We demonstrate that extremely rapid and weak periodic and non-periodic signals can easily be detected by using the autocorrelation of intensity as a function of time. We use standard radio-astronomical observations that have artificial periodic and non-periodic signals generated by the electronics of terrestrial origin. The autocorrelation detects weak signals that have small amplitudes because it averages over long integration times. Another advantage is that it allows a direct visualization of the shape of the signals, while it is difficult to see the shape with a Fourier transform. Although Fourier transforms can also detect periodic signals, a novelty of this work is that we demonstrate another major advantage of the autocorrelation, that it can detect non-periodic signals while the Fourier transform cannot. Another major novelty of our work is that we use electric fields taken in a standard format with standard instrumentation at a radio observatory and therefore no specialized instrumentation is needed. Because the electric fields are sampled every 15.625 nanoseconds, they therefore allow detection of very rapid time variations. Notwithstanding the long integration times, the autocorrelation detects very rapid intensity variations as a function of time. The autocorrelation could also detect messages from Extraterrestrial Intelligence as non-periodic signals.