A test set for communications systems includes a pseudo-noise sequence generator providing a test signal which is fed to a pair of signal channels. The first channel includes a spectrum shaping filter and a conditioning amplifier. The second channel includes a variable delay circuit, a spectrum shaping filter matched to the first filter, and an amplifier. The output of the first channel is applied to the system under test. The output of the system and the output of the second channel are compared to determine the degree of distortion suffered by the test signal due to the communications system.

A system for measuring a multipath radio channel impulse response by cross-correlating digital samples of a received pseudo-random signal with a digital copy of the transmitted signal. A transmitter within the system repeatedly transmits the pseudo-random signal across a multipath radio channel. A receiver within the system receives the transmitted signal, as well as delayed versions of the original signal, and digitally samples the received signals. A computer then cross-correlates the samples of the received signal with the digital stored version of the transmitted signal to produce a measure of the impulse response of the multipath radio channel.

In a system for locating the position of a transmitter, a platform containing an antenna is moved through a measurement path. The frequency received by the antenna is measured at measurement points distributed along a measurement path. The frequency is measured by cross correlating coherent pulses of the received frequency signal. An inertial navigation system on the platform indicates the position of the measurement path. A computer determines estimated locations by non-linear least squares convergence starting from trial locations. The non-linear least squares convergence is based on the frequency equation for the received frequency ##EQU1## in which f.sub.0, is the transmitter frequency, V is the antenna velocity and r is the range of the transmitter. The computer evaluates a cost function derived from the frequency equation, for each location estimated by the non-linear least squares convergence and selects the estimated location with the lowest cost function as the best solution.

Equipment is provided for determining the characteristics of a linear or non-linear system from its output y, for a quasi-random input x. The non-linear system may be a biological system. The computer described calculates first and second order kernels from the input signals applied to the system and the output signals received from the system.

For a delta modulated signal wave comprising a digital carrier wave modulated by an analog wave and represented accordingly as a bivalued digital data bit stream, a correlation function factor is generated by delaying the bit stream in time by an integral multiple of bits and accumulating the successive individual products over a predetermined number of bits of successive individual bits delayed in time and the corresponding currently appearing bits. The circuitry is extremely simple; readily procurable components only are required. A dual input exclusive OR (XOR) gating circuit is connected to the source of delta modulated signal bit stream and to an N-bit digital binary shift register also connected to the source. A stream of successive bivalued products of the current bits and the time delayed bits over a period of N-bits is obtained from the XOR gating circuit and applied to a bidirectional digital counting circuit from which an autocorrelation function factor is delivered.