Think DSP

“Think DSP” is a comprehensive resource that delves into the realm of Digital Signal Processing (DSP). It covers fundamental concepts, algorithms, and practical applications in the field. The content explores topics such as signal analysis, filtering, spectral analysis, and convolution. Readers can expect to gain a deep understanding of how signals are processed, manipulated, and analyzed in various digital systems. With a focus on both theoretical foundations and hands-on implementation, “Think DSP” equips readers with the knowledge and skills needed to work with digital signals effectively.

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Think DSP

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Chapter 8 Filtering and Convolution

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In this chapter I present one of the most important and useful ideas related to signal processing: the Convolution Theorem. But before we can understand the Convolution Theorem, we have to understand ...

Chapter 9 Differentiation and Integration

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This chapter picks up where the previous chapter left off, looking at the relationship between windows in the time domain and filters in the frequency domain. In particular, we’ll look at the effect o...

Chapter 11 Modulation and sampling

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In Section 2.3 we saw that when a signal is sampled at 10,000 Hz, a component at 5500 Hz is indistinguishable from a component at 4500 Hz. In this example, the folding frequency, 5000 Hz, is half of t...

Chapter 7 Discrete Fourier Transform

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We’ve been using the discrete Fourier transform (DFT) since Chapter 1 , but I haven’t explained how it works. Now is the time. If you understand the discrete cosine transform (DCT), you will understan...

Chapter 4 Noise

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In English, “noise” means an unwanted or unpleasant sound. In the context of signal processing, it has two different senses: As in English, it can mean an unwanted signal of any kind. If two signals i...

Chapter 6 Discrete cosine transform

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The topic of this chapter is the Discrete Cosine Transform (DCT), which is used in MP3 and related formats for compressing music; JPEG and similar formats for images; and the MPEG family of formats fo...

Chapter 1 Sounds and signals

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A signal represents a quantity that varies in time. That definition is pretty abstract, so let’s start with a concrete example: sound. Sound is variation in air pressure. A sound signal represents var...

Chapter 5 Autocorrelation

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In the previous chapter I characterized white noise as “uncorrelated”, which means that each value is independent of the others, and Brownian noise as “correlated”, because each value depends on the p...

Chapter 10 LTI systems

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This chapter presents the theory of signals and systems, using musical acoustics as an example. It explains an important application of the Convolution Theorem, characterization of linear, time-invari...

Chapter 0 Preface

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Signal processing is one of my favorite topics. It is useful in many areas of science and engineering, and if you understand the fundamental ideas, it provides insight into many things we see in the w...

Chapter 3 Non-periodic signals

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The signals we have worked with so far are periodic, which means that they repeat forever. It also means that the frequency components they contain do not change over time. In this chapter, we conside...