Complex signal transformation using a resistive network

A resistive network for providing the discrete Fourier transform of an input signal at an output thereof, comprising:

• first means responsive to the input signal and having a plurality of tap points for providing a signal vector representation of the state space of the input signal;
• a plurality of first conductors respectively coupled for receiving elements of said signal vector;
• a plurality of inverters each having an input and an output, said inputs of said plurality of inverters being respectively coupled for receiving said elements of said signal vector for providing inverted elements of said signal vector at said outputs of said plurality of inverters;
• a plurality of second conductors respectively coupled to said outputs of said plurality of inverters for conducting said inverted elements of said signal vector;
• a plurality of third conductors respectively coupled to the output of the resistive network;
• and
• a plurality of resistors having predetermined values and a predetermined connection scheme between said plurality of first conductors and said plurality of third conductors and between said plurality of second conductors and said plurality of third conductors, wherein said predetermined connection scheme and said predetermined values of said plurality of resistors are determined from a matrix representation of the sum of the products coefficients of the complex signal transformation.

A method of providing a complex transformation of an input signal vector at a plurality of outputs of a resistive network wherein the resistive network includes a plurality of first conductors for propagating elements of the input signal vector, a plurality of second conductors for propagating inverted elements of the input signal vector, a plurality of third conductors and a plurality of resistors having predetermined values and a predetermined connection scheme between the plurality of first conductors and the plurality of third conductors and between the plurality of second conductors and the plurality of third conductors, comprising the steps of:

• applying a plurality of voltages to the plurality of first conductors as the elements of the input signal vector;
• inverting each of said plurality of voltages for providing a plurality of inverted voltages;
• applying said plurality of inverted voltages to the plurality of second conductors;
• converting said plurality of voltages and said plurality of inverted voltages to a plurality of currents flowing through said plurality of resistors;
• and
• summing said plurality of currents into said plurality of third conductors for providing a spatial vector output signal proportional to the complex transformation of the input signal.