R. Data Encoding_S_9(2)

# R. Data Encoding_S_9(2) - Reading 1 Data Encoding Analog to...

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Reading 1 Data Encoding, Analog to Digital Conversion 1. Analog to Digital Conversion 2. Sampling and the Nyquist Criterion 3. Digital Data Encoding Schemes 4. Channel Capacity 5. Noisy Channel: Shannon Capacity 6. Conclusion 7. Appendix

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Prof. R. Dzhanidze CS M117. Reading , Data Encodding 1. Analog to Digital Conversion The Material also supports Lab Exercise #1; 2; 3; 4. An analog signal has an infinite number of possible levels, and an infinite number of data points are necessary to exactly record all the data of the signal. Digitally storing all the information of an analog signal would require a finite amount of storage space. The amount of information in the analog signal must be reduced through a process analog-to-digital conversion called pulse code modulation (PCM). To convert an analog signal to a digital signal, (A/D converter converts an analog signal to a digital signal that represents equivalent information) . the infinite number of data points must be reduced by sampling the signal at a certain interval, with pulse amplitude modulation (PAM) (see Figure 1). PAM converts the original analog signal to a discrete signal. The original signal is represented as a series of infinitely narrow pulses whose amplitude is equal to the value of the original signal at the start of a sampling interval. The length of the sampling interval is equal to the reciprocal of the sampling rate. Original Signal P ulse A mplitude M odulated S(t) S(t) t t Sampling Interval Figure 1: Conversion of analog signal to discrete signal using PAM. 2
Prof. R. Dzhanidze CS M117. Reading , Data Encodding However, the amplitude of each pulse has an infinite number of possible levels. Digitally storing all the information of the PAM signal would still require infinite storage space. The storage space of each pulse amplitude must be limited by quantizing the amplitude value and setting the maximum allowable value. This will limit the number of bits necessary to store the number. (Figure 2). For instance, we want to use only 8 bits to store each sample, and the maximum possible value of the analog signal is 10, then we can quantize the signal into multiples of 10 / 256 (0.03906). Each number will be represented as an 8-bit binary number between 0 and 255. To approximately reconstruct the original analog signal, each 8-bit sample must be multiplied by 0.03906. Original Signal Digitized Pulse S(t) S(t) t t Recovery of Original Signal S(t) t Figure 2: Conversion of analog signal to digital signal through PCM. 3

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Prof. R. Dzhanidze CS M117. Reading , Data Encodding In the Fourier transform of an analog signal, the bandwidth is the maximum frequency in the signal. If we limit the bandwidth of the original signal, we eliminate the high-frequency components. If we then sample the signal at a sampling rate greater than or equal to twice this bandwidth, this discrete signal contains all the information of the original signal (by the Nyquist criterion ). The bandwidth-limited signal can be reconstructed exactly from the discrete
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R. Data Encoding_S_9(2) - Reading 1 Data Encoding Analog to...

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