Signal Processing for Mechatronics

Textbook Signal Processing First Hardcover – March 8, 2003 by James H. McClellan, Ronald W. Schafer, Mark A. Yoder

References 1. LabVIEW for Engineers – February 7, 2010 by Ronald W. Larsen 2. LabVIEW Digital Signal Processing: and Digital Communications – May 6, 2005 by Cory Clark

Chapter 1

READING ASSIGNMENTS 1. Textbook Chapter 1, pp. 1-8 Slides and internet links

COURSE OBJECTIVE  Students will be able to:  Understand mathematical descriptions of signal processing algorithms  express the algorithms as computer implementations (Labview)  What are your objectives?

WHY do we USE DSP ?  Mathematical abstractions lead to generalization and discovery of new processing techniques  Computer implementations are flexible  Applications provide a physical context

Fourier Everywhere Telecommunications Ultrasound Sound & Music ECG, EMG, EEG Chromatograms CDROM, Digital Video Fourier Optics X-ray Crystallography Protein Structure & DNA Computerized Tomography Nuclear Magnetic Resonance: MRI Radioastronomy ref: Prestini, “The Evolution of Applied Harmonic Analysis”

Chapter Objectives Understanding the terms: signal and system Physical signals and systems Mathematical representation of signals and systems Case study

Understanding the terms: signal and system  Signals are patterns of variations that represent or encode information  Many signals are naturally thought of as a pattern of variations in time creating what we often call a time waveform.  Physical systems generates signal (phenomena or phenomenon) which are acquired by measurement systems  Signal in mathematics are represented by functions vary with time.

Example 1: recorded Speech signal ( CONTINUOUS-TIME SIGNAL )  It is one-dimensional continuous-time signal  This signal can be represented as a function of a single (time) variable, s(t).  This pattern evolves with time, creating what we often call a time waveform.

How to recode speech? Using Matlab Using LabView  Creating M file  Using Simulink Windows recorder or special software such

% Record your voice for 5 seconds. recObj = audiorecorder; disp('Start speaking.') recordblocking(recObj, 5); disp('End of Recording.'); % Play back the recording. play(recObj); % Store data in double-precision array. myRecording = getaudiodata(recObj); % Plot the waveform. plot(myRecording);  Creating M file Using Matlab

 Using Simulink: using Data Acquisition Toolbox

 Using Simulink: using DSP Toolbox

Using LabView

Example 2: Samples of a Speech Waveform: s[n] = s(nTs )- Example 2: Samples of a Speech Waveform: s[n] = s(nTs )- DISCRETE-TIME SYSTEM  sequence of numbers that can be represented as a function of an index variable that takes on only discrete values.  This can be represented mathematically as s[n] = s(nTs ), Where n is an integer n is an integer Ts is the sampling period. This can be done by sampling a continuous-time signal at isolated, equally spaced points in time

Application in Mechatronics

void main(){ float ADC_Value, POTValue; char txt[10]; Lcd_Init(); ADC_Init(); while(1){ ADC_Value = ADC_Get_Sample(0); Delay_ms(5); POTValue=( 5.0*ADC_VAlue/1023) ; FloatToStr(POTValue, txt); Lcd_Cmd(_LCD_CLEAR); // Clear display Lcd_Cmd(_LCD_CURSOR_OFF); // Cursor off Lcd_Out(1,1,txt); // Write text in first row Delay_ms(5); } }

Example 3: 2D signal  It is signal that can be represented by a function of two spatial variables  the value p(xo, yo) represents the shade of gray at position (x0, y0) in the image  the discrete form would be denoted as p[m,n] = p(m  x,n  y ), where both m and n would take on only integer values, and  x and  v are the horizontal and vertical sampling periods, respectively.

How to create 2D signal?

Mathematical Representation of Systems  a system is something that transforms signals into new signals or different signal representations.  a continuous-time system can be represented mathematically as Example 4The squarer of a continuous-time system; Systems operate on signals to produce new signals or new signal representations.

Mathematical Representation of Systems  a discrete system can be represented mathematically as Example 4 The squarer of a continuous-time system;

y(t) = [x(t)] 2 y(t) = [x(t)]

How to create Discrete Time signals?

Block diagram representation of a sampler. a system whose input is a continuous-time signal x(t) and whose output is the corresponding sequence of samples, defined by the equation the sampler system ="ideal continuous to discrete converter" or ideal C-to-D converter

Case study: Simplified block diagram for recording and playback of an audio CD.