D R . T A R E K T U T U N J I

P H I L A D E L P H I A U N I V E R S I T Y , J O R D A N

2 0 1 4

Analog to Digital Conversion

Digital Signal Processing

Analog to Digital Conversion

Sampling

The Conversion of a continuous-time signal into a discrete-time signal obtained by taking samples of the continuous-time signal at discrete-time instants

Quantization

The conversion of a discrete-time continuous-valued signal into a discrete-time, discrete-valued signal (i.e. digital signal)

Coding

Each discrete value is represented by a binary sequence

Ideal Sampler

Sample-and-Hold

Sampling

Sampling Example

Nyquist-Shannon Theorem

Sinusoidal Example: Sampling

Suppose x(t) = 5 cos (2pft) where f=10KHz

Find the discrete-time signal x(n) when sampling frequency is

fs = 50 KHz

fs = 100 KHz

Aliasing

Aliasing refers to an effect that causes different signals to become indistinguishable (or aliases of one another) when sampled.

Anti Aliasing Filter

An anti-aliasing filter is a filter used before a signal sampler, to restrict the bandwidth of a signal to approximately satisfy the sampling theorem

Analog to Digital Conversion

Quantization

• Rounding vs. Truncation

A/D Converter

Example

Sinusoidal Example: Quantization

Recall the signal x(t) = 5 cos (2pft) where f=10KHz

The sampled signal x(n) with fs =100 KHz was provided: [5, 4.05, 1.55, -1.55, -4.05, -5, -4.05, -1.55, 1.55, 4.05]

8-level quantization is used with range of 10 volts

Draw the xQ(n) signal

Provide the coding result

D/A Conversion

Zero-Order-Hold

Basic Components of DSP Systems

1. A lowpass analog antialiasing pre-filter that bandlimits the signal to be sampled to within the Nyquist interval.

2. An A/D converter (sampler and quantizer).

3. A digital signal processor.

4. A D/A converter (staircase reconstructor), possibly preceded by an equalizing digital filter.

5. A lowpass analog anti-image postfilter to complete the job of the staircase reconstructor and further remove the spectral images introduced by the sampling process.

Data Acquisition Systems

Conclusion

Analog to Digital operation involves the following stages: Sampling

Quantization

Coding

The sampling frequency should be at least larger than two times maximum frequency in the signals

Digital to Analog operation tries to reconstruct the analog signal using ZOH

References

Chapter 7. Signals and Systems using MATLAB by Luis Chaparro. Elsevier Publisher 2011.

Chapter 1 and 2. Introduction to Signal Processing by Sophacles Orfanidis 2010.