The sequential generating filter

The output of a linear network is the convolution of the input and the impulse response of the network. This fact can be used to produce a network with any specified impulse response, since the process of convolution consists of delay, multiplication and integration, all of which can be performed with electrical components. Two arrangements which convolute their input with an approximation to a prescribed time function are described. In the more satisfactory of these, termed the `sequential generating filter¿, the input is quantized, sampled and converted into a density-modulated train of pulses which trigger a sequential function generator. This function generator, which is the novel feature of the device, delivers an approximation to the desired impulse response every time it is triggered, and its total output is the sum of the impulse responses to all input trigger pulses. It is shown that there is a minimum permissible rate at which the input may be sampled, and that this is equal to the sum of the bandwidths of the input and of the desired impulse response. Because of the quantization of the input, and the deviation of designed impulse response from the ideal one, there are error outputs in addition to the desired output. These errors are critically assessed.