After an Introduction in Part (1), Part (2) of the paper presents a study of the relations between the attenuation and phase characteristics of 4-terminal networks and their response to an impulse of infinitely short duration applied to the input terminals. It is shown that a rigid relationship exists between the characteristics of 4-terminal networks and their impulse response. In particular:—(a) If the phase-shift produced by the network is proportional to frequency, the impulse response is even;(b) If the phase-shift produced by the network is 90° at all frequencies, the impulse response is odd.From this theoretical analysis is developed, in Part (3), a method of obtaining any desired impulse response by means of a circuit containing a multiple-section artificial line. The response is obtained by effecting appropriate amplitude reflections at the end of each section, these reflections being produced by means of small variable condensers.An experimental circuit is described enabling characteristics identical with those of any network to be obtained in a few minutes.A practical example is given of the design of a low-pass filter with linear phase-shift, as used in television circuits.The paper concludes with the practical consideration of filters having a phase-shift of 90° at all frequencies. It is shown that with the type of circuit described, practical designs are possible for:—(a) High-pass filters whose characteristics are satisfactory up to frequencies as high as 10 to 20 times the cut-off frequency;(b) Band-pass filters, if the band width is not too narrow;(c) Low-pass filters, if the frequencies to be transmitted are not too low.