Analog-to-digital converter using a pipelined memristive neural network

1. A pipelined analog-to-digital converter (ADC) system comprising:

a first ADC stage comprising a trainable neural network layer, wherein said first ADC stage is configured to (i) receive an analog input signal, and (ii) convert it into a first n-bit digital output representing said analog input signal;

a digital-to-analog converter (DAC) circuit comprising a trainable neural network layer, wherein said DAC circuit is configured to (iii) receive said first n-bit digital output, and (iv) convert it into an analog output signal representing said first n-bit digital output; and

a second ADC stage comprising a trainable neural network layer, wherein said second ADC stage is configured to (v) receive a residue analog input signal of said analog input signal, and (vi) convert it into a second n-bit digital output representing said residue analog input signal;

wherein said first and second n-bit digital outputs are combined to generate a combined digital output representing said analog input signal.

2. The system of claim 1 , wherein each of said first and second n-bit digital outputs is a 4-bit digital output.

3. The system of claim 1 , wherein said residue analog input signal is determined based, at least in part, on a comparison between said analog input signal and said analog output signal.

4. The system of claim 1 , further comprising one or more subsequent ADC stages connected in a pipelined arrangement, wherein each of said subsequent ADC stages comprises:

(i) a DAC circuit comprising a trainable neural network layer, wherein said DAC circuit is configured to receive an n-bit digital output from a preceding ADC stage and convert it into an analog output signal representing said n-bit digital output; and

(ii) an ADC circuit comprising a trainable neural network layer, wherein said ADC circuit is configured to receive a residue analog input signal of said analog input signal, and convert it into an n-bit digital output representing said residue analog input signal.

5. The system of claim 4 , wherein said first n-bit digital output, said second n-bit digital output, and all of said n-bit digital output of said subsequent ADC stages, are combined to generate said combined digital output.

6. The system of claim 1 , wherein said combined digital output comprises a number of bits equal to n-bits multiplied by the number of all of said ADC stages.

7. The system of claim 1 , wherein said n-bit digital output of a last of said subsequent ADC stages in the pipeline represents a least significant bits (LSB) portion of said combined digital output.

8. The system of claim 1 , wherein each of said trainable neural network layers is arranged as a memristive crossbar array comprising a synaptic weightings matrix, and wherein an output vector of each of said trainable neural network layers is calculated as a weighted sum of said outputs of said neurons multiplied by said synaptic weightings matrix.

9. The system of claim 8 , wherein, at a training stage of said system, each of said neural network layers is trained by an iterative process comprising:

(i) comparing said output vector of said neural network layer to a respective training input; and

(ii) adjusting, based on said comparing, said synaptic weightings matrix of said neural network layer, wherein said adjusting minimizes a cost function based on a gradient descent algorithm.

10. The system of claim 9 , wherein, with respect to each of said ADC stages, said training input comprises an n-bit portion of a desired digital output of said system, and wherein said n-bit portion corresponds to bit positions of said n-bit digital output of said ADC stage within said combined digital output.

11. An analog to digital (ADC) conversion method, the method comprising:

receiving an analog input signal;

converting said analog input signal, using a first ADC stage comprising a trainable neural network layer, into a first n-bit digital output representing said analog input signal;

converting said first n-bit digital output, using a digital-to-analog converter (DAC) circuit comprising a trainable neural network layer, into an analog output signal representing said first n-bit digital output; and

converting a residue analog input signal of said analog input signal, using a second ADC stage comprising a trainable neural network layer, into a second n-bit digital output representing said residue signal; and

combining said first and second n-bit digital outputs to generate a combined digital output representing said analog input signal.

12. The method of claim 11 , wherein each of said first and second n-bit digital outputs is a 4-bit digital output.

13. The method of claim 11 , wherein said residue analog input signal is determined based, at least in part, on a comparison between said analog input signal and said analog output signal.

14. The method of claim 11 , further comprising using one or more subsequent ADC stages connected in a pipelined arrangement, wherein said method comprises, with respect to each of said subsequent ADC stages:

(i) receiving, from a preceding ADC stage, an n-bit digital output;

(ii) converting said n-bit digital output, using a DAC circuit comprising a trainable neural network layer, into an analog output signal representing said n-bit digital output; and

(iii) converting a residue analog input signal of said analog input signal, using an ADC circuit comprising a trainable neural network layer, into an n-bit digital output representing said residue signal.

15. The method of claim 14 , wherein said first n-bit digital output, said second n-bit digital output, and all of said n-bit digital output of said subsequent ADC stages, are combined to generate said combined digital output.

16. The method of claim 11 , wherein said combined digital output comprises a number of bits equal to n-bits multiplied by the number of all said ADC stages.

17. The method of claim 11 , wherein said n-bit digital output of a last of said subsequent ADC stages represents a least significant bits (LSB) portion of said combined digital output.

18. The method of claim 11 , wherein each of said trainable neural network layers is arranged as a memristive crossbar array comprising a synaptic weightings matrix, and wherein an output vector of each of said trainable neural network layers is calculated as a weighted sum of said outputs of said neurons multiplied by said synaptic weightings matrix.

19. The method of claim 18 , wherein, at a training stage, each of said neural network layers is trained by an iterative process comprising:

(i) comparing said output vector of said neural network layer to a respective training input; and

(ii) adjusting, based on said comparing, said synaptic weightings matrix of said neural network layer, wherein said adjusting minimizes a cost function based on a gradient descent algorithm.

20. The method of claim 19 , wherein, with respect to each of said ADC stages, said training input comprises an n-bit portion of a desired digital output, and wherein said n-bit portion corresponds to bit positions of said n-bit digital output of said ADC stage within said combined digital output.