Alternatively, the transfer properties of a seismometer can be described in the time domain by its impulse response, which is the response of the system to an impulsive input signal. (An impulse in this sense is any signal whose time integral is undistinguishable from a unit step). The impulse response and the transfer function are Laplace transforms of each other, so they offer mathematically equivalent descriptions of the system. In the same way, the complex frequency response is the Fourier transform of the impulse response. The impulse response can directly be calculated from the poles and zeros of the transfer function. For a practical specification, the impulse response is less suitable because it is a transcendental function of infinite duration that is inconvenient to formulate.
The response of a seismograph to an arbitrary input signal can in principle be computed as the convolution of that signal with the impulse response. However, due to the infinite length of the latter, this may not be an efficient procedure. Also, a sampled version of the impulse response may not represent the analytical form correctly when the system is not strictly bandlimited. So computing the response of a system by convolution requires some precautions, and one would in most cases prefer to either do the computation in the frequency domain with the Fourier transformation, or to filter the input signal with a recursive filter that represents the seismograph, as explained in the next paragraph.