1 / 40

Digital Telephony

Digital Telephony. Analog signal. Digital signal. or data from. -tape -simulations -digital devices. Discrete signal. A/D converter. Analog. Quantiz- er. Sampler. DSP. D/A. SP. Digital Signal Processor. F s ³ 2. F max. Error is introduced. -digital computer -dedicated dig. hw

fiona-cash
Download Presentation

Digital Telephony

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Digital Telephony Digital Telephony

  2. Analog signal Digital signal or data from -tape -simulations -digital devices Discrete signal A/D converter Analog Quantiz- er Sampler DSP D/A SP Digital Signal Processor Fs³ 2.Fmax Error is introduced -digital computer -dedicated dig. hw -programmable hw Analog signal -voltage -speech -pressure Digital signal Analog/digital systems Digital Telephony

  3. Issues • Reconstruction accuracy • Conditions for perfect reconstruction • Digital signal is not just an approx. representation of an analog signal • Could be generated digitally • The processing being performed may not be realizable in analog • The theory of discrete time signal processing is independent of continuous Digital Telephony

  4. Digital vs. analog processing • DSP implementations are flexible, programmable and modular • More precise and repeatable • Performance and cost effectiveness (riding the microelectronics wave) • Direct mapping of mathematical expressions with less approximation possible (enables sophisticated algorithms) Digital Telephony

  5. Digital vs. analog ... • Digital hardware can be multiplexed better than analog. Allows integration of multiple operations and services on a h/w platform • Digital storage is more reliable, cheaper and more compact Digital Telephony

  6. On the other hand • Analog SP still offers higher bandwidth • Higher dynamic range • Can be very low power Digital Telephony

  7. Analog to Digital Conversion • To convert “real-world” analog signals to digital signals for processing • Sampling • Quantizing and coding X [n] Xq[n] Xa(t) Quantizer and Coder Sampler Analog signal Digital signal Discrete signal Digital Telephony

  8. Sampling • Uniform • One sample every T seconds (ideally) • x[n] = xa(nT), -¥<n<+¥ • Sampling period: T • Sampling frequency: Fs=1/T • Assume: xa(t) = Acos( 2pFt+q) = Acos(W t+q) • Then: x[n] = Acos[2pFnT+q] = Acos[W Tn+q] = Acos[wn+q], where w =W T is called the normalized or discrete domain frequency Digital Telephony

  9. f = F/Fs must be rational in order for x[n] to be periodic • If f = k/N, then x[n] is periodic with period N • Now, xa(nT) = Acos(W Tn+q) = Acos((W +2pk/T)Tn+q) is periodic in W with period 2p/T • Also, x[n] = Acos[wn+q] = Acos[(w+2pk) n+q] is periodic in w with period 2p Digital Telephony

  10. ¥ xs(t) = å xa(nT)d(t- nT) xa(t) convert to discrete sequence n=-¥ ´ x[n] = xa(nT) ¥ S(t) = åd(t- nT) n=-¥ Digital Telephony

  11. 1 2p 2p T 1 T • Let us look at the continuous time Fourier transform of xs(t) Xs(jW) = Xa(jW) * S(jW) S(jW) = å d(W-kWs) Xs(jW) = å Xa(jW -kjWs) ¥ k=-¥ ¥ k=-¥ Digital Telephony

  12. Thus, Xa(jW) must be bandwidth limited • If the max frequency in Xa(jW) is WN, then the sampling rate Ws³2WNensures no information is lost due to aliasing • This sampling rate is known as Nyquist rate • A lower sampling rate causes a distortion of the signal due to Aliasing • If no Aliasing occurs, the signal can be perfectly reconstructed by passing through an ideal low pass filter with Digital Telephony

  13. Xs(jW) Ws>2WN Reconstruction Hr(jW) Xr(jW) = Hr(jW) Xs(jW) if WN< Wc< (Ws-WN) then Xr(jW) = Xc(jW) -Wc Wc Digital Telephony

  14. Frequency response of ideal reconstruction filter T -Wc Wc Reconstruction Hr(jW) = { T, Wc<W£Wc 0, otherwise Impulse response of ideal reconstruction filter sin pt/T hr(t)= pt/T Digital Telephony

  15. Reconstruction • Xr(jW) = Hr(jW) Xs(jW) • xr(t) = xs(t) * hr(t) = [åk=-¥xa(kT) d(t-kT)] * hr(t) = åk=-¥xa(kT) hr(t-kT) = åk=-¥xa(kT) ¥ ¥ ¥ sin p(t-nT)/T p(t-nT)/T Digital Telephony

  16. xa(t) xs(t) hr(t) xr(t) Digital Telephony

  17. sin pt/T hr(t)= pt/T Sampling theorem • If the highest frequency contained in a signal xa(t) is W0 and the signal is uniformly sampled at a rate Ws³2W0, then xa(t) can be exactly recovered from its sample values using the interpolation function and then xa(t) = åk=-¥xa(kT) hr(t-kT), where {xa(kT) } are the samples of xa(t), and T=2p/Ws ¥ Digital Telephony

  18. Quantization and coding • Quantization: • Converting discrete time signal to digital • xq(n) =Q [x(n)] D Quantization step Digital Telephony

  19. Q(x) 3D 2D D -D/2 x -3D/2 -5D/2 -7D/2 7D/2 -D 3D/2 D/2 5D/2 -2D -3D -4D Digital Telephony

  20. Quantization • Rounding: Assign x[n] to the closest quantization level • Quantization error eq[n] = xq[n] - x[n] -D/2 £ eq[n] £ D/2 Uniformly distributed • mean = 0 • variance = D2/12 Digital Telephony

  21. Quantization • Range of quantizer: xmax-xmin • Quantization levels: m • Assuming uniform quantization D = = 2Xm/ (m-1) where Xm = (xmax-xmin)/2 is called the full-scale level of the A/D converter xmax-xmin m-1 Digital Telephony

  22. Coding • Coding is the process of assigning a unique binary number to each quantization level • Number of bits required ³ log2m • Alternatively, given b+1 bits D = (xmax-xmin)/2b+1 =Xm /2b • For A/D devices, the higher Fsand m, the less the error (and the more the cost of the device) Digital Telephony

  23. xq(n) x(n) Quantizer xq(n) x(n) + • Assuming dynamic range of A/D converter is larger than signal amplitude • SNR = 10 log10(sx/se) = 10 log10(sx/(D2/12)) = 10 log10(12.22bsx/(Xm)) =6.02b +10.8 + 20 log10(Xm/sx) eq(n) 2 2 2 2 2 Digital Telephony

  24. Uniformly Encoded PCM Number of bits per sample 13 80 12 11 10 60 9 Signal to Quantiiation Noise Ratio (dB) 8 40 20 dB 0 -40 -30 -20 -10 X/Xm Digital Telephony

  25. Example • What is the minimum bit rate that a uniform PCM encoder must provide to encode a high fidelity audio signal with a dynamic range of 40 dB? Assume the fidelity requirements dictate passage of a 20-kHz bandwidth with a minimum signal-to-noise ratio of 50 dB. For simplicity, assume sinusoidal input signals. Digital Telephony

  26. Companding • Companded PCM with analog compression and expansion Compressed Digital Codewords Output Signal Input Signal A/D D/A Linear PCM Encoder Linear PCM Decoder Compression Expansion Digital Telephony

  27. Segment Approximation Uniform quantization 111 110 101 Codewords 100 011 010 001 000 Input Sample Values Digital Telephony

  28. T1 Channel Bank 1 A/D 2 T1 transmission Line D/A Analog Inputs 24 • Eigth bits per PCM code word • companding functions with mu=255 Digital Telephony

  29. Performance of a m255 Encoder Signal-to-quantization noise ratio (dB) 40 Piecewise linear 8 bit m 255 33 27 30 22 8 bit m 255 20 7 bit m 100 10 -70 -60 -50 -40 -30 -20 -10 0 3 dB Signal Power of sinewave (dBm0) Digital Telephony

  30. Signal-to-total noise noise ratio 40 30 dB required for good communication 30 40 dB range of possible signals 20 10 -60 -50 -40 -30 -20 -10 0 3 dB Total Noise Power 15 dB at which persons find communication difficult -70 Signal Power relative to full-load signal (dBm0) Digital Telephony

  31. Error Performance • Fewer than 10% of 1 min intervals to have BER worse than 10E-6 • Fewer than 0.2% of 1 sec intervals to have BER worse than 10E-3 • 92% error free sec Digital Telephony

  32. DS1 Signal Format • (8x24)+1=193 bits in 125 ms • 193 x 8000 = 1.544 Mbs • Bit “robbing” technique used on each sixth frame to provide signaling information Digital Telephony

  33. Plesiochronous Transmission Rates Japanese Standard North America Standard European Standard 97728 kbits/s 564992 kbits/s x4 x4 97728 kbits/s 274176 kbits/s 139264 kbits/s x4 x3 x6 x3 34368 kbits/s 32064 kbits/s 44736 kbits/s x4 x5 x7 8448 kbits/s 6312 kbits/s x3 x4 x4 2048 kbits/s 1544 kbits/s x30 x24 64 kbits/s Digital Telephony

  34. Plesiochronous Digital Hierarchy Digital Telephony

  35. Digital Telephony

  36. Plesiochronous Digital Hierarchy • The output of the M12 multiplexer is operating 136 kbs faster than the agragate rate of four DS1 6.312 vs 4x1.544=6.176 • M12 frame has 1176 bits, i.e. 294-bit subframes ; each subframe is made of up of 49-bits blocks; each block starts with a control bit followed by a 4x12 info bits from four DS1 channels Digital Telephony

  37. Makeup of a DS2 Frame • 4 M bits (O11X X=0 alarm) • C=000,111 bit stuffing present/absent • nominal stuffing rate 1796 bps, max 5367 M1 01 02 03 04 C1 01 02 03 04 F0 01 02 03 04 C2 01 02 03 04 C3 01 02 03 04 F1 01 02 03 04 Bit stuffing M1 01 02 03 04 C1 01 02 03 04 F0 01 02 03 04 C2 01 02 03 04 C3 01 02 03 04 F1 01 02 03 04 Digital Telephony

  38. Regenerative Repeaters Amplifier Equalizer Regenerator Output Input Timing recovery • Spacing between adjacent repeaters Digital Telephony

  39. Digital Transmission Systems Digital Telephony

  40. PCM System Enhancements • North America • Superframe of 12 DS0’s has a sync sequence 101010 for odd (001110 for even frames) • Extended superframe • 24 frames - (4 S bits for frame allignment signal); 6 S bits for CRC-6 check; the rest 12 constitute 4 kbs data link Digital Telephony

More Related