Correlation filter

The correlation filter is an electronic circuit whose elements are a multiplier, an integrator and a signal source of a shape corresponding to the shape of the detected signal. The input signal, which is the sum of the noise and possibly the useful signal, is fed to one of the inputs of the multiplier. A reference signal is supplied to the other input of the multiplier, which coincides with the shape, frequency, and phase with the signal that needs to be detected. The output of the multiplier is connected to the input of the integrator.

In the event that the signal at the input coincides with the reference signal mixed with noise, the signal at the input of the integrator is close to the square of the reference (difference in amplitude decreasing due to attenuation), and, in addition, the product of noise with a close to zero expectation and reference signal. In this case, the signal at the output of the integrator has a large positive value - the square of the signal is always greater than zero, and the integral of the noise component is close to zero for a sufficiently long signal duration. If a mixture of a reference signal phase-shifted by π with noise is fed to the input, the signal at the output of the integrator, from considerations similar to those described in the previous paragraph, takes a high negative value. If the input signal does not coincide with the reference in shape or frequency, the output signal of the multiplier does not have constant sign, which means that the output signal of the integrator takes low values.

Alternating during transmission, signal segments matching in shape and frequency with the reference signal of the correlation filter and having a phase different by π can transmit a digital signal by changing the value of the output signal of the correlation filter to high positive or high negative.