# Digital Signal Processing

With the explosion of digital communications and digital media, the need for methods to process digital data is more important than ever. This book will begin with a look at the mathematical concepts behind digital processing, then will build on that with particular algorithms to do the work, and finally will present the actual implementations of these techniques in today's hardware and software systems. Many real-world algorithms are based on the techniques described in this book. JPEG images, MP3 songs, MPEG-2 videos, and ZIP files are all processed using digital processing techniques, and all of them will be discussed, at least conceptually. This book will not teach programming, and will probably not even provide much in the way of actual code, so we don't need to worry much about computer language dependence, except where otherwise noted. For some solid background information on the various mathematical theories in this book, consider reading Signals and Systems.

*This book is in a very early stage of production, and many of the pages either don't exist or only exist as bare stubs. Help and contributions from all wikibookians will be very much appreciated!*

## Table of Contents

edit### Digital Signals

edit### Transforms

edit- Continuous-Time Fourier Transform (CTFT)
- Discrete-Time Fourier Transform (DTFT)
- Discrete Fourier Transform (DFT)
- Fourier Series Expansion (FSE)
- Z Transform
- Hilbert Transform
- Fast Fourier Transform (FFT) Algorithm

### Digital Filters

edit- Digital Filters
- FIR Filter Design
- IIR Filter Design
- Filter Representation
- Tunable Filters
- Infinite Input Filtering
- Computer-aided Filter Design
- Ideal Filters
- Least Squares Design

### Analog Filter Modeling

edit### Digital Processing

edit### Filter Implementation

edit- Filter Verification
- Implementability

### Modulation

edit- Phase Modulation
- Sigma-Delta modulation

### Noise and Errors

edit- Finite wordlength effects
- Clipping
- Quantization Effects
- Roundoff errors
- Limit Cycles
- Discrete Stochastic Process

channel of noises

### Multirate Systems

edit- Upsampling and Downsampling
- Multirate Filters
- Decimation and Interpolation
- Polyphase decomposition

### Advanced Filters

edit- Dynamic Range Scaling
- Filter Sensitivity

### Spectral Analysis

edit- Classical
- nonparametric
- Parametric
- Linear Prediction

### Adaptive filters

edit- Wiener Filters
- Normal Equations
- Kalman Filtering