Introduction to Digital communication systems

1. Digital Communication Systems
Syed Ahmed Faran

2. Naturally analog or naturally digital
signal?
Hello
Salma!

3. Analog and digital

4. Analog to digital
• ADC (analog to digital convertor)
• ADC provide digitized data for digital processing
and transmission.

5. Sampling
• Essentially, ACD performs ‘sampling’.
• Sampling is multiplication of a message with a
sampling function.
• We will study 3 different kinds of sampling.

6. But first…
Remember?
Note:
•Fourier transform of a periodic function is always impulses.
•Convolution of a function f1 with an impulse function f2 results in shifting
spectrum of f1 to fundamental frequency of f2 (and integer multiples of
fundamental frequency).

7. 1. Natural sampling (gating)
xs(t)=x(t)xp(t)

8. 2. Impulse sampling (ideal sampling)
xs(t)=x(t)xp(t)

9. 3. Sample and hold (flat-top sampling)
xs(t)=p(t)
*[x(t)xδ(t)]
x(t)
p(t)
xs(t)
x(t)xδ(t)

10. Sampling theorem:
• A bandlimited signal having fc Hertz as highest
frequency component should be sampled at
uniform intervals Ts so that it can be uniquely
reconstructed, where:
• Or, sampling rate should be:
• This rate is known as Nyquist rate and the
criterion is called Nyquist criterion.

11. Why at least Nyquist rate?
• Consider again:
• What if ?