COMS 161 Introduction to Computing Title: Digitization Date: February 14, 2005 Lecture Number: 13

Announcements Exam 1 on Wednesday First research paper due ob Friday 2/16/05 First research paper due ob Friday Due 2/18/05

Review Numbers Numeric representation of letters Hexadecimal Binary to hexadecimal conversion Hexadecimal to binary conversion Binary Coded Decimal (BCD)

Outline Digitization Sound Sampling Aliasing Quantization

Sampling Creates a discrete set of numbers from an analog (continuous time) waveform Advantageous to sample a regular (periodic) spaced intervals amplitude time 6

Sampling amplitude time 6

Sampling amplitude time 6

Sampling amplitude time Twice as many samples 6

Sampling amplitude time Half as many samples 6

Samples As the sampling frequency increases So does the number of samples Time between each sample decreases The sampling frequency must be twice the highest frequency of interest Otherwise aliasing fs = 1 / t0 6

Aliasing Is the sampling rate is too low High frequencies fold on-top of the lower frequencies Aliasing demo 6

Quantization Converts a continuous value into a binary number Binning Samples are placed in the closest bin 6

Resolution and Dynamic Range Directly related to the number of quantization levels Depends on how much memory is needed to store individual sample amplitudes Or how much fidelity is needed 8-bit sound 16-bit sound 6

Resolution and Dynamic Range Maximum range of amplitudes of stored sounds Dynamic range 6

Resolution and Dynamic Range 111 110 101 100 011 010 001 000 3 bits 8 quantization levels Resolution is 1/8 the dynamic range 6

Resolution and Dynamic Range 111 110 101 100 011 010 001 000 Sampling times 6

Resolution and Dynamic Range 111 110 101 100 011 010 001 000 Sampled and quantized signal 6

Resolution and Dynamic Range Sampled and quantized signal Significant error 6

Resolution and Dynamic Range 1111 1110 1101 1100 1011 1010 1001 1000 0111 0110 0101 0100 0011 0010 0001 0000 4 bits 16 quantization levels Resolution is 1/16 the dynamic range 6

Resolution and Dynamic Range 1111 1110 1101 1100 1011 1010 1001 1000 0111 0110 0101 0100 0011 0010 0001 0000 Sampled and quantized signal Still significant error 6

Resolution and Dynamic Range Sampled and quantized signal

Resolution and Dynamic Range Comparison of 3 and 4 bit resolution White: 3 bit Yellow: 4 bit

Resolution and Dynamic Range 11111 00000 5 bits 32 quantization levels 6

Resolution and Dynamic Range Sampled and quantized signal

Resolution and Dynamic Range Comparison of 3, 4, and 5 bit resolution White: 3 bit Yellow: 4 bit Green: 5 bit

Double the Sampling Rate 11111 00000 Twice as many samples 6

Resolution and Dynamic Range Twice as many samples Twice as nice 6

Resolution and Dynamic Range Comparison of sampling rates Carolina blue: twice the number samples as green

Resolution and Dynamic Range More quantization levels Higher resolution More accuracy of sample values More samples Better fidelity Digital sounds are closer to the original analog signal 8

Resolution Illustrated 7

Storing Digital Sound Sample rate and resolution -- tradeoffs Voice and speech 8-bit resolution 5-10 KHz sample rate CD-quality music 16-bit or higher resolution 44 KHz 8

Storing Digital Sound Audio file compression Sound on the Web Downloading and playing sound files Streaming audio 8