1. 10.1 fourier analysis of signals using the DFT 10.2 DFT analysis of sinusoidal signals 10.3 the time-dependent fourier transform Chapter 10 fourier analysis of signals using discrete fourier transform

2. Figure 10.1 10.1 fourier analysis of signals using the DFT

3. Figure 10.2 true frequency spectrum error caused by ideal filter error caused by quantization and aliasing error caused by windowing in time domain and spectral sampling frequency response of antialiasing filter frequency spectrum of window sequence

4. 10.2 DFT analysis of sinusoidal signals 10.2.1 the effect of windowing 10.2.2 the effect of spectral sampling

5. 10.2.1 the effect of windowing Before windowing:

6. After windowing:

7. Figure 10.3(a)(b) Example 10.3 EXAMPLE before windowing after windowing effects of windowing ： (1) spectral lines are broadened to the mainlobe of window frequency spectrum (2) produce sidelobe, its attenuation is equal to sidelobe attenuation of window frequency spectrum

8. Figure 10.3(c)(d)(e) broadened spectral lines lead to: difficult to confirm the frequency ； reduced resolution mainlobe leads to ： produce false signal ； flood small signal. leakage: （ magnitudes of two frequency components interact each other ）

9. Conclusion: increase L can increase resolution Figure 10.10 EXAMPLE L=32 L=42 L=54 L=64 conservative definition （ exercise10.7 ）： resolution= main-lobe width

10. EXAMPLE changing the shape of window can change resolution Conclusion: shape of window has effect on frequency resolution

11. Determin window’s shape and length （ 2 ） for blackman window: look up the table （ 1 ） for kaiser windows:

12. 10.2.2 the effect of spectral sampling EXAMPLE Figure 10.5(a)(b)(f) After sampling Before sampling can not reach peak value N=64 N=128

13. N=64 Figure 10.6 EXAMPLE only reach the peak value and zero values N=128 Figure 10.7 N=64 N=128 conclusion : increase N can improve effect

14. Figure 10.9 EXAMPLE Conclusion: increase N can’t increase resolution N=32N=64N=128 N=1024 N=32 N=64 N=128 N=1024

15. EXAMPLE analyze effects of window length to DFT using MATLAB

16. L1=64;L2=128;N=128;T=1/64 n1=0:L1-1;x1=cos(2*pi*2*n1*T)+ cos(2*pi*2.5*n1*T) n2=0:L2-1;x2=cos(2*pi*2*n2*T)+ cos(2*pi*2.5*n2*T) k=0:N-1;X1=fft(x1,N);X2=fft(x2,N) stem(k,abs(X1));hold on; stem(k,abs(X2),’r.’); consideration ： how to get DFS of periodic sequence with period N using windowing DFT ？

17. 10.3 the time-dependent fourier transform 1.definition

18. Figure 10.11 Figure 10.12

19. summary 10.1 fourier analysis of signals using the DFT 10.2 DFT analysis of sinusoidal signals conclusion: effects of windowing and spectral sampling 10.3 the time-dependent fourier transform apply the conclusion in 10.2 in analysis of general signals

20. requirements ： effects of windowing and sampling to DFT line; concept of frequency resolution ， relationship among the shape and length of window, and the points of DFT; DFT analysis of sinusoidal signals.

21. exercises and experiment 10.2110.31(a)-(c) experiment31 34 and 35 （ draw them together ） 36 37 （ B ） 39 （ A ）