Signal Processing First Lecture 24 Amplitude Modulation AM

Signal Processing First Lecture 24 Amplitude Modulation (AM) 9/26/2020 © 2003, JH Mc. Clellan & RW Schafer 1

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 9/26/2020 © 2003, JH Mc. Clellan & RW Schafer 3

Table of Easy FT Properties Linearity Property Delay Property Frequency Shifting Scaling 9/26/2020 © 2003, JH Mc. Clellan & RW Schafer 4

Table of FT Properties Differentiation Property 9/26/2020 © 2003, JH Mc. Clellan & RW Schafer 5

Frequency Shifting Property 9/26/2020 © 2003, JH Mc. Clellan & RW Schafer 6

Convolution Property § Convolution in the time-domain corresponds to MULTIPLICATION in the frequencydomain 9/26/2020 © 2003, JH Mc. Clellan & RW Schafer 7

Cosine Input to LTI System 9/26/2020 © 2003, JH Mc. Clellan & RW Schafer 8

Ideal Lowpass Filter 9/26/2020 © 2003, JH Mc. Clellan & RW Schafer 9

Ideal LPF: Fourier Series 9/26/2020 © 2003, JH Mc. Clellan & RW Schafer 10

The way communication systems work How do we share bandwidth ? 9/26/2020 © 2003, JH Mc. Clellan & RW Schafer 11

Table of FT Properties Differentiation Property 9/26/2020 © 2003, JH Mc. Clellan & RW Schafer 12

Signal Multiplier (Modulator) § Multiplication in the time-domain corresponds to convolution in the frequency-domain. 9/26/2020 © 2003, JH Mc. Clellan & RW Schafer 13

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Amplitude Modulator § x(t) modulates the amplitude of the cosine wave. The result in the frequency-domain is two shifted copies of X(jw). 9/26/2020 © 2003, JH Mc. Clellan & RW Schafer 15

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DSBAM Modulator § If X(jw)=0 for |w|>wb and wc >wb, the result in the frequency-domain is two shifted and scaled exact copies of X(jw). 9/26/2020 © 2003, JH Mc. Clellan & RW Schafer 18

DSBAM Waveform § In the time-domain, the “envelope” of sinewave peaks follows |x(t)| 9/26/2020 © 2003, JH Mc. Clellan & RW Schafer 19

Double Sideband AM (DSBAM) “Typical” bandlimited input signal Frequency-shifted copies 9/26/2020 Lower sideband © 2003, JH Mc. Clellan & RW Schafer Upper sideband 20

DSBAM DEmodulator 9/26/2020 © 2003, JH Mc. Clellan & RW Schafer 21

DSBAM Demodulation 9/26/2020 © 2003, JH Mc. Clellan & RW Schafer 22

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 k. Hz (10 k. Hz bands) § FM radio: 88. 1 -107. 9 MHz (200 k. Hz bands) 9/26/2020 © 2003, JH Mc. Clellan & RW Schafer 23

FDM Block Diagram (Xmitter) Spectrum of inputs must be bandlimited 9/26/2020 © 2003, JH Mc. Clellan & RW Schafer 24

Frequency-Division De-Mux 9/26/2020 © 2003, JH Mc. Clellan & RW Schafer 25

Bandpass Filters for De-Mux 9/26/2020 © 2003, JH Mc. Clellan & RW Schafer 26

Pop Quiz: FT thru LPF 9/26/2020 © 2003, JH Mc. Clellan & RW Schafer 27