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 ContentsEdit

### Basic InformationEdit

### TransformsEdit

- 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 FiltersEdit

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

### Analog Filter ModelingEdit

### Digital ProcessingEdit

### Filter ImplementationEdit

- Filter Verification
- Implementability

### ModulationEdit

- Phase Modulation
- Sigma-Delta modulation

### Noise and ErrorsEdit

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

channel of noises

### Multirate SystemsEdit

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

### Advanced FiltersEdit

- Dynamic Range Scaling
- Filter Sensitivity

### Spectral AnalysisEdit

- Classical
- nonparametric
- Parametric
- Linear Prediction

### Adaptive filtersEdit

- Wiener Filters
- Normal Equations
- Kalman Filtering