Analog Digital -H Yani komeroglu

1. 1
INFORMATION: ANALOG AND DIGITAL
David Falconer & Halim Yanikomeroglu
Dept. of Systems and Computer Engineering
Carleton University

2. 2
Topics to be Covered
 Analog (continuous time, continuous amplitude) signals
 Analog to digital: PCM (pulse code modulation)
 Digital transmission

3. 3
Analog Signals
Analog (continuous-time, continuous-amplitude) signals (like
speech) have a certain bandwidth. Their power spectrum (power
spectral density) describes how their average power is
distributed with respect to frequency.
Power
spectral
density
(watts/Hz)
0 1 2 3 4 5 6 7....
“High-fidelity speech
Telephone speech
(limited by filtering)
Bandwidth

4. 4
Digital and Analog Signals
Some signals (like speech and video) are inherently analog; some
(like computer data) are inherently digital.
However both analog and digital signals can be represented and
transmitted digitally.
Advantages of digital:
» Reduced sensitivity to line noise, temp. drift, etc.
» Lower maintenance costs than analog.
» Low cost digital VLSI for switching and transmission.
» Uniformity in carrying voice, data, video, fax, etc.
» Better encryption.

5. 5
Pulse Code Modulation (PCM)
Key points
» PCM signal is developed by three steps: sampling, quantizing and
encoding.
» Quantizing noise is reduced by using variable sized steps. It is independent
of line length.
s(t) s(n)
Sample at t=n Quantize Encode
011010001...
Filter

6. 6
Sampling an Analog Signal
Sampling theorem: The original analog signal can be reconstructed if it is
sampled at a rate at least twice its bandwidth.
Reconstruction is by filtering samples with a low pass filter.
Sampling Samples Reconstruction

7. 7
Standard PCM in Wired Telephony
Voice circuit bandwidth is 3400 Hz.
Sampling rate is 8 KHz (samples are 125 s apart).
Each sample is quantized to one of 256 levels.
Each quantized sample is coded into a 8-bit word.
The 8-bit words are transmitted serially (one bit at a time) over a
digital transmission channel. The bit rate is 8x8,000 = 64 Kb/s.
The bits are regenerated at digital repeaters.
The received words are decoded back to quantized samples, and
filtered to reconstruct the analog signal.

8. 8
Quantization
Uniform Nonuniform
Input signal Input signal
Output signal Output signal
The more steps (levels) the less quantization noise. Nonuniform quantization
(e.g. -law) allows a larger dynamic range (important for speech).

9. 9
-Law Quantization and Coding
Standardized in North America.
Based on a logarithmic non-uniform quantizer.
Range of amplitudes divided into 8 segments, each segment with
16 uniformly spaced levels. Segment i is double the width of
segment i-1.
8 bit word: 1 bit for sign, 3 bits identify segment, 4 bits identify level
within segment.
Can show for n-bit word, signal to quantization noise ratio is
approximately 6n-10 [dB]; e.g., 38 dB for n=8 bits.
Most of the rest of the world uses a related logarithmic non-
uniformity, called A-law.

10. 10
1 2 3 4 24
1 2 3 4 5 6 7 8
S bit
24 PCM code words, each representing 1 sample
8 bits per code word
193 bits in 125 s
(1.544 Mb/s)
DS1 Format (-Law Countries)

11. 11
Adaptive Differential PCM (ADPCM)
Allows coding with a lower bit rate (with same fidelity) for speech,
based on predicting the next sample; e.g., 8 or 16 or 32 Kb/s.
More circuits accommodated in the same transmission bandwidth.
Quant.
Predictor
Predictor
+
+ +
Coder: Decoder:

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Regenerative Repeater
Regenerative
repeater
Regenerative
repeater
Amplifier/
equalizer
Regenerator
Timing circuit
Structure of a regenerative
repeater:
By appropriate repeater design and inter-repeater spacing, the effect of
occasional bit errors due to noise can be controlled. Received signal quality is
essentially independent of distance.

13. 13
PCM Transmission Formats and Spectra
..... 1 0 1 1 .......

Time Frequency
0 T 2T 3T -4/T -1/ -2/T -1/T 0 1/T 2/T 1/ 4/T
0 T 2T 3T 4T -3/T -2/T -1/T 0 1/T 2/T 3/T
0 T 2T 3T 4T -4/T -2/T -1/T 0 1/T 2/T 4/T
0 T 2T 3T 4T -1/2T 1/2T
Min. bandwidth
Unipolar RZ
Unipolar NRZ
Bipolar NRZ
Bandlimited
Power spectra

14. 14
Multilevel Transmission
1 0 1 1 0 0 0 1
0 T 2T 3T 4T
Binary:
L=2
4-level:
L=4
Bit rate =
1
T
log2 L
Bandwidth proportional to 1/T for NRZ signals

15. 15
Bandwidth Required for Digital Transmission
 required bandwidth is approximately
(bit rate)/(log2L) for L-level transmission.
 more levels  less bandwidth, but greater sensitivity to noise.
 Examples:
» 64 Kb/s PCM requires about 64 KHz for binary transmission, 32 KHz for 4-
level transmission.
» 14.4 Kb/s modem uses a symbol rate 1/T=2400 Hz, and the equivalent of
L=32.

16. 16
Channel Capacity
Shannon channel capacity formula:
» Highest possible transmission bit rate R, for reliable communication in a
given bandwidth W Hz, with given signal to noise ratio, SNR, is
R=Wlog2(1+SNR) bits/s
R/W = 0.332 SNR [dB] bits/s/Hz (for high SNR)
» Assumptions and qualifications:
– Gaussian distributed noise added to the signal by the channel, highly complex
modulation, coding and decoding methods.
– In typical practical situations, the above formula may be roughly modified by
dividing SNR by a factor of about 5 to 10.

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Summary
 All information signals can be represented, switched, stored and
transmitted digitally.
 We have discussed PCM systems and their key elements:
» sampling
» quantizing
» coding
» digital transmission
 We have discussed the related concepts of:
» the telephone set
» bandwidth
» the sampling theorem
» signal to quantization noise ratio
» channel capacity.

18. 18
More Information
R. Haughton, “The Telecommunications Mosaic”, Vol. 2, (sections II.1, II.2, II.3, II.4),
Vol. 3, (sections I.1, I.2, I.3, I.4)
E.B. Carne, “Telecommunications Primer”, Prentice-Hall, 1995, Chapters 2,3,4.
R.L. Freeman, “Telecommunications System Engineering”, (2nd ed.), Wiley, 1989.
Chapter 9.
J. Sklar, “Digital Communications”, Chapters 2 and 7