The behaviour of filters having jump-function inputs is investigated. The output of the filter is approximated by a jump function, and the ratio between the Laplace transforms of the two jump functions defines the jump-transfer function of the filter. A serial operator for the filter can then be written down, and approximate analysis carried out using time series. A method of deriving a serial number for any time function having an analytical form is stated. Tables are given showing the jump-transfer function and serial operator for commonly occurring filters, and a comparison is made with the method due to Tustin of calculating approximate responses. A high degree of mathematical rigour has not been aimed at in the treatment.