a brief story From Fourier Series to DFT.pptx

a story From Fourier Series to Descrete Fourier Transform

1. Digital Signal Analysis (Digital Signal Processing) Kholis Nurhanafi [email protected]

2. www.free-powerpoint-templates-design.com INTRODUCTION Sampling Theorem Aliasing WINDOWING, RMS, AMPLITUDE ENVELOPE AUTOCORRELATION, CROSS-CORRELATION, CONVOLUTION FOURIER TRANSFORM DISCRETE FOURIER TRANSFORM (DFT) FAST FOURIER TRANSFORM (FFT) ALGORITHM TIME-FREQUENCY ANALYSIS Short-Time Fourier Transform Wavelet Transform DSP WE ARE HERE

3. In the last meeting, students will be expected : Understanding the DFT concept. Being able to build their own DFT Program. Apply the DFT to any signals to get the frequency response. LEARNING OUTCOMES

4. INTRODUCTION & REVIEW TO FOURIER TRANSFORM FUORIER COEFFICIENT AS A FREQUENCY RESPONSE DISCRETIZED-FREQUENCY FOURIER TRANSFORM THE DISCRETE FOURIER TRANSFORM (DFT) DFT IN MATRIX FORM OUTLINE

5. INTRODUCTION & REVIEW   THE FOURIER TRANSFORM Continuos signal/ “ Analitycal Thing” Discrete signal/ Digital Signal ? Digital Instrument         Signal (time domain) Frequency Response Signal (time domain) Frequency Response

6. FUORIER COEFFICIENT AS A FREQUENCY RESPONSE THE FOURIER SERIES Fourier Coefficients

7. DISCRETIZED-FREQUENCY FT Fourier Coefficients in Exponential Form +

8. Fourier Coefficients in Exponential Form Fourier Coefficients in Exponential Form for Time Series Time Series/ Digital Signal “TOTALLY” DISCRETIZED FT

9. THE DISCRETE FOURIER TRANSFORM (DFT) THE DISCRETE FOURIER TRANSFORM

10. ARE WE DONE YET?

11. DFT IN MATRIX FORM DISCRETE FOURIER TRANSFORM IN MATRIX FORM

12. SUMMARY   Continuos signal/ “ Analitycal Thing” Discrete signal/ Digital Signal Digital Instrument     Signal (time domain) Frequency Response Signal (time domain) Frequency Response

13. REFERENCE Park, Tae Hong., 2010, Introduction to Digital Signal Processing, Computer Musically Speaking , World Scientific Publishing, Singapore. Proakis, John G., & Manolakis, Dimitris G. 1996. Digital Signal Processing:Principles, Algorithms, and Applications . New Jersey: Prentice Hall.

14. Generate a sine signal with Apply your own-build DFT to the signal. (can be done by excel, matlab , pyhon , etc ) Plot the signal. Plot the signal spectrum. If you find any problem, discuss it further with me and your friend. Send the both of your plot and summary of your discussion to : [email protected]   TO FILL YOUR FREE TIME

15. QUESTION?

16. NEXT MEETING DFT (Review) Fast Fourier Transform (FFT)

17. THANK YOU See You Next Week!