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Analog to Digital Conversion Guide

This document provides an overview of advanced digital systems, beginning with an introduction to analog and discrete-time signals. It describes how continuous analog signals can be converted to discrete digital signals using analog-to-digital conversion. This involves sampling the analog signal, quantizing it, and encoding it into a digital format. The Nyquist-Shannon sampling theorem states that a signal must be sampled at least twice as fast as its highest frequency to perfectly reconstruct the original signal. The document provides examples of sampling rates for different types of signals and explores representations of discrete-time signals including time shifting, reflection, and scaling. It also covers periodic, even, odd, unit impulse, and unit step signals.

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20 views30 pages

Analog to Digital Conversion Guide

This document provides an overview of advanced digital systems, beginning with an introduction to analog and discrete-time signals. It describes how continuous analog signals can be converted to discrete digital signals using analog-to-digital conversion. This involves sampling the analog signal, quantizing it, and encoding it into a digital format. The Nyquist-Shannon sampling theorem states that a signal must be sampled at least twice as fast as its highest frequency to perfectly reconstruct the original signal. The document provides examples of sampling rates for different types of signals and explores representations of discrete-time signals including time shifting, reflection, and scaling. It also covers periodic, even, odd, unit impulse, and unit step signals.

Uploaded by

sama abd elgelil
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Advanced

Digital Systems

Dr. Sahar Hamed


Outline
• Introduction
• Analog to Digital Conversion
• Nyquist–Shannon Sampling Theorem
• Continuous Time and Discrete Time Signals
Introduction

Continuous-Time Signal
X(t)

is defined for all time t contained in some interval on


the real line.

Discrete-Time Signal
X[n]

a sequence of values that correspond to particular


instants in time.
Examples of Continuous &
Discrete-Time Signals
Most of the signals are analog in nature:
• Voice
• Video
• Transducer/Sensor output

Examples of Discrete-Time Signals:


• Average budget
• Crime rate
• Total population
Analog Signals Vs Digital Signals
Analog Digital
• Analog signals are of much higher •Digital signal processing is more secure
density and can present more accurate because digital information can be easily
information. encrypted and compressed.
• Analog signals provide a more accurate • Digital signals can be transmitted over
representation of changes in physical long distances.
phenomena, such as sound, light,
temperature, position, or pressure.

• Analog signals are subject to noise and • Digital systems and processing are
distortion. typically more complex and consume
higher power dissipation.
Analog to Digital Conversion

Analog Analog
input output
Signal x(t) Signal y(t)
A/D Digital D/A
converter Signal Processor converter

Digital Signal Processing


Analog to Digital Conversion

A/D conversion can be viewed as a three-step process

7
Analog to Digital Conversion
• Sampling: Convert the continuous time & value signal to discrete-time &
continuous value signal.

Quantization: Convert the discrete-time & continuous value signal to


discrete-time & value signal

Coding: Convert the discrete-time & value signal to a digital data format

8
Different sampling rate

9
Nyquist–Shannon Sampling Theorem

• If an analog signal is sampled at a rate that exceeds the


signal’s highest frequency by at least a factor of two,
the original analog signal can be perfectly recovered
from the discrete values produced by sampling.

𝑓𝑠 ≥ 2𝑓𝑚𝑎𝑥

10
The sampling rate
• The sampling rate

• If a signal is sampled at T = 1mS,


the sampling rate will be fs = 1/1m = 1KHZ
(i.e., 1000 samples per second)

11
Example
What is the sampling rate for a voice signal that has
frequencies up to 3KHZ?

Fs = 2 * 3000 = 6000samples/sec (HZ)

What is the sampling rate for a sound that has


frequencies up to 30KHZ?

Fs = 2 * 30000 = 60000samples/sec (HZ)


12
Test your understanding
Determine the Nyquist sampling rate of the signal.

1. X(t) = 3 Sin (5000π + 17)


2. S(t) = 3Cos (50πt) + 10 Sin (300πt) – Cos (100πt)

13
Signal Representation
Continuous time signal
Signal Representation
Discrete time signal

X[n]
Discrete Time Signal – Time Shifting
Discrete Time Signal – Reflection
Discrete Time Signal – Time Scaling
Exponential Signals
𝑥 𝑛 = 𝐴 ∝𝑛
Test Your Understanding

Plot x[n] & determine y[n]


Periodic Signals
For a continuous time signal: The signal is said
to be periodic if x(t) = x(t+T)
Periodic Signals

For a discrete time signal: The signal is said to


be periodic if x[n] = x[n+N]
Even & Odd Signal
X(-t) = X(t)

X[-n]=X[n]

X(-t) = -X(t)

X[-n]= -X[n]
Even & Odd decomposition of
discrete time signals

Any signal can be broken into a sum of


two signals: Odd & Even
Discrete-Time Unit Impulse
Discrete-Time Unit Step
Relation between
Unit Impulse & Unit Step
Reading List
• Signals & Systems, Allan Oppenheim & Allan Wilsky
Chapter 1
Thank You

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