The Scientist and Engineer's Guide to
Digital Signal Processing
By Steven W. Smith, Ph.D.

Chapter 15: Moving Average Filters

The moving average is the most common filter in DSP, mainly because it is the easiest digital filter to understand and use. In spite of its simplicity, the moving average filter is optimal for a common task: reducing random noise while retaining a sharp step response. This makes it the premier filter for time domain encoded signals. However, the moving average is the worst filter for frequency domain encoded signals, with little ability to separate one band of frequencies from another. Relatives of the moving average filter include the Gaussian, Blackman, and multiple-pass moving average. These have slightly better performance in the frequency domain, at the expense of increased computation time.

• Implementation by Convolution
• Noise Reduction vs. Step Response
• Frequency Response
• Relatives of the Moving Average Filter
• Recursive Implementation