Lecture1 - Lecture 1: Basic Concepts ECE 514 Fundamental...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
1 Lecture 1: Basic Concepts ECE 514 Fundamental notions and properties What is a random experiment? l Randomness is associated with uncertainty, ignorance, etc. Ex: 1. Take an input perfectly known to you and apply it to a filter with a known impulse response. l Don’t know the input? L Random? What constitutes randomness? 2. Observe a sinusoidal wave on an oscilloscope. Is it random? Why? Random Experiment Definition : A random experiment is one in which the output cannot be perfectly known from a mere knowledge of the input. Properties: v A random experiment is theoretically repeatable v Its output, however, cannot be predicted exactly q If we cannot predict the face of a die throw, what is the next best thing? Example Example : If we throw a coin “n” times and obtain “n h heads, what can we say about the outcome heads? (Assuming n goes to infinity) n h /n = relative frequency If we can’t predict, exactly, what does the frequency tell you? Quality Assurance 1000 250 150 500 100 Tot 360 150 60 150 0 5W 200 100 0 50 50 2W 440 0 90 300 50 1W Tot. 10K 1000 100 10 P. Rat. Resistor Values Interpretation l Pick a resistor at random, and try to say something about your pick. (Remark: same thing when you pick a stock, using “history,” try to “smartly” choose the right one) What are the chances (probability) that you pick a 10 W resistor? v P(10 W ) = 100/1000 = 0.1 (elementary event) v P(2 W) = 200/1000 = 0.2 l One may want to know how likely they are at picking a 100 W and it be 2W. P(10 W , 2 W) = 50/1000= 0.05
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2 RADAR Example Example: In Radar, we typically transmit an EM pulse and listen for the return. We have two scenarios: H 0 : x(t) = S(t) + n(t) t = 1, … T. H 1 : x(t) = n(t) where n(t) is random l We are interested in designing a rule (a receiver) to say “target present” with very high “accuracy” (probability) L P(detection) is high, ideally, close to 1. Remarks Examples are varied, Is there a unified way of formulating the problems and solve them? We can form all different types of possible combinations (events) as subsets of the whole set. The association practice of events is reminiscent of sets and Boolean algebra. Formalism required comes from Set Theory Review of set Theory Definition : A set is a collection of objects called “elements” Ex: {All flying insects}, {table, chair, bed} v The first set is countable (maybe finite) v The second set is finite and has a cardinality of 3 (finite number of elements) Review of Set Theory l
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 09/24/2009 for the course ECE 514 taught by Professor Krim during the Fall '08 term at N.C. State.

Page1 / 6

Lecture1 - Lecture 1: Basic Concepts ECE 514 Fundamental...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online