	Although DSP has long been considered an EE topic, recent developments have also generated signifi cant interest from the computer science community. DSP applications in the consumer market, such as bioinformatics, the MP3 audio format, and MPEG-based cable/satellite television have fueled a desire to understand this technology outside of hardware circles. Designed for upper division engineering and computer science students as well as practicing engineers, Digital Signal Processing Using MATLAB and Wavelets emphasizes the practical applications of signal processing. Over 100 MATLAB examples and wavelet techniques provide the latest applications of DSP, including image processing, games, fi lters, transforms, networking, parallel processing, and sound. The book also provides the mathematical processes and techniques needed to ensure an understanding of DSP theory. Designed to be incremental in diffi culty, the book will benefi t readers who are unfamiliar with complex mathematical topics or those limited in programming experience. Beginning with an introduction to MATLAB programming, it moves through filters, sinusoids, sampling, the Fourier transform, the z-transform and other key topics. An entire chapter is dedicated to the discussion of wavelets and their applications. A CD-ROM (platform independent) accompanies the book and contains source code, projects for each chapter, and the fi gures contained in the book. FEATURES: Contains over 100 short examples in MATLAB used throughout the book Includes an entire chapter on the wavelet transform Designed for the reader who does not have extensive math and programming experience Accompanied by a CD-ROM containing MATLAB examples, source code, projects, and fi gures from the book Contains modern applications of DSP and MATLAB project ideas

Digital Signal Processing Using MATLAB and Wavelets

By Michael Weeks

Chapter 5 - Sampling

We live in an analog world, in that the signals that interest us are typically continuous. Our computers are digital devices, meaning that they can store only finite, discrete data, limited in both precision and magnitude. Thus, we need to approximate signals before we can store and manipulate them. How do we bridge the gap between the real world and the synthetic one of our computers? This chapter addresses this central question.

Sampling is the process of getting a digital signal from an analog one. When we sample a signal, we record, every so often, a value. Sampling can lead to many data values. For example, a 3-minute song, sampled at 16 bits at 44,100 Hz (for two channels), produces:

Changing the units to make them uniform makes this:

$\left(3 \; minutes \frac{60 \; seconds}{1 \; minute}\right) \times \left(16 \fr... ...8 \; bits}\right) \times \left(44100 \; \frac{samples}{second}\right) \times 2$

$(180 \; seconds) \times \left(2 \; \frac{bytes}{sample}\right) \times \left(44100 \; \frac{samples}{second}\right) \times 2$

180 X (2 bytes) X 44100 X 2 = 31,752,000 bytes, approximately 30 MB.

But do we really need to store 30 MB of data for a 3-minute song? Actually, there are other ways of storing this data. The MP3 format is one such solution. It is popular due to the fact that a song stored as an MP3 sounds very close to the original, while only requiring about 10% of the space.

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Chapter 5 - Sampling

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