Modulation and coding course- lecture 2

Mportant features of digital communication systems- Some basic concepts and definitions as signal classification, spectral density, random process, linear systems and signal bandwidth.
Nội dung trích xuất từ tài liệu:
Modulation and coding course- lecture 2Digital Communications I:Modulation and Coding Course Period 3 – 200/ Catharina Logothetis Lecture 2Last time, we talked about: Important features of digital communication systems Some basic concepts and definitions as signal classification, spectral density, random process, linear systems and signal bandwidth. Lecture 2 2Today, we are going to talk about: The first important step in any DCS: Transforming the information source to a form compatible with a digital system Lecture 2 3 Formatting and transmission of baseband signal Digital info. Textual Formatsource info. Pulse Analog Transmit Sample Quantize Encode modulate info. Pulse Bit stream waveforms Channel Format Analog info. Low-pass Decode Demodulate/ filter Receive Textual Detectsink info. Digital info. Lecture 2 4Format analog signals To transform an analog waveform into a form that is compatible with a digital communication, the following steps are taken: 1. Sampling 2. Quantization and encoding 3. Baseband transmission Lecture 2 5Sampling Time domain Frequency domain xs (t ) = xδ (t ) × x(t ) X s ( f ) = Xδ ( f ) ∗ X ( f ) x(t ) | X(f )| xδ (t ) | Xδ ( f ) | xs (t ) | Xs( f )| Lecture 2 6Aliasing effect LP filter Nyquist rate aliasing Lecture 2 7Sampling theorem Analog Sampling Pulse amplitude signal process modulated (PAM) signal 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. Lecture 2 8 Quantization Amplitude quantizing: Mapping samples of a continuous amplitude waveform to a finite set of amplitudes. Out In Average quantization noise powerQuantized Signal peak power values Signal power to average quantization noise power Lecture 2 9Encoding (PCM) A uniform linear quantizer is called Pulse Code Modulation (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 Lecture 2 10 Quantization example amplitude x(t) 111 3.1867 110 2.2762 Quant. levels 101 1.3657 100 0.4552 011 -0.4552 boundaries 010 -1.3657 001 -2.2762 x(nTs): sampled values xq(nTs): quantized values 000 -3.1867 Ts: sampling time PCM tcodeword 110 110 111 110 100 010 011 100 100 011 PCM sequence Lecture 2 11Quantization error Quantizing error: The difference between the input and output of a quantizer e(t ) = x(t ) − x(t ) ˆ Process of quantizing noise Qauntizer Model of quantizing noise y = q( x) AGC x(t ) ˆ x(t ) x(t ) ˆ x(t ) x e(t ) + e(t ) = x(t ) − x(t ) ˆ Lecture 2 12Quantization error …Quantizing error: Granular or linear errors happen for inputs within the dynamic range of quantizer Saturat ...