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Computer Networks

Learn about analog to digital signal conversion, sampling, quantization, and more in computer networks to grasp the fundamentals of data transmission. Explore examples of analog and digital transmissions and how noise affects signal quality.

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Computer Networks

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  1. Computer Networks Digitization

  2. t Transfer of an Analog Signal s(t) Signal at the sender (original) • When analog data (voice, pictures, video) are transformed into analog electrical signal and transmitted through the media, the transmission impairments of the media change the signal. • The noise is added to the signal and the result is a signal that does not look very much like the original. • When the signal is amplified the noise is amplified, too. • It is hard to extract the original signal. Noise Noise Signal at the receiver t Computer Networks

  3. Why we are going digital? • The receiver of the digital signal samples the received signal using the clock at the sender. • It is only required that it detects whether the voltage is positive or negative. • If positive it generates positive pulse • If negative it generates negative pulse • As a consequence the received signal is exactly the same as the one that was sent. • Ocasionally errors can appear, but there are methods for their detection and correction. Signal at the sender (original) s(t) Noise Signal with noise Signal at the receiver r(t) Computer Networks

  4. Digital versus Analog Transmission • Advantages of digital communication • Regenerator receiver • Different kinds of digital signal are treated identically Original pulse Regenerated pulse Propagation distance Voice Data A bit is a bit! Media Computer Networks

  5. Examples of Analog and Digital Transmission • Analog transmission • Local loop in PSTN (Public Switched Telephone Network) • Cable television • Digital Transmission • Long-distance circuits in PSTN • All kinds of LANs Computer Networks

  6. Analog-to-digital Conversion (A/D) • Transformation of analog (continuous) signals into digital signals • Infinite number of values of the amplitude need to be represented (coded) as a digital stream with a minimum loss of information • The device that codes the analog signal into digital signal is called a coder. The device that performs the inverse operation is called a decoder. Both are usually assembled in one box called a codec. Computer Networks

  7. CODEC V V Codec t t CODer-DECoder Computer Networks

  8. Sampling the Analog Signal • Nyquist Sampling Theorem • Analog signal can be recovered if sampled at frequency equal or greater than its maximum frequency. • In other words, • If s(t) is a contnouus signal with a frequency spectum that stisfies S(f) ≤ fmax for all frequencies in S(F), • then it can be recovered from a discrete signal consisting of samples taken from s(t) with frequency that is at least twice as big as fmax . Computer Networks

  9. Sampling – Example s(t) s1 (t) t t Samples from the analog signal Analog signal Computer Networks

  10. Quantization • Each sample obtained by the sampling process has a different amplitude. • This would require an infinite number of values to be transmitted. • To reduce the size of the problem the process of quantization is used. • Quantization • A method dividing the range of amplitude of the samples into finite number of levels, • assigning sign and magnitude to each of these values, and • Coding each of the levels with a binary equivalent Computer Networks

  11. Quantization - Example • The range of amplitude is divided into 128 negative and 128 positive levels (only some of them are shown on the diagram) • The value of each sample is associated with one level • Each level is translated into its seven-bit binary equivalent • The sign of the level is translated into additional bit +125 +125 +100 +75 +50 +25 0 +024 00011000 +102 01100100 +110 +105 +102 +88 +038 00100110 +110 01101110 +48 +048 00110000 +124 01111101 +38 +39 +26 +24 +39 00100111 +105 01101001 +26 00011010 +85 01011000 -25 -50 -75 -100 -125 -15 -015 10001111 -50 -80 1101000 Sign bit + is 0 , - is 1 -80 -50 10110010 Computer Networks

  12. Quantization Error • By replacing the value of the original sample with the value of the level, an intentional error called quantization error is introduced. • Quantization error can be regarded as noise. • The error depends on the number of levels used • If 2N quantization levels are used, the number of bits per sample is N. • More quantization level means lower quantization noise and more bits per sample. Computer Networks

  13. Pulse Code Modulation (PCM) • The process of sampling, quantization, binary encoding and digita-to digital encoding is known as pulse code modulation • PCM is usually used to transform voice signals. • Voice data (phone conversation) is limited to below 4000Hz • Require 8000 sample per second • Each analog sample is assigned a digital value of 8 bits. • Therefore the speed of a digitized voice channel is 64 Kbps Computer Networks

  14. Look at this presentation created by one of the former students. You can read more about how the voice is digitized and try the animation that shows the steps in the process of transforming the voice into a digital signal. Sampling the Voice Computer Networks

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