CS Lecture 10:

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1 CS Lecture 10: Digital Encoding---Representing the world in symbols Review: Analog vs Digital (Symbolic) Information Text encoding: ASCII and Unicode Encoding pictures: Sampling Quantizing

2 Analog vs. Digital Information Recall: Analog Information is continuous information about the real world, any piece containing in principle an infinite amount of information; Digital Information is discrete information represented by symbols, each of which represents one indivisible unit of information. Π = A B a b Αβγδ A é $

3 Converting Binary to Decimal Write the powers of two from right to left (starting at 1) over the number, and add up those corresponding to 1 s:

4 Converting Binary to Decimal Write the powers of two from right to left (starting at 1) over the number, and add up those corresponding to 1 s: =

Counting in Binary Now we can see how to count in binary: Decimal Binary 0 0 1 1 2 10

5 Counting in Binary Now we can see how to count in binary: Decimal Binary Think Odometer with two digits! 13

6 Converting Decimal to Binary To go from base 10 to base 2, just reverse the process of binary -> decimal; go from left to right and ask yourself: could this power of two help make the sum I need? Example: Convert 112 to binary: ? +? +... =

7 Digitizing the world: Text A character set is a list of characters and the numbers (binary codes) used to represent each one.

The ASCII Character Set ASCII (American Standard Code for Information Interchange) was the first encoding system for the character set used on modern

8 The ASCII Character Set ASCII (American Standard Code for Information Interchange) was the first encoding system for the character set used on modern computers, and represented 128 characters by the numbers It includes all the Roman letters, punctuation, and control characters, some obsolete!

9 ASCII Encoding Example: Hello, world! H -> 72 e -> 101 l -> 108 l -> 108 o -> 111,, -> 44 -> 32 (blank) w -> 119 o -> 111 r -> 114 l -> 108 d -> 100! -> 33

10 Unicode Character Set ASCII was extended to 256 numbers, but still is not enough for international use. Unicode can represent 1,114,112 symbols using numbers 0 1,114,111. Unicode is a superset of ASCII -- the first 256 characters correspond exactly to the extended ASCII character set.

Digitizing Text So, text encoding is simple: just replace each character by its number; decoding is just the reverse process; computers are very fast at

11 Digitizing Text So, text encoding is simple: just replace each character by its number; decoding is just the reverse process; computers are very fast at this kind of manipulation: Text: Four score and seven years ago our fathers brought forth on this continent a new nation, conceived in Liberty Encoding:

12 Digitizing the World: Representing pictures How could we describe this image with symbols (i.e., numbers)? What would the numbers represent? How many would we need? How would we organize the description? Is a picture worth ONLY a thousand words?

13 Digitizing Images What we will end up with is something very different from last lecture s look at my hair

14 Digitizing Images DIGITIZING is the process of converting analog information to digital (symbolic) form, usually for storage and manipulation by computer. There are two steps to digitizing images: Choose a resolution and sample the image; and Quantize each sample into a number representing a color.

15 Digitizing an Image: Sampling Sampling: Taking measurements (of color) at discrete pixels within the image. What resolution (pixels/inch) should we use? Photo is 2.5 x 3.5 inches

16 Digitizing an Image: Sampling Sampling: Taking measurements (of color) at discrete locations within the image. 16 samples per inch (in each direction)

17 Digitizing an Image: Sampling Sampling: Measure the color for each pixel, and record that color. 16 pixels per inch

18 Digitizing an Image: Sampling Sampling: Measure the color for each pixel, and record that color. 32 pixels per inch

19 Digitizing an Image: Sampling The question is always: How much resolution is enough? Compare: Sony TV: 56 Pixels per inch Macbook Pro Retina Display: 220 pixels per inch iphone 4: 326 PPI, iphone 6: 661 PPI

20 What is color? How can we describe a color?

21 RGB Encoding The RGB color model is an additive model, in which red, green, and blue (RGB) colors are combined in various ways to reproduce other colors. + + =

22 RGB Encoding Color is expressed as an RGB value three numbers that indicate the relative contribution of each of these primary colors. Color mixing example: Turn on all red and all green and no blue, which results in a bright yellow.

23 Quantization of colors Quantization is the process of assigning numbers to the intensity of red, green, and blue colors in an analog image.

24 Encoding colors with bits TrueColor is 24 bit depth : 8 bits for red, 8 bits for blue, 8 bits for green Each color has 256 possibly intensities 24 color bits è or 16,777,216 colors Using fewer bits gives less accurate colors:

25 A Sampling of RGB Color Codes

26 The Result: A Dog in Bits

27 Digitizing Images What we will end up with is something very different from last lecture s look at my hair

28 Digitizing Images What we will end up with is something very different from last lecture s look at my (analog) hair

29 Digitizing Images What we will end up with is something very different from last lecture s look at my hair

30 Digitizing Images What we will end up with is something very different from last lecture s look at my hair

31 Digitizing Images What we will end up with is something very different from last lecture s look at my hair

32 Digitizing Images At the smallest level, we end up with pixels (=picture elements), which represent one color, represented by a number. The most important question is: How much detail do you need, how good an approximation is necessary?

33 Digital Audio What is sound? How do we convert the analog information in sound into digital form? What are the consequences of digitizing on our uses of sound (for music, for example)? 33

34 Hearing We hear sound when a series of air compressions vibrate a membrane in our ear. The inner ear sends signals to our brain. The rate of this vibration is measured in Hertz, and the human ear can hear sounds in the range of roughly 20Hz - 20KHz. 34

35 Sound Wave Properties Wavelength: distance between waves (affects pitch -- high or low sounds) Amplitude: strength of power of waves (volume) Frequency: the number of times a wave occurs in a second. 35

36 Microphones and Speakers Microphones convert acoustical energy (sound waves) into electrical energy (the audio signal). Speakers do the same thing in reverse: convert electrical energy into acoustical energy. 36

37 Important Note about Electronic Signals An analog signal continually fluctuates in voltage up and down (analog electricial information represents analog sound information). Sound wave: Electrical wave: A digital signal has only two levels represent the bits 0 and Digital wave : 37

38 Recall: Digitizing an Image Sample each pixel and digitize it using 8 bits for each of primary colors Quantization: determine a discrete value for each pixel.

39 Digitizing Audio Information The same idea can be used for audio information: Digitize the signal by sampling: periodically measure the voltage record the numeric value as bits 39

40 Sampling Audio Information Sampling: periodically measure the voltage and record the numeric value. Some data is lost, but a reasonable sound is reproduced. 40

CS101 Lecture 18: Audio Encoding. What You ll Learn Today

CS101 Lecture 18: Audio Encoding Sampling Quantizing Aaron Stevens (azs@bu.edu) with special guest Wayne Snyder (snyder@bu.edu) 16 October 2012 What You ll Learn Today How do we hear sounds? How can audio