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Unformatted text preview: 4 Binary (digital) data transmission In modern communications, it it increasingly common to transmit digital rather than analog data. In their simplest form, digital transmissions encode everything as binary 1s or 0s, rather than the continuous signal range possible with an analog broadcast. Obvious examples are internet communications, digital cable / satellite , and digital cell phone service. As an example, the decimal number 89 is represented in binary as 01011001. This could represent a decimal number, the ASCII character y, or a sampled voltage level determined by an analog to digital converter. We can represent this digital data by a message signal m ( t ) as shown in Fig. 94 This message would be generated, for example, by a computer serial port t A- A ) ( t m 1 1 1 1 b T Figure 94: or USB port. The amount of time occupied by each bit is called the bit period T b . Intuitively, we know that the smaller the bit period, the faster we are transmitting data. We can also describe the transmission speed by the bit rate, R usually in bits per second. The bit rate is of course the reciprocal of the bit period. Faster data transmission implies increased bandwidth, giving us the empirical relation bandwidth R = 1 T b . (69) Transmitting this digital signal is no different than transmitting any other message. We want to shift it in frequency so that it occupies a unique frequency band where it will not interfere with messages being transmitted over the same channel. We already know how to modulate and demodulate this message using either AM or FM techniques; what follows can be thought of simply as more examples of these modulation schemes. 4.1 Digital DSB-SC Modulation (BPSK) We can start by writing the digital message mathematically as m ( t ) = A summationdisplay n =0 b n parenleftbigg t- nT b T b parenrightbigg (70) 87 The coefficients b n represent either +1 for a 1 or -1 for a 0. These multiply a rectangular pulse function parenleftbigg t T b parenrightbigg = p ( t ) with a width of T b (one bit period) shifted over by nT b . The important thing here is that each bit in the binary data stream results in a rectangular pulse p ( t ) with a width of T b . We can modulate this message using DSB-SC modulation in the same way as was de- scribed in section 2.3. A block diagram of the procedure is reproduced in Fig. 95. The ) 2 cos( ) ( t f t c TX p = l ) ( t m ) ( t s Figure 95: message is modulated with a cosine at the carrier frequency which shifts its spectrum up and down by f c . This gives s ( t ) = m ( t ) cos(2 f c t ) . The simplicity of the message (either A ) allows us to write s ( t ) = braceleftbigg A cos(2 f c t ) , b n = +1- A cos(2 f c t ) , b n =- 1 or s ( t ) = braceleftbigg A cos(2 f c t ) , b n = +1 A cos(2 f c t ) , b n =- 1 (71) The second form shows that in the DSB-SC modulated message, a binary 1 and 0 are differentiated by a phase shift of 180 ( ) in the transmitted signal. The actual frequency) in the transmitted signal....
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This note was uploaded on 07/16/2009 for the course SYSC 3501 taught by Professor Osama during the Summer '09 term at Carleton CA.
- Summer '09