WG Entrepreneurship: Members, Meetings, and Modules

Within the WG Entrepreneurship, members from various universities have come together to focus on material used in engineering education. Presentations, workshops, and modules aim to boost entrepreneurial skills in students through critical learning experiences. The group has rich experience in running interdisciplinary projects, workshops, and open innovation processes to address European problems. The Cluster Symposium on Entrepreneurship in Engineering Education brings together students, professors, and academic staff to explore innovative approaches in education.

• Entrepreneurship
• Engineering Education
• Critical Skills
• Interdisciplinary Projects
• Workshops

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1. 307 X. Other Applications of Time-Frequency Analysis Applications (13) Acoustics (14) Data Compression (15) Spread Spectrum Analysis (16) System Modeling (17) Economic Data Analysis (18) Signal Representation (19) Seismology (20) Geology (21) Astronomy (22) Oceanography (23) Satellite Signal Analysis (24) Image Processing?? (1) Finding Instantaneous Frequency (2) Signal Decomposition (3) Filter Design (4) Sampling Theory (5) Modulation and Multiplexing (6) Electromagnetic Wave Propagation (7) Optics (8) Radar System Analysis (9) Random Process Analysis (10) Music Signal Analysis (11) Biomedical Engineering (12) Accelerometer Signal Analysis

2. 308 10-1 Sampling Theory Number of sampling points == Sum of areas of time frequency distributions + the number of extra parameters How to make the area of time-frequency smaller? (1) Divide into several components. (2) Use chirp multiplications, chirp convolutions, fractional Fourier transforms, or linear canonical transforms to reduce the area. [Ref] X. G. Xia, On bandlimited signals with fractional Fourier transform, IEEE Signal Processing Letters, vol. 3, no. 3, pp. 72-74, March 1996. [Ref] J. J. Ding, S. C. Pei, and T. Y. Ko, Higher order modulation and the efficient sampling algorithm for time variant signal, European Signal Processing Conference, pp. 2143-2147, Bucharest, Romania, Aug. 2012.

3. 309 Analytic Signal Conversion ( ) x t ( ) ( ) x t ( ) t = + x t jx a H Shearing shearing Area

4. 310 Step 1 Analytic Signal Conversion Step 2 Separate the components (a) (b) + Step 3 Use shearing or rotation to minimize the area to each component Step 4 Use the conventional sampling theory to sample each components

5. 311 ( ) = x n x n 1/ F d t t t sinc x n ( ) x t = n d t n ( ): t x Hilbert transform of x(t) H ( ) x t ( ) ( ) x t ( ) t = + (1) x t jx a H ( ) ( ) ( ) ( ) ( ) t = + + + x t x t x t x t x (2) 1 2 a a K ( ) ( ) ( ) (3) = 2 exp 2 y t j a t x t k = 1, 2, , K k k k ( ) n (4) = x y n k = 1, 2, , K , , d k k t k ( ) ( ) = 2 2 t k exp 2 j a n x n , , k k t k

6. 312 ) t n ( ) = sinc y t x n (1) , k d k , t k n ( ( ) ( ) = 2 exp 2 x t j a t y t (2) k k k ( ) ( ) ( ) ( ) t = + + + x t x t x t x (3) 1 2 a K ( ) x t ( ) = Re (4) x t a

7. 313 Theorem: If x(t) is time limited (x(t) = 0 for t < t1and t > t2) then it is impossible to be frequency limited If x(t) is frequency limited (X(f) = 0 for f < f1and f > f2) then it is impossible to be time limited threshold |X(t, f)| >

8. 314 t [t1, t2] and f [f1, f2] t f ( ) x t ( ) x t ( ) f ( ) f 2 2 2 2 = + + + 1 1 dt dt X df X df 1 1 t f err 2 2 ( ) x t 2 dt x1(t) = x(t) for t [t1, t2] , x1(t) = 0 otherwise X1(f) = FT[x1(t)], For the Wigner distribution function (WDF) ( ) x t ( ) ( ) ( ) 2 2 = = , , , W t f df X f W t f dt x x ( ) ( ) x t 2 = , W t f dfdt dt = energy of x(t). x

9. 315 ( ) x t ( ) ( ) ( ) 2 2 = = , , W t f df X f W t f dt x x t f ( ) x t ( ) x t ( ) f ( ) f 2 2 2 2 + + + 1 1 dt dt X df X df 1 1 t f 2 2 t f ( ) ( ) ( ) ( ) = + + + 1 1 , , , , W t f dfdt W t f dfdt W t f dfdt W t f dfdt x x x x t f 1 1 2 2 t t f t ( ) ( ) ( ) ( ) = + + + 1 2 1 2 , , , , W t f dfdt W t f dfdt W t f dfdt W t f dfdt x x x x t t t f 1 1 2 1 1 2 t t f t ( ) ( ) ( C ) ( D ) + + + 1 2 1 2 , , , , W t f dfdt W t f dfdt B W t f dfdt W t f dfdt x A x x x t t t f 2 1 1 2 t f ( ) f-axis 2 2 , fW t f dfdt x t 1 err 1 1 D ( ) x t 2 dt B f2 A t-axis t1 t2 f1 C

10. 316 10-2 Modulation and Multiplexing With the aid of (1)the Gabor transform (or the Gabor-Wigner transform) (2)horizontal and vertical shifting, dilation, shearing, generalized shearing, and rotation. [Ref] C. Mendlovic and A. W. Lohmann, Space-bandwidth product adaptation and its application to superresolution: fundamentals, J. Opt. Soc. Am. A, vol. 14, pp. 558-562, Mar. 1997. [Ref] S. C. Pei and J. J. Ding, Relations between Gabor transforms and fractional Fourier transforms signal processing, vol. 55, issue 10, pp. 4839-4850, IEEE Trans. Signal Processing, 2007. and their applications for

11. 317 Example 2 2 1 1 0 0 -1 -1 -2 -2 -20 0 20 -20 0 20 (a) G(u), consisted of 7 components (b) f(t), the signal to be modulated FT We want to add f(t) into G(u) 5 0 -5 -10 -5 0 5 10 (no empty band)

12. 318 5 5 unfilled T-F slot 0 0 -5 -5 -20 0 20 -20 0 20 (c) WDF of G(u) (d) GWT of G(u) 2 5 1 0 0 -1 -5 -2 -20 0 20 -20 0 20 (e) multiplexing f(t) into G(u) (f) GWT of (e)

13. 319 Conventional Modulation Theory The signals x1(t), x2(t), x3(t), ., xK(t) can be transmitted successfully if K B = Allowed Bandwidth k 1 k Bk: the bandwidth (including the negative frequency part) of xk(t) Modulation Theory Based on Time-Frequency Analysis The signals x1(t), x2(t), x3(t), ., xK(t) can be transmitted successfully if K = A Allowed Time duration Allowed Bandwidth k 1 k Ak: the area of the time-frequency distribution of xk(t) The interference is inevitable. How to estimate the interference?

14. 320 10-3 Electromagnetic Wave Propagation Time-Frequency analysis can be used for Wireless Communication Optical system analysis Laser Radar system analysis Propagation through the free space (Fresnel transform): chirp convolution Propagation through the lens or the radar disk: chirp multiplication

15. 321 Fresnel Transform (See pages 267-271) 1 0 a c b d z Fresnel transform == LCT with parameters = 1 (1) STFT WDF (2)

16. 322 (4) Spherical Disk y-axis x-axis direction of wave propagation R radius of the disk = R plane 1 0 1 a c b d = Disk LCT 1/ R

17. 323 RA RB disk A disk B D 1 0 1 1 0 1 1 0 a c b d D LCT = 1/ 1/ R R 1 B A 1 / D R D A = ( ) 1 + + 1 1 1 1 1 / R R R R D D R A B A B B

18. 324 10-3 Accelerometer Signal Analysis The 3-D Accelerometer ( ) can be used for identifying the activity of a person. z-axis y: 0 z: -9.8 z-axis y-axis y-axis tilted by x-axis z-axis y-axis y: -9.8sin z: -9.8cos

19. 325 Using the 3D accelerometer + time-frequency analysis, one can analyze the activity of a person. Walk, Run (Pedometer ) Healthcare for the person suffered from Parkinson s disease

20. 326 3D accelerometer signal for a person suffering from Parkinson s disease The result of the short-time Fourier transform Y. F. Chang, J. J. Ding, H. Hu, Wen-Chieh Yang, and K. H. Lin, A real-time detection algorithm for freezing of gait in Parkinson s disease, IEEE International Symposium on Circuits and Systems, Melbourne, Australia, pp. 1312-1315, May 2014

21. 327 10-5 Music and Acoustic Signal Analysis Music Signal Analysis Acoustic Voiceprint (Speaker) Recognition Speech Signal (1) ( voiceprint) (2) (3) ( ) (4) (5) 94

22. 328 (a) (b) (c) (d) f f f f t t t t large energy middle energy small energy large energy Typical relations between time and the instantaneous frequencies for (a) the 1sttone, (b) the 2ndtone, (c) the 3rdtone, and (d) the 4thtone in Chinese. X. X. Chen, C. N. Cai, P. Guo, and Y. Sun, A hidden Markov model applied to Chinese four-tone recognition, ICASSP, vol. 12, pp. 797-800, 1987.

23. 329 300 250 200 150 100 50 0 0.5 1 1.5 2 2.5 3 1, 2, 3, 4

24. 330 10-6 Other Applications Biomedical Engineering ( (ECG), (EMG), , ) Communication and Spread Spectrum Analysis Economic Data Analysis Seismology Geology Astronomy Oceanography Satellite Signal

25. 331 Short-time Fourier transform of the power signal from a satellite 500 450 400 350 300 250 200 150 100 50 0 2006.5 2007 2007.5 2008 2008.5 2009 2009.5 2010 2010.5 2011 C. J. Fong, S. K. Yang, N. L. Yen, T. P. Lee, C. Y. Huang, H. F. Tsai, S. Wang, Y. Wang, and J. J. Ding, Preliminary studies of the applications of HHT (Hilbert-Huang transform) on FORMOSAT-3/COSMIC GOX payload trending data, 6th FORMOSAT-3/COSMIC Data Users' Workshop, Boulder, Colorado, USA, Oct. 2012

26. 332 astronomy satellite over 700 km communication human life vocal signal, ECG vocal signal oceanography over 1000m geology ocean crust

27. 333 (1) Google http://scholar.google.com.tw/ ( )

28. 334 (2) IEEE http://ieeexplore.ieee.org/Xplore/guesthome.jsp (3) Wikipedia (4) Github ( code) (5) http://eqworld.ipmnet.ru/index.htm tables (6) http://www.lib.ntu.edu.tw/ http://www.lib.ntu.edu.tw/tulips

29. 335 (7) (8) (9) SCI Step 1: http://scientific.thomson.com/mjl/ Step 2: Search Terms Search Type Full Journal Title Search Step 3: SCI

30. 336 (10) : journal papers Wikipedia conference papers journal papers Wikipedia (11) review survey tutorial journal papers ( Paper Title Abstract Papers journal papers )