Fourier Series LABVIEW GUI Documentation

Transcription

1 Furier Series LABVIEW GUI Dcumentatin INTRODUCTION The Furier Series GUI is meant t be used as a learning tl t better understand the Furier Series. The user is able t input the amplitude and frequency f 5 separate sine waves and sum them tgether. The result f this summatin is pltted in real time in rder fr the user t see hw the changes affect the resultant signal. The user can then input the amplitude and frequency f a square, sawtth, r triangle wave and attempt t apprximate each f these waves by summing the five sine waves tgether. If the user is unable t btain the crrect Furier cefficients and frequencies required fr each f the five sine waves, the GUI allws fr the user t aut apprximate each f the waves. The crrect cefficients are then displayed next t the user inputs. The user can then check the inputs with the aut-apprximated cefficients. Multiple tabs are available under the main pltting screen, the first f which displays an FFT f bth the Furier apprximatin and actual signal. The next tab displays a lw pass filter which allws the user t change the lwer cut-ff frequency and see its effects n the apprximated signal and its FFT. The final tab displays a band-pass filter which allws the user t see the effects f applying bth a high and lw cut-ff frequency t the Furier apprximatin. FILES NEEDED FurierGUI.exe Furier_LabVIEW_GUI.pdf Furier_LabVIEW_GUI_Assignment.pdf LABVIEW VI The LABVIEW VI created fr this GUI was setup in such a way that the user culd see the effect f changes made in real time. The frnt panel, which is the interface the user sees, can be seen in Figure 1. The user can input the amplitude and frequency f five different sine waves, which the GUI then sums tgether and plts. Three separate waves can then be apprximated by the user alng with the ptin f aut-apprximatin by the GUI itself. The cefficient values used in the atu-apprximatin can be fund in Appendix A. An FFT, lw-pass filter, and band-pass filter can als be applied t the summed signals by clicking thrugh the tabs. OPERATING THE GUI When the LABVIEW GUI is initially pened it will lk like Figure 3. Furier Series LABVIEW rev6/8/006 GUI Dcumentatin 1

2 Figure 1: LABVIEW GUI All f the values are initially set t default values, including the cut-ff frequencies f each f the filters lcated n the separate tabs. The sine waves, ne f which is shwn in Figure, can be altered by the user and are then summed by the GUI and pltted. Figure : 1 f 5 Sine wave Inputs The amplitude and frequency values can either be typed directly int the left-hand bx r adjusted by clicked the up and dwn arrws. The bx t the right is used as an amplitude verificatin, when the aut-apprximatin is in use, it acts as a cmparisn between the input value and the value that shuld have been input. Furier Apprximatin This GUI is set-up t apprximate either a square, sawtth, r triangle wave. Figure 5 shws the selectr as well as the amplitude and frequency input fr these sample signals. Furier Series LABVIEW rev6/8/006 GUI Dcumentatin

3 Figure 3: Wave Parameters and Selectr The wave parameters allw fr the amplitude and frequency t be input by the user fr either f the three sample signals. The user can then input an amplitude and frequency fr the sample wave and attempt t determine the cefficients required fr the five summed sine waves in rder t apprximate each f the sample signals. If the user is having truble btaining the crrect cefficients, the aut-apprximatin buttn, seen in Figure 5, can be utilized. Figure : Aut-Apprximatin Switch Regardless f which sample wave is selected and what parameters have been selected fr that wave, the GUI will autmatically apprximate the sample using five sine waves. It will then utput the crrect cefficients needed in the bx t the right f the sine wave input, as seen in Figure 3. Figure 6 shws the GUI aut-apprximating a square wave f amplitude 1 and frequency 1. Furier Series LABVIEW rev6/8/006 GUI Dcumentatin 3

4 Frequency Spectrum Figure 5: LABVIEW GUI Square Wave Apprximatin The user can als lk at the frequency cntent f the signals by clicking n the TAB entitled FFT Original and Apprximatin. Figure 7 shws the frequency spectrum plt f the square wave with an amplitude and frequency f 1 and its Furier apprximatin, as seen in Figure 6. Figure 6: FFT f Original and Apprximated Signal Furier Series LABVIEW rev6/8/006 GUI Dcumentatin

5 Nte that in Figure 7 nly the first five frequencies match between the apprximatin and the actual wave. This is due t the fact that nly five sine waves were used in the apprximatin. Filtering The user als has the ability t view the effects f tw different filters n the Furier apprximated signals. The first f these filters, a lw-pass filter, allws the user t decrease the lwer cut-ff frequency and watch as the cntributin f each sine wave is taken ut f the summed signal. The lw pass filter effects n the square wave can be seen in Figure 8. Figure 7: Lw-Pass Filter Effects The ther filter that can be applied is a band-pass. This filter allws the user t select individual wave frequencies by bringing the lwer cut-ff just belw the desired frequency and the higher cut-ff just abve. The band-pass filter effects n the square wave can be seen in Figure 9 fr a frequency f 3. Figure 8: Band-Pass Filter Effects Furier Series LABVIEW rev6/8/006 GUI Dcumentatin 5

6 APPENDIX A FOURIER COEFFICENTS Table A-1 shws the methd fr calculating the Furier Cefficients using autapprximatin. Table A-1: Furier Cefficient Determinatin Wave Amplitude Frequency Sine Wave Amplitude Frequency (Hz) Square x π 1 π 3 π 5 π 7 π x π 1 1 x π Sawtth x 3 x π 3 3 x π Triangle x x π 5 π 1 x π 3 x π 5 π 7 x π x and crrespnd t the user-defined input amplitude and natural frequency f the signal. Furier Series LABVIEW rev6/8/006 GUI Dcumentatin 1