### Analogue to Digital Conversion (PCM and DM)

```Analogue to Digital Conversion
(PCM and DM)
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The advantages offered by digital modulation

Performance
Digital pulse modulation permits the use of regenerative repeaters, when placed
along the transmission path at short enough distances, can practically eliminate
the degrading effects of channel noise and signal distortion.

Ruggedness
A digital communication system can be designed to withstand the effects of channel
noise and signal distortion

Reliability
Can be made highly reliable by exploiting powerful error-control coding techniques.

Security
Can be made highly secure by exploiting powerful encryption algorithms

Efficiency
Inherently more efficient than analogue communication system in the trade-off
between transmission bandwidth and signal-to-noise ratio

System integration
To integrate digitized analogue signals with digital computer data
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Digitizing Analogue Data
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Pulse Code Modulation (PCM)


The simplest technique for transforming analogue data into
digital signals is pulse code modulation (PCM).
sampling theorem:
 “If a signal is sampled at regular intervals at a rate
higher than twice the highest signal frequency, the
samples contain all information in original signal”


strictly have analog samples


eg. 4000Hz voice message, requires 8000 samples per
second
Pulse Amplitude Modulation (PAM)
assign each a digital value
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Figure Components of PCM encoder
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Figure Three different sampling methods for PCM
Sampling called pulse amplitude modulation (PAM), the result is still analogue
signal with non-integral value.
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Figure Nyquist sampling rate for low-pass and bandpass signals
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Example
For an intuitive example of the Nyquist theorem, let us
sample a simple sine wave at three sampling rates: fs = 4f
(2 times the Nyquist rate), fs = 2f (Nyquist rate), and
fs = f (one-half the Nyquist rate). Figure 4.24 shows the
sampling and the subsequent recovery of the signal.
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PCM Block Diagram
Quantisation


The results of sampling is a set of
amplitude which can be infinite of nonintegral values between two limits Vmin
and Vmax.
Divide the range into L steps, each of
height Δ
Vmax  Vmin


L
We approximate the sampled value to the
quantised value (midpoint) (quantisation
error)
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Figure 4.26 Quantization and encoding of a sampled signal
Δ=[20V-(-20V)]/8 = 5V
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Quantisation level L,
depends on the range of the amplitudes and how accurately
we need. L= 2n, audio communication , L=256. less L more
quantisation error.
Quantisation error:
Quantisation is a approximation process. –Δ/2 ≤ error ≤ Δ/2
The contribution of the Quantisation error to the SNRdB of the
signal depends on the number of the quantisation level L, or
the bits per sample nb. nb = log2 L
signal to quantisation error (or noise) ratio
SNRdb = 6.02nb + 1.76 dB
Each additional bit used for quantizing increases
SNR by about 6 dB, which is a factor of 4.
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Example
What is the SNRdB in the example of Figure 4.26?
Solution
We can use the formula to find the quantization SNR. We
have eight levels and 3 bits per sample, so
SNRdB = 6.02×(3) + 1.76 = 19.82 dB
Increasing the number of levels increases the SNR.
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Encoding
Each quantised value can be coded to an nb bit code
word.
Bit rate = sampling rate × number of bit per sample
= fs × nb = fs × log2L
We want to digitize the human voice. What is the bit rate,
assuming 8 bits per sample?
The human voice normally contains frequencies from 0 to 4000
Hz. So the sampling rate and bit rate are calculated as follows:
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PCM bandwidth
The minimum bandwidth of a PCM signal
Bmin = nb × B analogue
We have a low-pass analog signal of 4 kHz. If we send the analog
signal, we need a channel with a minimum bandwidth of 4 kHz. If
we digitize the signal and send 8 bits per sample, we need a
channel with a minimum bandwidth of 8 × 4 kHz = 32 kHz.
Maximum data rate of a channel
Rmax = 2 × B × log2L
Minimum required bandwidth
R
Bmin 
2  log2 L
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Delta Modulation (DM)



PCM finds value of amplitude of each sample;
DM finds the change from the previous sample.
function
 can move up or down one level (Δ) at each
sample interval
has binary behavior
 function only moves up or down at each
sample interval
 hence can encode each sample as single bit
1 for up or 0 for down
Figure The process of delta modulation
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Figure Delta modulation and demodulation components
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PCM verses Delta Modulation


DM has simplicity compared to PCM but
has worse SNR
issue of bandwidth used

for good voice reproduction with PCM:




data compression can improve on this
still growing demand for digital signals


want 128 levels (7 bit) & voice bandwidth 4khz
need 8000 x 7 = 56kbps
use of repeaters, TDM, efficient switching
PCM preferred to DM for analog signals
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