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Pulse Code Modulation. PCM is a method of converting an analog signal into a digital signal. (A/D conversion) The amplitude of Analog signal can take any value over a continuous range i.e. it can take on an infinite values. Digital signal amplitude can take on finite values. - PowerPoint PPT Presentation
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Pulse Code ModulationPCM is a method of converting an analog
signal into a digital signal. (A/D conversion)The amplitude of Analog signal can take any
value over a continuous range i.e. it can take on an infinite values.
Digital signal amplitude can take on finite values.
Analog signal can be converted into digital by sampling and quantizing.
Cont.
Cont.The amplitude of analog signal m(t) lie in the
range (-mp, mp) and is partitioned into L sub-intervals each of magnitude 2mp/L
Binary pulse codes
QuantizingDigital signals come from variety of sources
e.g. computerSome sources are analog but are converted
into digital form by variety of techniques such as PCM and DM
For quantizing , we limit the amplitude of m(t) to a range(-mp, mp) as shown in the previous slides
This amplitude is uniformly divided into L subintervals and each interval is ,
Cont.A sample value is approximated by the mid
point of the intervalThe quantized samples are coded and
transmitted as binary pulsesAt the receiver some pulses will be detected
incorrectlyThere are two types of errors
Quantization errorPulse detection error
Cont.In almost all practical schemes, the pulse
detection error is very small compared to the quantization error and can be ignored
Now we analyze the quantization error
Cont.
Cont.
Cont.The integral of the cross product terms is zero
and we obtain,
Because the sampling rate is 2B, hence the total number of samples over the averaging interval is 2BT
This is called the mean of the quantization error
Cont.The quantized levels are separated by 2mp/LSince sample value is approximated by the
midpoint of the subinterval in which the sample falls
The maximum quantization error is The mean square quantizing error is
Cont.
Cont.
Non-uniform quantizationSNR is an indication of the quality of the received
signalIdeally we would like to have constant SNRUnfortunately, the SNR is directly proportional to
the signal power, which varies from talker to talkerThe signal power can also vary because of the
connecting circuitsSNR vary even for the same talker, when the
person speaks softlySmaller amplitudes pre-dominate in speech and
larger amplitude much less frequent.This means the SNR will be low most of the time
Cont.The root of this difficulty is that the
quantization steps are of uniform valueThe quantization noise is directly
proportional to the square of the step size.The problem can be solved by using smaller
steps for smaller amplitudes as shown in fig. on the next slide
Cont.
Cont.The same result can be obtained by first
compressing a signal and then using uniform quantization
The input-output characteristics of compressor are shown in fig.
Cont.The horizontal axis is normalized input signal
and the vertical axis is the output signal y.The compressor maps the input signal into
larger increments Hence the interval delta(m) contains large
number of steps when m is smallThe quantization noise is small for smaller input
signalThus loud talker and stronger signals are
penalized with higher noise steps in order to compensate the soft talker and weak signals
Compression LawsThere are two laws regarding compressions(1)This law is used in North America and Japan
(2) A-LawThis law is used in Europe and the rest of the
word
Cont.The compressed samples are restored to their
original values at receiver by using an expanderThe compressor and expander together are
called compandor.Compression of a signal increases its bandwidth
but in PCM, we are not compressing the signal but its samples the number of samples does not change, therefore bandwidth does not rise
When meu-law compandor is used then output SNR is
Transmission BW and output SNRFor binary PCM, we assign distinct group of
n binary digits to each of the L quantization levels
Each quantized level is encoded into n-bitsMinimum channel BW isThis is the theoretical minimum transmission
bandwidth required to transmit the PCM signal
Example 6.2A signal m(t) band-limited to 3kHz is sampled
at a rate 33.33% higher than Nyquist rate, a maximum acceptable error in the sample amplitude is 0.5% of the peak amplitude. The quantized samples are binary coded. Find the minimum channel BW required to transmit the coded signal. If 24 such channels are time-division multiplexed, determine the minimum transmission BW required to transmit the multiplexed signal
Solution
Exponential Increase of output SNR
SNR in decibel scale
Cont.
Example 6.3
Comments on Logarithmic UnitsVery small and very large values are
expressed in logarithmic units
T1 carrier systemA schematic of T1-system is shown in fig.
Cont.
Cont.
Differential Pulse Code Modulation
Taylor's series
Cont.
Analysis of DPCM
Cont.
Delta Modulation
Cont.
Cont.
Delta Modulator
Delta Demodulator
Delta Modulator output
Working of DM