Popular in Course
Popular in Electrical Engineering
This 2 page Class Notes was uploaded by Dorris Borer on Monday September 28, 2015. The Class Notes belongs to ESE250 at University of Pennsylvania taught by Staff in Fall. Since its upload, it has received 7 views. For similar materials see /class/215456/ese250-university-of-pennsylvania in Electrical Engineering at University of Pennsylvania.
Reviews for DIGAUDIOBASICS
Report this Material
What is Karma?
Karma is the currency of StudySoup.
You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!
Date Created: 09/28/15
ESE250 Spring 2010 January 28 2010 Big Idea Week 3 Lossless Compression Not all characters words sounds or images carry the same amount of information and we can use this fact to reduce the number of bits required to store or transmit a data stream without discarding any information That is the things we perceive directlyicharacters words sounds imagesican typically be compressed considerably without loss such that they can be decompressed to represent the original exactly The trick here is simple in concept Not all things characters word notes gures occur with equal frequency ag In this class we will say compute or digital much more often than we will say sparrow or peloton you will nd far more e s on this page than z s http er1wikipedia orgwiki Letterifrequency Since we encouter some things more frequently than others we can give them smaller encodings fewer bits Today s text message lexicon employs one form of this concept by using abbreviations for common phrases eg LOL CULSR BFF B4 This embodies an important engineering principle make the common case inexpensive fast small low energy By carefully de ning the set of things that can occur a universe of possibilities and assuming or observing a particular frequency of occurence we can make this notion mathematically precisei allowing us to both quantify the encoding size and even ask questions about the optimal smallest possible encodingithat is the true information content in the sequence of things Consider recording the daily weather for a year For the sake of simplicity let us assume we can describe the weather as one of four cases sunny cloudy rain snow Let w be the weather on day i that takes on one of these four values The number of bits it would take us to record this for a year would be 1365 totalibits Z l d0 where lln ts is the count of the number of bits in the encoding of bitswil If we encoded each of the four cases with 2 bits ag bitssunny00 bits cloudy01 bits rain10 bitssnowll then one year of weather observations would require 730 bits Now if we knew that on average only 5 of the days had snow 45 were sunny 10 were rain and 40 were cloudy then we might select an encoding bitssunny0 bcloudy10 brain110 bsnowlll This encoding would require around 621 bits about 164 sunny days 146 cloudy days 36 rain days and 19 snow days While we can be precise about encoding when we de ne a universe of things this still leaves open the question of the best set of things to consider ag characters words phrases notes intervals University of Pennsylvania ESE250 Spring 2010 February 4 2010 Big Idea Week 4 Time Frequency Representations and Conversion There are many different ways to represent information For example we might represent time as 1 year date month and hours in Universal Time 2 elapsed seconds since midnight UT January 1 1970 3 years into the reign of the current monarch days since the last equinox and hours since sunrise or sunset or 4 days hours and minutes to graduation Which one is most convenient depends on what we want to do with the information Some representations may be more natural for data collection others may be more convenient for certain kinds of processing and some representations may expose more structure in the data allowing greater compression or understanding In the case of sound samples in time are a very direct way to capture and reproduce acoustic pressure waves We can take these samples directly by converting analog voltages from a microphone to digital samples and we can use them directly to drive a speaker by converting the digital samples back to voltages However time samples are not the most ef cient way to represent the common structure that often occurs in the patterns of acoustic pressure waves that humans call sound because of the manner in which those patterns are perceived For example arrays of time samples do not offer the most directly compressible representation For many operations it is more convenient to describe work with and store sounds using a representation based upon frequency content rather than time varying amplitudes Musical notes for example can be represented directly by their frequencies with one or a few frequencies often de ning the sound wave exactly for a period of a very large number of time samples As an alternative to representing a sound sequence as a discrete set of amplitude samples in time we can also represent sound as a weighted sum of harmonics i discrete sine and cosine waves whose frequencies are multiples of a base frequency the fundamental That is rather than representing a sound wave as a vector of time samples SbmpleE3T7 Skimple72T7 Sample7T Sample0 ShmpldT7 SlzmpldQT7 SlzmpleBT7 we can represent it as a vector of coef cients a00a91a01a92a02 chosen such that Sampleh ace cos0t 151 sint an cost 152 sin2t 102 cos2t for all t E 0T 7T 2T 72T The relationship between time and frequency representations for sampled signals can be geometrically interpreted as a linear change of basis between different frames of reference in the typically high dimen sional vector space comprised of all possible time samples This brings the powerful and highly ef cient computational machinery of linear algebra to bear on the problem of audio signal processing University of Pennsylvania
Are you sure you want to buy this material for
You're already Subscribed!
Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'