analog to digital conversion. ( pcm ,dm with short descriptions )

1. ANALOG-TO-DIGITAL
CONVERSION
By
Md. Fazle Rabbi
16CSE057

2. 4.2
ANALOG-TO-DIGITAL CONVERSION

3. 4.3
 Pulse Code Modulation (PCM)
 Delta Modulation (DM)
• To change an analog signal to digital data we use two techniques,
ANALOG-TO-DIGITAL CONVERSION

4. 4.4
Pulse Code Modulation (PCM)

5. 4.5
PCM

6. 4.6
Figure 1 Components of PCM encoder

7. 4.7
Sampling
• Analog signal is sampled every TS secs.
• Ts is referred to as the sampling interval.
• fs = 1/Ts is called the sampling rate or sampling frequency.
• There are 3 sampling methods:
• Ideal - an impulse at each sampling instant
• Natural - a pulse of short width with varying amplitude
• Flattop - sample and hold, like natural but with single amplitude
value
• The process is referred to as pulse amplitude modulation
PAM and the outcome is a signal with analog (non
integer) values

8. 4.8
Figure 2 Three different sampling methods for PCM

9. 4.9
According to the Nyquist theorem, the
sampling rate must be
at least 2 times the highest frequency
contained in the signal.
Nyquist theorem

10. 4.10
Figure 3 Nyquist sampling rate for low-pass and bandpass signals

11. 4.11
Figure 4 Recovery of a sampled sine wave for different sampling rates

12. 4.12
Quantization

13. 4.13
Steps of Quantization

14. 4.14
Figure 5 Quantization and encoding of a sampled signal

15. 4.15
Quantization Levels
• The midpoint of each zone is assigned a value from
0 to L-1 (resulting in L values)
• Each sample falling in a zone is then approximated
to the value of the midpoint.

16. 4.16
Quantization Error
• When a signal is quantized, we introduce an error -
the coded signal is an approximation of the actual
amplitude value.
• The difference between actual and coded value
(midpoint) is referred to as the quantization error.
• The more zones, the smaller  which results in
smaller errors.
• BUT, the more zones the more bits required to
encode the samples -> higher bit rate

17. 4.17
Encoding
• The last step in PCM is encoding.
• If the number of quantization levels is L, the number
of bits is nb=log2 L.
• The bit rate can be found from the formula.
Bitrate = Sampling rate X Number of bites per
sample= ƒs X nb

18. 4.18
Encoding
• Bmin = c x N x 1/r
= c x ƒs X nb x 1/r
= 0.5 x ƒs X nb x 1/r
= c x ƒs X nb

19. 4.19
Find the Transmission of a low pass analog signal
using PCM

20. 4.20
Delta Modulation

21. 4.21
Delta Modulation
• This scheme sends only the difference between
pulses, if the pulse at time tn+1 is higher in
amplitude value than the pulse at time tn, then a
single bit, say a “1”, is used to indicate the positive
value.
• If the pulse is lower in value, resulting in a negative
value, a “0” is used.
• This scheme works well for small changes in signal
values between samples.
• If changes in amplitude are large, this will result in
large errors.

22. 4.22
Figure 6 Delta modulation components

23. 4.23
Figure 7 The process of delta modulation

24. 4.24
Thank you