Transmission systems Lecture 11 Sampling and quantization in

Transmission systems Lecture 11. Sampling and quantization in PDH transmission Systems. Linear quantization and nonlinear quantization.

Transmission systems Sampling

Transmission systems Pulse-amplitude modulation – 1, 2 А pulse-amplitude modulation - 1 t А pulse-amplitude modulation - 2 flat top pulse t

Transmission systems S(f) Flower G(F) Spectrum of the signal pulse-amplitude modulation Fupper F ΔFр К LPF Flower Fupper Fd-Fupper Fd+Fupper 2 Fd-Fupper Fd 2 Fd+Fupper F

Transmission systems The block diagram of PAM-tract El_Key 1 1 PAMgr-1 Ucontr 1 Amp 1 2 El_Key 2 • Ucontr 2 N Ucontr. N Amp 2 PAМ-2 El_Key 3 U'contr С Output U"contr •

Transmission systems Functioning PAM tract PAMgroup-1 U'contr U"contr Т discr /N t. PAM 1 t tcharging tdischarge PAMgroup-2 t. PAM-2 t t t

Transmission systems Diode Switches PAM signals а) VD 2 VD 1 • • VD 4 UPAM (t) Us(t) VD 3 • • + • _ Ucontr • • VD 1 • VD 2 b) UPAM (t) Us(t) VD 3 • • + VD 4 Ucontr • • _

Transmission systems Transistor switches PAM signals b) VT 1 • Us(t) • UPAM (t) R С • • • Ucontr

Transmission systems Quantization

Transmission systems Principle of quantization U quant (t) Urestriction U(t) U i+1 Ui ΔU/2 U i-1 ΔU/2 ΔUquantization step If the amplitude of the reference is more than ΔUquant /2, the amplitude of the reference is changed into a big side, and vice versa. t

Transmission systems Amplitude characteristic quantizing devices а) b) Uoutput ΔUquant/2 Uinput ΔUquant/2 ΔUquant U*restriction > Uinput > U**restriction Zone restrictions band quantization Uinput < U**restriction Zone restrictions Uinput > U*restriction Urestriction

Transmission systems Quantization noise Uoutput 0 t Uinput ∆Uquant/2 t Quantization error t power of quantization noise

Transmission systems Quantization Details Number of bits per code, n Number of quantizing steps, 2 n S/N, d. B 7 128 42 8 256 48 10 1024 60 12 4096 72 A system transmitting voice signals must be able to accommodate signals of about 60 d. B in dynamic range (i. e. a voltage rage of 1000 : 1). To achieve this with uniform quantization, the number of bits per code word should be at least 10 (1024 quantization steps). To conserve bandwidth, 8 -bit code words are used, but the quantizing steps are not equal and this nonuniform quantization improves the dynamic range.

Transmission systems Nonlinear quantization

Transmission systems Uoutput Nonlinear quantization Urestriction Uinput(t) Uquant(t) t

Transmission systems Nonlinear quantization А quant linear А quant nonlinear А quant admissible Рs Рs min Рs max = Prestriction Protection signal from quantization noise (ratio signal / quantization noise) for linear and nonlinear quantization

Transmission systems Nonlinear quantization In North America and Japan the μ-law characteristic is used for companding. This is represented by the function: where x - input amplitude μ - amount of compression and is chosen to be 255 Another compander characteristic used in Europe and many other parts of the world is the A-law curve. According to ITU-T Recommendation G. 711, this is defined by the equations: where x = normalized input level Y = normalized quantized steps ln = natural logarithm A = amount of compression and is chosen to be 87. 6

μ – law compander characteristics

A – law compander characteristics

Transmission systems Number Segment Code Quantization step Number of levels with a nonlinear quantization Number of levels with a linear quantization 7 111 ΔU 7=64ΔUo 128 2048 1024 ΔUo 1 6 110 ΔU 6=32ΔUo 112 1024 512 ΔUo 1/2 5 101 ΔU 5=16ΔUo 96 512 256 ΔUo 1/4 4 100 ΔU 4=8ΔUo 80 256 128 ΔUo 1/8 3 011 ΔU 3=4ΔUo 64 128 64 ΔUo 1/16 2 010 ΔU 2=2ΔUo 48 64 32 ΔUo 1/32 1 001 ΔU 1=ΔUo 32 32 16 ΔUo 1/64 0 000 ΔUo 16 16 0 1/128 Segm ent Standard lower bound The upper boundary of segment

Nonlinear quantization Transmission systems Protection of a sinusoidal signal from the quantization noise in the A- and μ - law companding. А quant, d. B 50 А-87, 6/13 40 ● μ-255/15 30 ● ● 20 33 ● 27 22 Norm for protection from quantization noise 10 -70 -60 -50 -40 -30 -20 -10 0 10 рs, d. B