This paper presents a detailed investigation of the properties of a general class of least‐mean‐square‐fit (LMSF) smoothers in the presence of a white or colored input sequence. The results of the investigation show that the LMSF can be described as a low‐pass filter whose frequency response characteristics can be calculated exactly. A particularly useful result derived from the frequency response characteristics is the LMSF equivalent bandwidth. It was shown that knowledge of LMSF bandwidth, plus knowledge of the input bandwidth, provides the second‐order statistical description of the LMSF output noise process. Results of the analysis are verified by extensive computer simulation.