Neuronal Computation Using High Order Statistics

Report
DCSP-1: Introduction
Jianfeng Feng
DCSP-1: Introduction
Jianfeng Feng
Office: CS313
[email protected]
DCSP-1: Introduction
Jianfeng Feng
Office: CS313
[email protected]
http://www.dcs.warwick.ac.uk/~feng/dcsp.html
Time
• Tuesday
11.00 –- 12.00
• Wednesday 12.00 — 1.00
• Thursday
10.00 -- 11.00
From this week, seminar starts
Tian GE
room S0.20
room S0.17
room CS101
Announcement for Seminars
DCSP seminars (to cover DCSP tutorial
problems) start in Week 2 (this week).
Assignment
The DSP assignment coursework will be
issued in Week 4
The coursework is worth 20% of the module
assessment and the submission
deadline
is 12 noon on Thursday Week 10 (i.e., 15th March 2011).
References
• Any good book about digital communications
and digital signal processing
References
• Any good book about digital communications
and digital signal processing
• Wikipedia, the free encyclopedia
References
• Any good book about digital communications
and digital signal processing
• Wikipedia, the free encyclopedia
• Lecture notes is available at
http://www.dcs.warwick.ac.uk/~feng/teaching/dcsp.html
• This module is one of the hardest or
easiest in our dept. since it heavily relies
on math
• This module is one of the hardest easiest
in our dept. since it heavily relies on math
• As usual, the harder a module is, the more
useful it will be.
• This module is one of the hardest in our
dept. since it heavily relies on math
• As usual, the harder a module is, the more
useful it will be.
• Would be a big, big mistake if you miss too
many lectures
http://www.complextoreal.com/
• Communications is not an easy science. The math is heavy, and intuition is
slow to develop. To complicate things further, the field does not stay put.
New concepts are always coming to the fore.
• This website offers tutorials I have written on various topics in analog and
digital communications that will help you cut through this complexity. I keep
adding to this collection, albeit very slowly. It usually takes me a year or two
to write each new topic.
• Our field represents a pinnacle of human achievement in applied
mathematics. During our education, most of us don't develop the intuitive
understanding of these beautiful ideas. I have tried to make these tutorials
as simple as is possible given all the math. I hope I have been successful in
taking you closer to the "aha" moment.
Today’s outline
• Introduction
• Module summary
• Data transmission
Introduction
Movie, music, sound
Detect what you are
thinking
Now?
Using
Fourier Transform
Brain signal
When he was diagnosed with motor neurone disease aged just
21, Stephen Hawking was only expected to live a few years. He
will be 70 this month, and in an exclusive interview with New
Scientist he looks back on his life and work
• What do you think most about during
the day?
Women. They are a complete mystery
The information carrying signals are divided
into two broad classes
• Analog
• Digital
Analog Signals
Analog signals are continuous electrical signals that
vary in time as shown below.
Most of the time, the variations follow that of the nonelectric (original) signal.
The two are analogous hence the name analog.
Example:
Telephone voice signal is analog.
The intensity of the voice causes electric
current variations.
At the receiving end, the signal is reproduced in
the same proportion.
Digital Signals
Digital signals are non-continuous, they change in
individual steps.
They consist of pulses or digits with discrete levels or
values.
The value of each pulse is constant, but there is an
abrupt change from one digit to the next.
The values are anywhere within specific ranges and
we define values within a given range.
Digital Signals
Advantages
The ability to process a digital signal means that
errors caused by random processes can be
detected and corrected.
Digital signals can also be sampled
instead of continuously monitored and multiple
signals can be multiplexed together to form one
signal.
Because of all these advantages, and because
recent advances in wideband communication
channels and solid-state electronics have
allowed scientists to fully realize these
advantages, digital communications has grown
quickly.
Digital communications is quickly edging out
analog communication because of the vast
demand to transmit computer data and the
ability of digital communications to do so.
Today’s outline
• Introduction: daily life to deal with DS
• Module summary
• Data transmission
Module Summary
• Data transmission:
Channel characteristics,
signalling methods,
interference and noise,
synchronisation,
data compression and encryption;
• Data transmission:
• Information Sources and Coding:
Information theory,
coding of information for efficiency and error protection;
• Data transmission:
• Information Sources and Coding:
• Signal Representation:
Representation of discrete time signals in time and frequency;
z transform and Fourier representations;
discrete approximation of continuous signals;
sampling and quantisation;
stochastic signals and noise processes;
• Data transmission:
• Information Sources and Coding:
• Signal Representation:
• Filtering:
Analysis and synthesis of discrete time filters;
impulse response and infinite impulse response filters;
frequency response of digital filters; poles and
zeros;
filters for correlation and detection;
matched filters;
•
•
•
•
Data transmission:
Information Sources and Coding:
Signal Representation:
Filtering:
• Digital Signal Processing applications:
Processing of images using digital techniques.
Today’s outline
• Introduction: daily life to deal with DS
• Module summary
• Data transmission
Channel characteristics,
signalling methods,
Data Transmission
1.1 General Form
• A modulator that takes the source signal and transforms
it so that it is physically suitable for the transmission
channel
• A transmitter that actually introduces the modulated
signal into the channel, usually amplifying the signal as it
does so
• A transmission channel that is the physical link between
the communicating parties
• a receiver that detects the transmitted signal on the
channel and usually amplifies it (as it will have been
attenuated by its journey through the channel)
• A demodulator that receives the original source signal
from the received signal and passes it to the sink
Digital data is universally represented by strings of 1s or 0s.
Each one or zero is referred to as a
bit.
Often, but not always, these bit strings are interpreted as
numbers in a binary number system.
Thus 1010012=4110.
The information content of a digital signal is equal
to the number of bits required to represent it.
Thus a signal that may vary between 0 and 7 has an
information content of 3 bits.
Written as an equation this relationship is
I= log2(n)
bits
where n is the number of levels a signal may take.
It is important to appreciate that information is a
measure of the number of different outcomes a value
may take.
The information rate is a measure of the speed with
which information is transferred. It is measured in
bits/second or b/s.
Examples
Audio signals. An audio signal is an example of an analogue signal.
It occupies a frequency range from about 200 Hz to about 15KHz.
Speech signals occupy a smaller range of frequencies, and telephone
speech typically occupies the range 300 Hz to 3300 Hz..
The range of frequencies occupied by the signal is called its
bandwidth.
B
• Fs = 500; t = 0:1/Fs:29.6;
•
x = cos(2*pi*t*200)+randn(size(t));
•
y= cos(2*2*pi*t*200)+randn(size(t));
•
w=x+y;;
•
z= cos(4*2*pi*t*200)+randn(size(t));
•
h=w+z;
•
• >> sound(x,Fs)
• >> plot(x)
A signal is bandlimited if it contains no
energy at frequencies higher than some
bandlimit or bandwidth B
Examples
Television. A television signal is an analogue signal created by
linearly scanning a two dimensional image.
Typically the signal occupies a bandwidth of about 6 MHz.
Teletext is written (or drawn) communications that are interpreted
visually.
Telex describes a message limited to a predetermined set of
alphanumeric characters.
Reproducing cells, in which the daughter cells's DNA contains
information from the parent cells;
A disk drive
Our brain
Disadvantage of DSC
Could you find out one or two?
The conversion of analogue and
digital signals
In order to send analogue signals over a digital
communication system, or process them on a digital
computer, we need to convert analogue signals to
digital ones.
This process is preformed by and analogue-to-digital
converter (ADC).
The analogue signal is sampled (i.e. measured at
regularly spaced instant)
The conversion of analogue and
digital signals
In order to send analogue signals over a digital
communication system, or process them on a digital
computer, we need to convert analogue signals to
digital ones.
This process is preformed by and analogue-to-digital
converter (ADC).
The analogue signal is sampled (i.e. measured at
regularly spaced instant)
The converse operation to the ADC is performed by a
digital-to-analogue converter (DAC).
The ADC process is governed by an important law.
Nyquist-Shannon Theorem
(will be discussed again in Chapter 3)
An analogue signal of bandwidth B can be
completely recreated from its sampled from
provided its sampled at a rate equal to at
least twice it bandwidth.
That is
S >= 2 B
Nyquist sampling rate 2B
Example, a speech signal has an approximate
bandwidth of 4KHz.
If this is sampled by an 8-bit ADC at the Nyquist
sampling, the bit rate R is
R = 8 bits x 2 B=6400 b/s
Input fre =1 Hz, Nyquist = 2Hz
2
1.5
0
1
0
1
1.5
1
1
0.5
0
-0.5
-1
-1.5
-2
0
0.5
2
We can not recover the red sig.
2
1.5
0
1
1
1
0
1
1
1.5
1
1
1
0.5
0
-0.5
-1
-1.5
-2
0
0.5
2
How to find the bandwidth of a
signal?

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