sampling and digital convertion

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EEL 3552C Analog and Digital Communications

Dr. Lei Wei

Chapter 6 Sampling and Analog to Digital Conversion

Why digital?

Efficient, secure, easy to control quality, cheap DSP chips, better

spectrum efficiency.

How to digitize?

Sampling and A/D conversion, which will be covered in this chapter.

First of all, let us review why digital? # Now, how to digitize analog signals? This picture

shows what we need to do?


Dr. Lei Wei


6.1 Nyquist sampling theory

Let us consider a signal in Fig. (a) and its spectrum in (b). If we multiple the impulse train

in time domain (fig (c)), in frequency domain it becomes convolution between G(f) (fig

(b)) with Dn, keeping in mind 0 should be s=1/Ts

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We can perfectly recover analogue signal if fs=1/Ts >=2B

2B is called Nyquist sampling rate.

If fs=1/Ts

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Signal recovery:

We copy the sinc function to each sampling point and then sum all signals together to recover the original analogue signal.

This is not easily to understand.


Dr. Lei Wei



Is ideal sampling implementable? No!

Is ideal filter practically implementable? No!

In practices, we use simple sampling and hold device.

Unfortunately, the ideal filter is not implementable. In practices, we use sampling and

hold device. When holding time Tp is approaching to zero, it converges to ideal

sampling. How Tp affects the sampling?

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in frequency domain, it is multiplication between the broad sinc function and ideal sampled signal. So, if Tp is very small, the effect

on the spectrum at low frequency is limited.

1/Tp


Dr. Lei Wei



In practices, we also use a pulse generator and a LPF to reconstruct

the analog signal.

Similarly, we can reconstruct the analogue using a pulse and a LPF.

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In practices, we also use a pulse generator and a LPF to reconstruct

the analog signal.

In fact, the pulse does not need to be in any regular form. Here we can draw a simple

pulse.


Dr. Lei Wei



In practices, what happen if the signal bandwidth is not limited to B?

It will cause aliasing.

In practices, #

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Aliasing problem and its effect on reconstructed signal

Taking another look at aliasing problem#


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Anti-aliasing filter is simply a bandlimited filter which forces the signal

bandwidth limited to B.

In practices, Anti-aliasing filter is #

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Other sampling method: Natural top sampling

Now let us look at other sampling methods. #


Dr. Lei Wei



Re-construction of Natural top sampled signal is similar to the ideal

sampled signal.

We can smooth the top by averaging over a period Tp. See the

following illustrate.

Different types of sampling methods can be interchanged#

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Application of Sampling theory:

(1) different pulse modulation

schemes;

PAM

PWM

PPM

(2) Time division multiplexing.

Sampling theory has many applications, #


Dr. Lei Wei



Application of Sampling theory:

(2) Time division multiplexing

Sampling at different time, can be used as TDM which is alternative to FDM method#.

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Dr. Lei Wei



Review: FDM, lecture 10, slide 7

In 1970s FDM was the key technology. See#.


Dr. Lei Wei



today: CDM, code division multiplexing

Today, many wireless systems have moved to CDMA#.

sampling and digital convertion

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