Pulse Code Modulation. Lesson 16. BME 333 Biomedical Signals and Systems - J.Schesser

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1 Pulse Code Modulation Lesson 16 10

2 How do we send the samples of f(t) Do we send the actual values of each sample? This method is susceptible to noise Do we convert the actual values of each sample into a binary digit and then transmit the samples as a binary stream? Yes but? How accurate, how precise, and how many bits (decimal places of the sample) do we use? We use predefined levels and choose the level closest to the signal. This is called Pulse Code Modulation Example: 8 levels needs 3 bits; 16 levels needs 4 bits, etc. However we now have a new kind of distortion: Quantization Error. 11

3 Pulse Code Modulation Actual Code Binary-Coded Bit Slot Time Slot 12

4 Shannon s Sampling Theory Channel Capacity C = Channel Capacity B = Channel Bandwidth L = Quantization Levels C = 2 B log 2 (L) C = log 2 (8) = 18, 000bps 13

5 Quantization Error Actual Code Binary-Coded Absolute Error % Error -6.26% % 4.93% -7.29% -1.48% Time Slot Bit Slot 14

6 Signal-to-Noise Ratio P P signal noise SNR SNR SNR SNR = = db db db = ( A X 1 R P P signal noise L ( A X 1 R noise L S ) = 2 ( X ) s ( X ) P P noise = 10log( SNR) 2 = 10log ) 2 signal noise X = 20log X s noise 2 Σ A X 1 s + + X noise X o R L 15

7 C = Channel Capacity B = Channel Bandwidth SNR = Signal to Noise Ratio Shannon s Sampling Theory Channel Capacity in Noise Shannon s Limit C = B log 2 (1+ SNR) C = 3000 log 2 (1+1000) = 29, bps SNR db = 10 log 10 (SNR) SNR db 10 SNR = 10 SNR db C = B log 2 ( ) C = 1000 log 2 (1+10 ) = 29, bps 16

8 A PCM System Analog-to-digital converter Sampler Quantizer Encoder Digital Encoded Signal Samples of Quantized m(t) Analog signal m(t) Analog samples PCM Quantizer* Decoder LP Filter Digital-to-analog converter Some Bit Rates: Digital encoded Signal transmitted over a communications channel Voice: 4kHz BL Spectrum =4x10 3 x 2 samples/sec x 8 bits/sample =64kbits/sec Reconstructed m(t) with possible quantization errors * To remove the digital signal from any noise on the communications channel Video: 4MHz BL Spectrum=4x10 6 x2x8 = 64Mb/s 17

9 Examples of PCM Digital Recording Audio CDs - 2 channel Stereo DVDs - 6/7 channel surround sound MP3 Video DVDs Telecommunications Modern optical telecommunications SONET/SDH Basic SDH signal/frame 9 rows X 270 columns = 2430 bytes 9 rows X 9 columns = 81 bytes for overhead (line and equipment health, administration, timing, etc.) 9 rows X 261 columns = 2349 bytes for payload 2430 bytes x 8000 samples/second (based on telephony of 4kHz BL signal) x 8 bits/byte = line rate of Mb/s STS-3/STM bytes for payload x 8000 s/s x 8 bits/byte = Mb/s ATM Asynchronous Transfer Method Etc. 18

10 Examples of PCM Capacities Requirements Voice: 4k Hz x 2 = 8000 samples/s x 8 bits (256 levels) = 64 kbits/s Video: 4M Hz x 2 = 8,000,000 samples/s x 8 bits = 64 Mb/s SONET/SDH payload capacities: kbit channels in a payload of an STM-1 (301 channels can also be used for overhead) = M bits Cable TV supports 300 video channels = 19.2 Gigabits/s STM-64 = 9.9 Gigabits Need to use compression schemes to reduce the size of a video channel. 19

11 Angle Coding Modulation Phase-shift Keying (PSK) send out a signal y(t)=acos[ω o t+fϕ(t)] where f(t) = π for a one f(t) = -π for a zero Frequency-shift Keying (FSK) send out a signal y(t)=acos(ω o ± Ω)t where + Ω for a one - Ω for a zero 20

12 Homework Problem (1) A BL signal with maximum frequency 1000 Hz is sampled at the Nyquist rate of 2000 samples per second. It is then quantized to 8 levels. What is the bit rate of the coded signal? Repeat for 16 levels and 256 levels. Problem (2) 20 BL signals (1000 Hz) are sampled at the Nyquist Rate and then quantized to 16 levels. Calculate the pulse width of each bit to support the multiplex of these 20 signals. Calculate the bit rate. Repeat for 200 signals. Problem (3) Consider N signals, each BL (1 Hz) and is quantized to 16 levels. If a transmission system can handle 40 bits per second, how many messages can be sent? Repeat for 10Mbps. Problem (4) Consider a BL signal with maximum frequency 1000 Hz is sampled at the Nyquist rate. The signal is quantized into 8 levels. The SNR db for this channel is 10db. Will this channel work? What would you have to do to make this channel work? 21

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