The document discusses different types of digital filters including Infinite Impulse Response (IIR) filters and multirate filters. IIR filters use feedback and have an infinite impulse response. They are potentially unstable but more efficient than FIR filters. IIR filters are usually designed to duplicate analog filter responses and implemented as cascaded second-order sections. Multirate filters involve changing the sample rate, such as decimation which decreases the sample rate, and interpolation which increases the sample rate. Adaptive filters can modify their transfer function based on an optimization algorithm to model non-stationary signals and are used for applications like echo cancellation.