 16 24 - 200

0

200

0 2 4 6

- 200

0

200

0 2 4 6 - 200

0

200

0 2 4 6

Segments FFT Filter IFFT

Low Pass

Low Pass

+ +

= =

(FFT Convolution for

smoothing discontinuities

of consecutive records)

Rev

0

2000

4000

0 8 16 24

- 200

0

2 4

0 2 4 6

Rev Ord

Rev Rev

Rev Rev Ord

36

Averaging in the Time or Frequency

Domain

Autospectrum : Acc (Resampled)

0,0000,0020,0040,0060,0080,0100,0120,0140,0160,0180,020

0 50 100 150 200 250 300 350 400

Order [-]

RM

S m

/s2

Autospectrum : Acc (Averaged)

0,0000,0020,0040,0060,0080,0100,0120,0140,0160,0180,020

0 50 100 150 200 250 300 350 400

Order [-]

RM

S m

/s2

Time History : Acc (Averaged)

-0,08

-0,06

-0,04

-0,02

0,00

0,02

0,04

0,06

0,08

0,0 0,2 0,4 0,6 0,8 1,0

Revolution [-]

m/s

2

Time : Acc (Resampled)

-1

1

3

5

7

9

11

0,0 0,2 0,4 0,6 0,8 1,0

Revolution [-]

m/s

2

Resampled signal Synchronously averaged signal

37

Wavelets

FIR Filters : Clipboard : s

-2

-10

12

3

0 250 500 750 1000

Time [s]

U

Time History : Clipboard : s

-2-10123

0 250 500 750 1000Time [s]

U

FIR Filters : Clipboard : s

-2

-1

01

2

3

0 250 500 750 1000

Time [s]

U

FIR Filter : QMF - db 2, Lp

0,0

0,5

1,0

1,5

0,0 0,3 0,5 0,8 1,0

Normalised Frequency [-]M

ag

nit

ud

e

FIR Filter : QMF - db 2, Hp

0,0

0,5

1,0

1,5

0,0 0,3 0,5 0,8 1,0

Normalised Frequency [-]

Mag

nit

ud

e

FRF of Quadrature mirror filters Approximation

Details

LP filter

HP filter

Denoising

38

Structure Vibration Analysis

Time History : Ram za kab. pravy

-0,10

-0,05

0,00

0,05

0,10

0 10 20 30

Time [s]

m

ME’scope ODS (Operational

Deflection Shape) software Time History : Ram za kab. pravy

-10

-5

0

5

10

0 10 20 30

Time [s]

m/s

2

Double integration

Signal Analyser

Input acceleration data

Export

39

Histograms

Time History : PODLAHA

-30

-20

-10

0

10

20

0 5 10 15 20

Time [s]

[m/s

^2

]

Time History : SEDACKA

-30

-20

-10

0

10

20

0 5 10 15 20

Time [s]

[m/s

^2

]

Statistics : PODLAHA

0

500

1000

1500

2000

2500

3000

-24 -16 -8 0 8 16 24

[m/s^2]

Nu

mb

er

Histogram

Cab floor acceleration

Statistics : SEDACKA

0

500

1000

1500

2000

2500

3000

-24 -16 -8 0 8 16 24

[m/s^2]

Nu

mb

er

Statistics : PODLAHA

-25-20-15-10-505

10152025

-24 -16 -8 0 8 16

[m/s 2]

Exp

ecte

d V

alu

es o

f

No

rmall

y D

istr

ibu

ted

Data

Statistics : SEDACKA

-25-20

-15-10

-505

1015

2025

-24 -16 -8 0 8 16

[m/s 2]E

xp

ecte

d V

alu

es o

f

No

rmall

y D

istr

ibu

ted

Data

Seat pan acceleration

Histogram

Normal

distribution

Straight line

Non-linearity

effect

40

Rain-flow Counting Method

Statistics : Sequence of local extremes

-30

-20

-10

0

10

20

30

0 5 10 15

Index

Ex

tre

me

s f

or

Ra

infl

ow

Time History : Signal

-30

-20

-10

0

10

20

30

0 10 20 30 40

Time [s]

0,8

4

5,8

8

10,9

2

15,9

6

21,0

0

26,0

4

31,0

8

36,1

2

-15,96

-5,88

4,2014,28

01020304050607080

Nu

mb

er

of

cycle

s

Amplitude

Mean

3D Rain-flow Balda’s algorithm 2D Rain-flow

0

100

200

300

400

500

0,84

4,20

7,56

10,92

14,28

17,64

21,00

24,36

27,72

31,08

34,44

Amplitude

Nu

mb

er

of

cy

cle

s

Analysis of fatigue data

41

Stress-Life Fatigue Analysis

Statistics : Test : x

-20

-10

0

10

20

30

0 10 20 30 40

Amplitude

Ra

infl

ow

- M

ea

n V

alu

es

vs

. A

mp

litu

de

s

Endurance Limit

S-N Curve

10

100

1000 10000 100000 1000000

Number of cycles

Str

es

s a

mp

litu

de

Statistics : Test : x

0,00

0,05

0,10

0,15

0,20

0,25

0,30

0,35

0 1000 2000 3000

Index

Fa

tig

ue

Da

ma

ge

,

Pa

lmg

ren

-Min

er'

s R

ule

(Sm

=0

)

Statistics : Test : x

0,00

0,05

0,10

0,15

0,20

0,25

0,30

0,35

0 1000 2000 3000

Index

Fa

tig

ue

Da

ma

ge

,

Pa

lmg

ren

-Min

er'

s R

ule

(Sm

<>

0)

Amplitude vs. Mid Value of Cycles Stress-Number Curve

Zero Mid Value of Cycles Non-Zero Mid Value of Cycles

Cumulative Damage Cumulative Damage

42

Programming language Operators

+, -, *, /, ^, ==, ~=, <, >, <=, >=

Signals, variables

x1, x2[n], a[n1][n2], c, del, …

Instructions

for, while, exit, if - else, { }

Functions

iif, sin, cos, tan, atn, abs, sqr,

mag, angle, unwrap, ones, exp,

log, avg, sum, cumsum, length,

max, min, filter, …

Text box for inserting a script

43

VB Code versus Scripts

For i = 0 To m - 1

For j = 0 To n - 1

S = 0

For k = 0 To p - 1

S = S + a(i, k) * b(k, j)

Next k

c(i, j) = S

Next j

Next i

Example: Computation of the matrix product

Visual Basic code Matlab script

>> c=a*b;

Scripts facilitate programming

VB Code -

Predefined

algorithms

VB Code -

Predefined

algorithms

Script

statements

Script

interpreter

44

Features of Scripts

Easy to understand and to use

Based on C++ an Matlab, handling with signals as

vectors and matrixes

Set of built-in functions for signal processing (FFT, IFFT,

Hilbert, …)

Repeating instructions (for, while)

Saving results as a part of projects

Graphic output (MS Graphs)

Code debugging (TraceOn, TraceOff, TraceIn, TraceOut)

45

Creating the Library of Subroutines

List of subroutines Statements of Script Parameters

A subroutine call: _SubroutineName(@Ident1, @Ident2, @Ident3, ..)

An example: _norm(x, a);

Build-in

statements

and functions

can be

extended by

subroutines,

which are

designed by

a software

user.

46

'Pocet vzorku: ‘; n = 1024; n; FS = get(x1,'freq'); M = 20;

index = [0;cumsum(ones(n-1))];

hanning = 1- cos(2*pi*index/n);

d = [ ];

for(i=1;i<=M;i=i+1)

{

status(i); rem('poznámka');

a = extract(x1,round(n*(i-1)/3),n);

if(i==1) variables;

a = a * hanning;

b = (mag(fft(a,'real'),fft(a,'imag'))/n*2/sqr(2))^2;

c = [sqr(2)*b[0]/2, extract(b,1,n/2-1)];

d = [d, c]

};

e = transpose(d); pwr = avg(e,M);

rms = sqr(pwr); 'CrLf‘; 'CrLf‘; 'Autospektrum: ‘; 'CrLf‘;

set(rms,n/FS,'freq'); set(rms,'Hz‘,'unit'); format(rms,‚0.000')

Example of a Script Code

Weighted and averaged

frequency spectrum

a

b

c

a b c

signal matrix

column

column

column

a b

c

transposition

47

Additional Functionality in Gear

Diagnostics Resulting from Scripts

Polar Plot

-0,4

-0,2

0,0

0,2

0,4

-0,4 -0,2 0,0 0,2 0,4

[m/s2]

[m/s

2]

Rem(‘Script for polar plots’);

a=input1; fi=input2/27;

r=0.3+a;

x=r*cos(fi); y=r*sin(fi);

save(x); save(y) 0 2 4 6 8

10

12

14

16

18

20

22

24

26

14

710

1316

1922

2528

3134

3740

0,000,010,020,03

[(m/s2)^2]

27-tooth wheel

40-tooth wheel

Rem(‘Averaging synchronized with hunting frequency’);

x=extract(input1,0, 18*27*40*6);

x=set(x,6,'columns');

y=transpose(x); y=avg(y,6);

y=set(y,486/27,'freq');

y=set(y,40,'columns'); matrix(y^2)

48

Evaluation of the ARX Model

using a Script Input - Output Signals

-8

-6

-4

-2

0

2

4

6

8

0,0 0,2 0,4 0,6 0,8 1,0

Time [s]

x=input1;y=input2; z=[y(-1),y(-2),x,x(-1),x(-2)]; c=z\y;

a=[c[0];c[1]]; b=[c[2];c[3];c[4]];

'Model ';

'y = a1*y(-1) + a2*y(-2) + b0*x + b1*x(-1) + b2*x(-2)';'CrLf';'CrLf';

'Coefficients';'CrLf';'a = ';a;'CrLf';'b = ';b;'CrLf';'

sy=get(c,'param1')/len(y);

'Model error standard deviation ';sqr(sy);'CrLf';

zz=diag(invs(prod(tr(z),z)));

'Coefficient error standard deviations';'CrLf';sqr(sy*zz);'CrLf';

freqz(b,a,1000,'mag');

Results Model y = a1*y(-1) + a2*y(-2) + b0*x + b1*x(-1) + b2*x(-2)

Coefficients

a = [1,9175 -0,9816]

b = [0,2436 -0,4130 0,2421]

Model error standard deviation 0,1023

Coefficient error standard deviations

[5,523E-03 5,521E-03 3,231E-03 3,483E-03 3,427E-03]

Frequency Response

0,001

0,01

0,1

1

10

100

0,0 0,1 0,2 0,3 0,4 0,5

Frequency Relative to Nyquist Frequency

49

Linear Algebra and Signal Processing in

Scripts of the Signal Analyzer Software

MATLAB Signal Analyzer

Matrix & vector product yes

Array multiplication as the element by element product yes

Matrix left division of a column vector yes

Matrix inversion and pseudoinversion yes

Svd, chol (Cholesky factorization) yes

Roots, poly, trace, eig, det, cond yes

Filter, conv, deconv, fft, ifft, angel, abs, unwrap, ar, arx, ... yes

Sparse matrices not implemented yet

50

Research Work

Vold-Kalman order tracking

Sound quality

Kalman filter for estimating a random constant

Angular vibration

Quadrature mixing

Spectral analysis based on autoregressive (AR)

modeling

Pisarenko’s method

Music pseudospectrum

51

Vold-Kalman Order Tracking Filter

Vold-Kalman One-Pole Filter : Generator : SweptSine

-80

-60

-40

-20

0

0 10 20 30 40 50 60 70 80 90 100

Time [s]

RM

S d

B / r

ef

0,7

07

1-pole filter 2-ple filter 3-pole filter 4-pole filter

Abs(H)

Time History : Clipboard : Col 1

0

50

100

150

200

0 20 40 60 80 100

Time [s]

Hz

Swept sine frequency V-K Filter centre frequency

Second generation filter First generation filter

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10

-6

10 -5

10 -4

10 -3

10 -2

10 -1

10 0

1

2

5

10

20

50

100

200

500

r =

Filter frequency response

2f /fs

52

Pass-By Noise Analysis Enabling

De-Dopplerisation

Time History : 3r : Left

-1,5

-1,0

-0,5

0,0

0,5

1,0

1,5

0 1 2 3 4 5 6Time [s]

[Pa]

Vold-Kalman : 3r : Left

20

30

40

50

60

70

80

-10 -5 0 5 10

Position [m]

RM

S d

B(A

)/re

f 2E

-5

[Pa]

27 ord 54 ord 81 ord

3r : Inst Speed

500

1000

1500

2000

2500

0 2 4 6

Time [s]

RP

M

Vold-Kalman : 3r : Left

0,97

0,98

0,99

1,00

1,01

1,02

-10 0 10

Position [m]

c/(

c-v

)

RPM profile Doppler factor c/(c-v) Noise level of RPM orders

Sound pressure time history

53

Sound Quality Analysis

Vold-Kalman : vyfuk_L_mono.wav 2 : Signal

-25000

-20000

-15000

-10000

-5000

0

5000

10000

15000

20000

25000

0 5 10 15

Time [s]

[-]

2 ord

4 ord

6 ord

8 ord

Filtered signal synthesis

54

Hilbert Transform & Phase Demodulation

Transmission Error Measurements

55

Quadrature Mixing

s(t)

- j sin(ωct) cos(ωct)

xReal(t)

xImag(t)

LPF

LPF

Real part

Imag part

Complex signal

Time History : Generator 1 : Sine1/PM - 1

-2

-1

0

1

2

0,0 0,2 0,4 0,6 0,8 1,0

Time [s]

U

FIR Filters : Generator 1 : Sine1/PM - 1

-2,5

-2,0

-1,5

-1,0

-0,5

0,0

0,0 0,2 0,4 0,6 0,8

Time [s]

rad

Phase demodulation of

amplitude and phase

modulated harmonic signals

Modulated

harmonic signal

Modulation

signal

56

Kalman Filter for Estimating a Random

Constant

Time History : data1 : Col 1

475476477478479480481482

0 100 200 300

Time [s]

U

Statistics : data1 : Col 1

0

100

200

300

400

500

600

476 478 480

U

Nu

mb

er

Time History : data1 : Kalman Filter (Col 1)

475476477478479480481482

0 50 100 150 200 250 300

Time [s]

U

Difference 1 : data1 : Kalman Filter (Col 1)

-10

-5

0

5

10

15

10 110 210 310

Time [s]

U

ADC wideband noise due

to the thermal effect Grounded-input histogram

Filter output Cumulative difference

iy

is

i

kkk ys

0

57

AR Modeling in Spectral Analysis

Decaying signal 500-order AR model coefficients

FFT Autospectrum AR Spectrum

AR Model 6 : MA5_8 : Signal

-3,0

-2,0

-1,0

0,0

1,0

2,0

3,0

0 100 200 300 400 500

Index

Co

effic

ien

ts

AR Spectrum : MA5_8 : AR Model

0,000

0,003

0,006

0,009

0,012

0,015

0 5000 10000 15000

Frequency [Hz]

RM

S V

FFT Autospectrum : MA5_8 : Signal

0,000

0,003

0,006

0,009

0,012

0,015

0 5000 10000 15000

Frequency [Hz]

RM

S V

tMtMttt eyayayayAR ...: 2211

Time History : MA5_8 : Signal

-0,8-0,6-0,4-0,20,00,20,40,6

0,0 0,1 0,2 0,3 0,4

Time [s]

V

2

1

2 2exp1

M

mm mfTjaTfPSD

58

Pisarenko’s and MUSIC Methods

Time History : Sine1+Sine2+Noise

-1,5

-1,0

-0,5

0,0

0,5

1,0

1,5

2,0

0,0 0,2 0,4 0,6 0,8 1,0

Time [s]

U

Autospectrum : Sine1+Sine2+Noise

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0 10 20 30 40

Frequency [Hz]

RM

S

Eigenanalysis : Sine1+Sine2+Noise

4,1

Hz

20,4

Hz

0,0

0,2

0,4

0,6

0,8

0 10 20 30 40 50

Frequency [Hz]

RM

S

100-sample record of a signal Pisarenko’s method

FFT Autospectrum

Sine1: 4 Hz, Amplitude 1 Sine2: 20 Hz, Amplitude 0.5

Background

noise level

Eigenanalysis : Sine1+Sine2+Noise

4,05

Hz

20,1

5 H

z

-50

0

50

100

150

0 10 20 30 40 50

Frequency [Hz]

Mu

sic

Pse

ud

osp

ectr

u

m d

B

MUSIC method

59

Conclusion

The paper describes software that supports signal processing education at the Faculty of Mechanical engineering of the VŠB Technical University of Ostrava.

The signal processing lectures are extended by a set of exercises based on measurements performed as a result of the research work for industry.

Students that are working with Signal Analyzer can analyze imported measurement data or make their own noise measurements using a sound card as the first step to become experts.