sampling

# sampling - 5 Digital representation of analog signals...

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5 Digital representation of analog signals Transmitting a digital message follows the scheme shown in Fig. 122. The message m ( t ) originates from a source capable of generating digital data, for example a hard drive. Each bit occupies a time period T b seconds and the corresponding data rate is R = 1 /T b bits per second. We modulate the message using one of the schemes previously discussed to get s ( t ) which is transmitted over a channel. For example, we could be transferring a ±le over a wireless network connection. digital message source modulator 1 0 1 0 1 0 0 ) ( t m ) ( t s channel ) ( t s channel demodulator 1 0 1 0 1 0 0 ) ( t m digital message recipient b T Figure 122: Transmission of digital data. At the other end of the channel, we receive s ( t ) (assuming no change due to the channel) and demodulate back to the digital baseband signal which is sent to the recipient. In the ±le transfer example, the recipient would be the hard drive on another computer. The bit period T b would be chosen based on the available channel bandwidth and noise performance requirements. In we increase T b , the data transfer will occur more slowly, and if we decrease T b , data will be transferred more quickly. Many digital communications systems are designed to transmit analog data in real time. For example, a cellular phone digitizes the speech waveform recorded by a microphone and transmits a digital waveform which is used to reconstruct the speech for playback in the speaker of another phone. Transmitting analog data introduces additional considerations as illustrated in Fig. 123. We start with an analog message m a ( t ), in this example the output of a speaker. This message is continuous in time. To represent it digitally, we must generate samples of the message which then can be coded as binary data for subsequent transmission. We sample m a ( t ) by recording its value every T s seconds. The sampling rate or frequency is f s = 1 /T s and we call T s the sampling period. The new sampled message m s ( t ) now takes on a value only at times which are a multiple of T s as indicated in the ±gure. 108

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modulator 1 0 1 0 1 0 0 ) ( t m ) ( t s channel ) ( t s channel demodulator 1 0 1 0 1 0 0 ) ( t m b T MIC Sound Analog message source eg. ) ( t m a s T sample ) ( t m s A/D s T ) ( t m s D/A Interpolation filter Speaker ) ( t m a eg. Analog message recipient Figure 123: Transmission of an analog message as a digital data stream. The samples are still analog data which can take on any value. These data are next passed through an analog to digital (A/D) converter which approximates the message samples as binary codes. Generally, many bits are used to represent each sample and therefore the bit period T b must be smaller than the sample period T s . Put another way, if we have a sampling frequency f s and represent each sample with m bits, then the bit rate must be R = mT s . (100) The output of the A/D converter is now a digital message which is modulated, transmitted and received as in Fig. 122.
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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.

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sampling - 5 Digital representation of analog signals...

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