Lesson_33 - EEL 3135: Discrete-Time Signals and Systems Dr....

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EEL 3135: Discrete-Time Signals and Systems Dr. Fred J. Taylor, Professor Lesson Title: Modulation Lesson Number: 33 [Section 12.2 – 12.3] Background: Communications and wireless communications is an enabling technology. Over the years the textures of communications and communication protocols have evolved from simple to complex. The basic structure of a communications system is abstracted in Figure 1. For commercial radio applications, the two most commonly encountered protocols are amplitude modulation (AM) and frequency modulation (FM). Their environments are summarized in Table 1. Figure 1: Communications system. Table 1: Commercial Radio Item AM FM Carrier frequency 540-1600 kHz 88.1-107.9 MHz Transmission Bandwidth 10kHz 200kHz Audio bandwidths 3-5kHz 15kHz AM Modulation In Chapter 12 basic modulation and demodulation schemes, which are core to communications, are presented and analyzed. The basic building blocks are multipliers (sometime referred to mixers), adders, and filters. Even though these technologies have been previously studied, but will be reviewed in depth when necessary. This process will begin with a study of the mixer (multiplier) shown in Figure 2 which defines a communications process called double-sideband amplitude modulation (DSAM or AM-DS). Figure 2: Basic mixer (modulator) circuit. The information carried by the signal y(t) = x(t) cos( ϖ c t), where ϖ c is called the carrier frequency, rides on the time varying envelope of the cosine ware and is correlated to the information process x(t), thus giving rise to the name amplitude modulation. The output of the mixer can be expressed as: y(t) = (1/2)x(t)e j ϖ c t + (1/2)x(t)e -j ϖ c t 1. Information Transmitter Channel Receiver Information 1 x(t) cos( ϖ c t) y(t) = x(t) cos( ϖ c t)
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EEL 3135: Discrete-Time Signals and Systems Dr. Fred J. Taylor, Professor From previously studied applications of the Fourier transform, it then follows that the spectrum of y(t) is given by: Y(j ϖ ) = (1/2)(X(j( ϖ - ϖ c ) + X(j( ϖ + ϖ c )) 2. Since multipliers are non-linear device, they have the ability to create new frequencies beyond those externally supplied signal sources which is the case here. Example Consider the case where the modulating signal x(t) is a square pulse train with a DC level (bias) and the carrier frequency is 5 times higher than the repetition frequency of x(t). The outcome is shown in Figure 3. The envelope of the carrier signal c(t) is seen to be correlated to that of x(t). In Figure 4 the magnitude frequency response of x(t), c(t), and y(t) are displayed. It can be seen that the spectrum of carrier is essentially a two-sided line spectrum. The modulated output is also seen to have the spectrum of x(t) centered about each of the carrier sidebands (upper and lower). A question to be engaged momentarily is how noe determined the location of these subband frequencies. » t=0:.001:1; x=(0.125*square(2*pi*5*t))+1;
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Lesson_33 - EEL 3135: Discrete-Time Signals and Systems Dr....

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