Nonlinear functions, such as arctangent, logarithm, and square root are commonly used in Digital Signal Processing. In practice, a textbook approximation algorithm is often used to compute these functions. These approximations are typically of mysterious origin and optimized for a certain application or implementation. Consequently, they may not be ideal for the application at hand. This talk describes a method for designing approximations using Chebfun (www.chebfun.org), an open-source software system for numerical computation with functions. With Chebfun, it is possible to quickly determine polynomial and rational approximations for any function with as many interpolation points as needed. This talk will cover a few basic topics in approximation theory and then work through several practical examples that can be directly employed in fixed point and floating point DSP applications.