#### Transcript Neuronal Computation Using High Order Statistics

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?