1. Prof. Nizamettin AYDIN naydin@yildiz.edu.tr http://www.yildiz.edu.tr/~naydin Advanced Digital Signal Processing 1

2. Amplitude Modulation 2

3. Review of FT properties –Convolution multiplication –Frequency shifting Sinewave Amplitude Modulation –AM radio Frequency-division multiplexing –FDM

4. Table of Easy FT Properties Delay Property Frequency Shifting Linearity Property Scaling

5. Table of FT Properties Differentiation Property

6. Frequency Shifting Property

7. Convolution Property Convolution in the time-domain MULTIPLICATION corresponds to MULTIPLICATION in the frequency- domain

8. Cosine Input to LTI System

9. Ideal Lowpass Filter

10. Ideal LPF: Fourier Series

11. The way communication systems work How do we share bandwidth ?

12. Table of FT Properties Differentiation Property

13. Signal Multiplier (Modulator) Multiplication in the time-domain corresponds to convolution in the frequency-domain.

15. Amplitude Modulator x(t) modulates the amplitude of the cosine wave. The result in the frequency-domain is two shifted copies of X(j  ).

18. DSBAM Modulator If X(j  )=0 for |  |>  b and  c >  b,the result in the frequency-domain is two shifted and scaled exact copies of X(j  ).

19. DSBAM Waveform In the time-domain, the “envelope” of sine- wave peaks follows |x(t)|

20. Double Sideband AM (DSBAM) “Typical” bandlimited input signal Frequency-shifted copies Upper sidebandLower sideband

21. DSBAM DEmodulator

22. DSBAM Demodulation

23. Frequency-Division Multiplexing (FDM) Shifting spectrum of signal to higher frequency: –Permits transmission of low-frequency signals with high-frequency EM waves –By allocating a frequency band to each signal multiple bandlimited signals can share the same channel –AM radio: 530-1620 kHz (10 kHz bands) –FM radio: 88.1-107.9 MHz (200 kHz bands)

24. FDM Block Diagram (Xmitter) Spectrum of inputs must be bandlimited

25. Frequency-Division De-Mux

26. Bandpass Filters for De-Mux

27. Pop Quiz: FT thru LPF

28. Sampling and Reconstruction (Fourier View) 28

29. Sampling Theorem Revisited –GENERAL: in the FREQUENCY DOMAIN –Fourier transform of sampled signal –Reconstruction from samples Review of FT properties –Convolution  multiplication –Frequency shifting –Review of AM

30. Table of FT Properties Delay Property Frequency Shifting Scaling

31. Amplitude Modulator x(t) modulates the amplitude of the cosine wave. The result in the frequency-domain is two SHIFTED copies of X(j  ). Phase

32. DSBAM: Frequency-Domain “Typical” bandlimited input signal Frequency-shifted copies Upper sideband Lower sideband

33. DSBAM Demod Phase Synch

34. Quadrature Modulator TWO signals on ONE channel: “out of phase” Can you “separate” them in the demodulator ?

35. Demod: Quadrature System

36. Quadrature Modulation: 4 sigs 8700 Hz 3600 Hz

37. Ideal C-to-D Converter Mathematical Model for A-to-D FOURIER TRANSFORM of x s (t) ???

38. Periodic Impulse Train Fourier Series

39. FT of Impulse Train

40. Impulse Train Sampling

41. Illustration of Sampling

42. Sampling: Freq. Domain EXPECT FREQUENCY SHIFTING !!!

43. Frequency-Domain Analysis

44. Frequency-Domain Representation of Sampling “Typical” bandlimited signal

45. Aliasing Distortion If  s < 2  b, the copies of X(j  ) overlap, and we have aliasing distortion. “Typical” bandlimited signal

46. Reconstruction of x(t)

47. Reconstruction: Frequency-Domain

48. Ideal Reconstruction Filter

49. Signal Reconstruction Ideal bandlimited interpolation formula

50. Shannon Sampling Theorem “SINC” Interpolation is the ideal –PERFECT RECONSTRUCTION –of BANDLIMITED SIGNALS

51. Reconstruction in Time-Domain

52. Ideal C-to-D and D-to-C Ideal SamplerIdeal bandlimited interpolator