Analog to Digital Conversion Meredith Matteson, Lenoir City High School Mentor: Aysha Shanta Young Scholars Program July 22, 2016 The University of Tennessee Knoxville

Outline Practical Applications Signals Analog signals Digital signals Conversion of Analog signals to Digital signals Sampling Nyquist - Shannon Sampling Theorem Quantization Coding Project and Conclusion

Application Common examples Telephone Television Radio Computer Camera Video Recorder

Signal Defined as as any physical quantity that varies with time, space, or any other independent variable or variables. The X-axis is the time and the Y-axis represents some other vector characteristic. Represented by a function (Examples: cosine or sine)

Analog Signal Analog - of or relating to a device or process in which data is represented by physical quantities that change continuously. [1]

Digital Signal Digital - of or relating to information that is stored in the form of the numbers 0 and 1. [2]

Analog to Digital Conversion Sampling Quantization Coding [6].

Data at regular X - axis intervals Discrete time Sampling Data at regular X - axis intervals Discrete time [6]. Analog Digital

Importance of Frequency in Sampling Time period - time it takes for the signal to come back to the starting point Frequency = 1/time period Direct relationship between frequency and sampling rate Shows the difference between high and low frequency waves. [3]

Nyquist - Shannon Sampling Theorem Fsample > 2 * Fmaximum If the maximum frequency is 100 Hz, the sample frequency must be at least 200 Hz.

Importance of Sampling Inappropriate number of samples can cause a false reconstruction. Solid line is actual wave. Broken line is reconstructed line. [5].

Defined levels on the Y axis Levels = 2number of bits Quantization Defined levels on the Y axis Levels = 2number of bits Quantization error Loss of data Discrete Time Signal [7]. Quantized Signal that has been forced onto levels.

Coding Binary Sequencing on the Y axis Defined by a certain number of bits Digital devices only recognize 1’s and 0’s.

Analog Voice Recording

Comparison of the Original Analog signal to the Sampled Signal

The Digital Signal with a 4 bit quantizer

Comparison of all three signals

Conclusion Analog to Digital Conversion allows for any set if continuous data to be transmitted and processed digitally. 3 Step Process Sampling Quantization Coding Audio Recording

References [1]. Analog vs. Digital [Graphic of just the analog signal]. (n.d.). Retrieved July 5, 2016, from https://learn.sparkfun.com/tutorials/analog-vs- digital/digital-signals [2]. Digital.signal.discret.svg [Graphic of a digital signal]. (2014, August 27). Retrieved July 5, 2016, from https://commons.wikimedia.org/wiki/File:Digital.signal.discret.svg [3].Experiment 01: Sampling and Quantization of signals using MATLAB. (n.d.). BRAC University. Retrieved July 13, 2016. [4]. [Graphic of a low frequency curve and a high frequency curve]. (n.d.). Retrieved July 5, 2016, from http://metaldetectorsa.co.za/frequently-asked-questions/frequency-and-your-metal-detector/ [6]. Marshall, D. (2001, April 10). Nyquist's Sampling Theorem. Retrieved July 13, 2016, from https://www.cs.cf.ac.uk/Dave/Multimedia/node149.html [5]. Kunath, S. (n.d.). Analog to Digital Conversion [Image of Analog and Digital signal side by side.]. Retrieved July 5, 2016, from http://www.dilettantesdictionary.org/index.php?search=1&searchtxt=analog-to-digital [7]. Proakis J.G. and Manolakis D. G. (1996). Digital Signal Processing: Principles, Algorithms, and Application. New Jersey: Prentice-Hall, Inc. [8]. 007 Signal Path Series. (2013). Retrieved July 15, 2016, from http://www.mixrevu.com/?p=article

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Acknowledgements This work was supported primarily by the ERC Program of the National Science Foundation and DOE under NSF Award Number EEC-1041877. Other US government and industrial sponsors of CURENT research are also gratefully acknowledged.