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Quantizing error:–Granular or linear errorshappen for inputs within the dynamic range of quantizer –Saturation errorshappen for inputs outside the dynamic range of quantize •Saturation errors are larger than linear errors •Saturation errors can be avoided by proper tuning of AGC •Quantization noise variance:

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  1. BÀI 3: Format (Channel coding) Đặng Lê Khoa Email:danglekhoa@yahoo.com dlkhoa@fetel.hcmuns.edu.vn Facuty of Electronics & & Telecommunications, HCMUNS 1 Facuty of Electronics Telecommunications, HCMUNS
  2. Facuty of Electronics & Telecommunications, HCMUNS 2
  3. • 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: ∞ σ = E{[ x − q( x)] } = ∫ e 2 ( x) p( x)dx = σ Lin + σ Sat 2 q 2 2 2 −∞ L / 2 −1 ql2 q2 σ 2 Lin =2∑ p ( xl )ql Uniform q. σ Lin 2 = l =0 12 12 2006-01-26 Facuty of Electronics & Lecture 2 Telecommunications, HCMUNS 3
  4. 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 2006-01-26 Facuty of Electronics & Lecture 2 Telecommunications, HCMUNS 4
  5. 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. compression+expansion companding y = C ( x) ˆ x x(t ) y (t ) ˆ y (t ) ˆ x(t ) x ˆ y Compress Qauntize Expand Transmitter Channel Receiver 2006-01-26 Facuty of Electronics & Lecture 2 Telecommunications, HCMUNS 5
  6. Statistical of speech amplitudes • In speech, weak signals are more frequent than strong ones. Probability density function 1.0 0.5 0.0 1.0 2.0 3.0 Normalized magnitude of speech signal • Using equal step sizes (uniform quantizer) gives low for weak signals ⎛S⎞ and high for strong signals. ⎜ ⎟ ⎛S⎞ ⎝ N ⎠q ⎜ ⎟ – Adjusting the step ⎝ N ⎠ of the quantizer by taking into account the speech statistics size q improves the SNR for the input range. 2006-01-26 Facuty of Electronics & Lecture 2 Telecommunications, HCMUNS 6
  7. Baseband transmission • To transmit information through physical channels, PCM sequences (codewords) are transformed to pulses (waveforms). – Each waveform carries a symbol from a set of size M. – Each transmit symbol represents bits of the PCM words. k = log 2 M – PCM waveforms (line codes) are used for binary symbols (M=2). – M-ary pulse modulation are used for non-binary symbols (M>2). 2006-01-26 Facuty of Electronics & Lecture 2 Telecommunications, HCMUNS 7
  8. PCM waveforms • PCM waveforms category: Nonreturn-to-zero (NRZ) Phase encoded Return-to-zero (RZ) Multilevel binary +V 1 0 1 1 0 +V 1 0 1 1 0 NRZ-L -V Manchester -V Unipolar-RZ +V Miller +V 0 -V +V +V Bipolar-RZ 0 Dicode NRZ 0 -V -V 0 T 2T 3T 4T 5T 0 T 2T 3T 4T 5T 2006-01-26 Facuty of Electronics & Lecture 2 Telecommunications, HCMUNS 8
  9. PCM waveforms … • Criteria for comparing and selecting PCM waveforms: – Spectral characteristics (power spectral density and bandwidth efficiency) – Bit synchronization capability – Error detection capability – Interference and noise immunity – Implementation cost and complexity 2006-01-26 Facuty of Electronics & Lecture 2 Telecommunications, HCMUNS 9
  10. Spectra of PCM waveforms 2006-01-26 Facuty of Electronics & Lecture 2 Telecommunications, HCMUNS 10
  11. M-ary pulse modulation • M-ary pulse modulations category: • M-ary pulse-amplitude modulation (PAM) • M-ary pulse-position modulation (PPM) • M-ary pulse-duration modulation (PDM) – M-ary PAM is a multi-level signaling where each symbol takes one of the M allowable amplitude levels, each representing k = log 2of PCM words. bits M – For a given data rate, M-ary PAM (M>2) requires less bandwidth than binary PCM. – For a given average pulse power, binary PCM is easier to detect than M-ary PAM (M>2). 2006-01-26 Facuty of Electronics & Lecture 2 Telecommunications, HCMUNS 11
  12. PAM example 2006-01-26 Facuty of Electronics & Lecture 2 Telecommunications, HCMUNS 12
  13. Facuty of Electronics & Telecommunications, HCMUNS 13
  14. Facuty of Electronics & Telecommunications, HCMUNS 14
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