Basics DSP AV intro

1. Introduction (sampling – quantization) 2. Signals and Systems 3. ZTransform 4. The Discreet and the Fast Fourier Transform 5. Linear Filter Design 6. Noise 7. Median Filters More flexible. • Often easier system upgrade. • Data easily stored memory. • Better control over accuracy requirements. • Reproducibility. • Linear phase • No drift with time and temperature

Basics on Digital Signal Processing

Introduction

Vassilis Anastassopoulos Electronics Laboratory, Physics Department,

University of Patras

Outline of the Course

1 Introduction (sampling – quantization)

2 Signals and Systems

3 Z-Transform

4 The Discreet and the Fast Fourier Transform

5 Linear Filter Design

6 Noise

7 Median Filters

-0.2 -0.1 0 0.1 0.2 0.3

-0.1 0 0.1 0.2 0.3

Analog & digital systems

Digital vs analog processing

Digital Signal Processing (DSPing)

• More flexible

• Often easier system upgrade

• Data easily stored -memory

• Better control over accuracy

• Finite word-length effect

Limitations

DSPing: aim & tools

Software

• Programming languages: Pascal, C / C++

• “High level” languages: Matlab, Mathcad, Mathematica…

Applications

• Predicting a system’s output

• Implementing a certain processing task

• Studying a certain signal

• General purpose processors (GPP), -controllers

• Digital Signal Processors (DSP)

• Programmable logic ( PLD, FPGA )

DSPing Fast

Faster

Related areas

Applications

Important digital signals

Unit Impulse or Unit Sample The most important signal for two reasons

Digital system example

Filter Antialiasing

A/D

Digital system implementation

• Sampling rate

• Pass / stop bands

KEY DECISION POINTS:

Analysis bandwidth, Dynamic range

• No of bits Parameters

1 2 3

AD/DA Conversion – General Scheme

AD Conversion - Details

Sampling

Sampling

How fast must we sample a continuous signal to preserve its info content?

Ex: train wheels in a movie

25 frames (=samples) per second

Frequency misidentification due to low sampling frequency

Train starts wheels ‘go’ clockwise

Train accelerates wheels ‘go’ counter-clockwise

1

Why?

Rotating Disk

How fast do we have to instantly

stare at the disk if it rotates

with frequency 0.5 Hz?

The sampling theorem

A signal s(t) with maximum frequency fMAX can be

recovered if sampled at frequency fS > 2 fMAX

Condition on fS?

fS > 300 Hz

t) cos(100 π t)

π sin(300 10

t) π cos(50 3

* Multiple proposers: Whittaker(s), Nyquist, Shannon, Kotel’nikov

Nyquist frequency (rate) fN = 2 fMAX or fMAX or fS,MIN or fS,MIN/2

Naming gets

confusing !

Sampling and Spectrum

Sampling low-pass signals

(c)

(c) fS 2 B aliasing !

Aliasing: signal ambiguity

in frequency domain

into band of interest Filter it before!

Attenuation AMIN : depends on

• ADC resolution ( number of bits N)

AMIN, dB ~ 6.02 N + 1.76

• Out-of-band noise magnitude

Other parameters: ripple, stopband frequency

(c) Antialiasing filter

1

Under-sampling

1

Using spectral replications to reduce

sampling frequency fS req’ments.

m

BCf

2S

f1

m

BCf

Quantization and Coding

q

N Quantization Levels

RMS10

log20ideal

 e q uncorrelated with signal

 ADC performance constant in time

Assumptions

2 2 FSR V T

0

dt

2 ωt sin 2

FSR V T

1 input

2

FSR V 12

q q/2

q/2 -

q de q e p

2 q e )

SNR of ideal ADC - 2

[dB]

1.76 N

Actually (2) needs correction factor depending on ratio between sampling freq

& Nyquist freq Processing gain due to oversampling

- Real signals have noise

- Forcing input to full scale unwise

- Real ADCs have additional noise (aperture jitter, non-linearities etc)

Real SNR lower because:

Coding - Conventional

Coding – Flash AD

DAC process

Oversampling – Noise shaping

f b The oversampling process takes apart

the images of the signal band

f s /2

Quantization noise in Oversampling converters

When the sampling rate increases (4 times) the quantization noise spreads over a larger region The quantization noise power in the signal band is 4 times smaller

PSD

Signal

Quantization noise Nyquist converters

Quantization noise Oversampling converters

Quantization noise Oversampling and noise shaping converters Spectrum at the output of a noise

shaping quantizer loop compared to those obtained from Nyquist and

A discreet-time system is a device or algorithm

that operates on an input sequence according to

some computational procedure

Linear, Time Invariant Systems

y

0

) (

) (

Linear Systems - Convolution

5+7-1=11 terms

Linear Systems - Convolution

5+7-1=11 terms

a n

y

1 0

) (

) (

) (

General Linear Structure

Simple Examples

Linearity – Superposition – Frequency Preservation

The END

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