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Fundamentals of Digital Communication

Fundamentals of Digital Communication. Digital communication system. Input Signal Analog/ Digital. Low Pass Filter. Sampler. Quantizer. Source Encoder. Channel Encoder. Multiplexer. Carrier. Modulator. Pulse Shaping Filters. Line Encoder. To Channel. De- Modulator.

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Fundamentals of Digital Communication

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  1. Fundamentals of Digital Communication

  2. Digital communication system Input Signal Analog/ Digital Low Pass Filter Sampler Quantizer Source Encoder Channel Encoder Multiplexer Carrier Modulator Pulse Shaping Filters Line Encoder To Channel De- Modulator Receiver Filter Detector From Channel Carrier Ref. Signal at the user end Digital-to-Analog Converter Channel Decoder De- Multiplexer

  3. Sampling Time domain Frequency domain

  4. LP filter Nyquist rate aliasing Aliasing effect

  5. Sampling process Analog signal Pulse amplitude modulated (PAM) signal Sampling theorem • Sampling theorem: A bandlimited signal with no spectral components beyond , can be uniquely determined by values sampled at uniform intervals of • The sampling rate, is called Nyquist rate.

  6. Average quantization noise power • Signal peak power • Signal power to average quantization noise power Out Quantized values In Quantization • Amplitude quantizing: Mapping samples of a continuous amplitude waveform to a finite set of amplitudes.

  7. Encoding (PCM) • Pulse code modulation (PCM): Encoding the quantized signals into a digital word (PCM word or codeword). • Each quantized sample is digitally encoded into an l bits codeword where L in the number of quantization levels and

  8. Quant. levels boundaries x(nTs): sampled values xq(nTs): quantized values Quantization example amplitude x(t) 111 3.1867 110 2.2762 101 1.3657 100 0.4552 011 -0.4552 010 -1.3657 001 -2.2762 000 -3.1867 Ts: sampling time t PCM codeword 110 110 111 110 100 010 011 100 100 011 PCM sequence

  9. Process of quantizing noise Qauntizer Model of quantizing noise AGC + Quantization error • Quantizing error: The difference between the input and output of a quantizer

  10. Uniform q. Quantization error … • Quantizing error: • Granular or linear errors happen for inputs within the dynamic range of quantizer • Saturation errors happen for inputs outside the dynamic range of quantizer • Saturation errors are larger than linear errors • Saturation errors can be avoided by proper tuning of AGC • Quantization noise variance:

  11. Uniform and non-uniform quant. • Uniform (linear) quantizing: • No assumption about amplitude statistics and correlation properties of the input. • Not using the user-related specifications • Robust to small changes in input statistic by not finely tuned to a specific set of input parameters • Simply implemented • Application of linear quantizer: • Signal processing, graphic and display applications, process control applications • Non-uniform quantizing: • Using the input statistics to tune quantizer parameters • Larger SNR than uniform quantizing with same number of levels • Non-uniform intervals in the dynamic range with same quantization noise variance • Application of non-uniform quantizer: • Commonly used for speech

  12. compression+expansion companding Non-uniform quantization • It is done by uniformly quantizing the “compressed” signal. • At the receiver, an inverse compression characteristic, called “expansion” is employed to avoid signal distortion. Compress Quantize Expand Channel Transmitter Receiver

  13. Transmitting Analog Data with Digital Signals • To convert analog data into a digital signal, there are two basic techniques: • Pulse code modulation (used by telephone systems) • Delta modulation

  14. Pulse Code Modulation • Analog waveform is sampled at specific intervals • “Snapshots” are converted to binary values

  15. Pulse Code Modulation (continued) • Binary values are later converted to an analog signal • Waveform similar to original results

  16. Pulse Code Modulation (continued) • The more snapshots taken in the same amount of time, or the more quantization levels, the better the resolution

  17. Pulse Code Modulation (continued) • Because the human voice has a fairly narrow bandwidth • Telephone systems digitize voice into either 128 levels or 256 levels • Called quantization levels • If 128 levels, then each sample is 7 bits (2 ^ 7 = 128) • If 256 levels, then each sample is 8 bits (2 ^ 8 = 256)

  18. Pulse Code Modulation (continued) • How fast do you have to sample an input source to get a fairly accurate representation? • Nyquist says 2 times the bandwidth • Thus, if you want to digitize voice (4000 Hz), you need to sample at 8000 samples per second

  19. Delta Modulation • An analog waveform is tracked using a binary 1 to represent a rise in voltage and a 0 to represent a drop

  20. Source Coding • To eliminate redundancy • Huffman Coding • Shannon-Fano Coding • To maximize information rate in a transmission • What is Information Rate ? • Information per bit  Entropy

  21. Channel Coding • Error Control Coding • To reduce the impact of channel errors by controlled introduction of redundancy • Decrease in effective data rate • Increased coding gain • Forward Error Correcting Codes • Linear Block Codes • Convolutional Codes • ARQ methods

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