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

2. Lecture 21 Amplitude Modulation Digital Signal Processing 2

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4. LECTURE OBJECTIVES Review of FT properties –Convolution multiplication –Frequency shifting Sinewave Amplitude Modulation –AM radio Frequency-division multiplexing –FDM Reading: Chapter 12, Section 12-2

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

6. Table of FT Properties Differentiation Property

7. Frequency Shifting Property

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

9. Cosine Input to LTI System

10. Ideal Lowpass Filter

11. Ideal LPF: Fourier Series

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

13. Table of FT Properties Differentiation Property

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

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

19. 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  ).

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

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

22. DSBAM DEmodulator

23. DSBAM Demodulation

24. 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)

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

26. Frequency-Division De-Mux

27. Bandpass Filters for De-Mux

28. Pop Quiz: FT thru LPF