Adaptive digital quantization noise cancellation filters for mash ADCs

1. A method for tracking a transfer function for digital quantization noise cancellation in a multi-stage analog-to-digital converter (ADC), the method comprising:

injecting a dither signal at a quantizer of a front end of the multi-stage ADC, wherein the dither signal is a maximum length linear feedback shift registers sequence;

determining a cross-correlation function of a digital output signal of the multi-stage ADC and the dither signal to determine a transfer function of the multi-stage ADC; and

updating coefficients of a programmable filter for digital quantization noise cancellation based on the cross-correlation function.

2. The method of claim 1 , wherein:

the digital output signal is an output signal of the front end of the multi-stage ADC;

the transfer function is a noise transfer function of the front end; and

the programmable filter filters an output signal of a back end of the multi-stage ADC.

3. The method of claim 1 , wherein:

the digital output signal is an output signal of a back end of the multi-stage ADC;

the transfer function is a signal transfer function of the back end; and

the programmable filter filters an output signal of the front end of the multi-stage ADC.

4. The method of claim 1 , further comprising:

decimating the cross-correlation function to determine decimated coefficients;

wherein updating the coefficients of the programmable filter comprises updating the coefficients based on the decimated coefficients.

5. The method of claim 1 , further comprising:

decimating an output signal of the multi-stage ADC by one or more decimation filters to generate a decimated output signal; and

filtering the decimated output signal by the programmable filter.

6. The method of claim 1 , further comprising:

normalizing the cross-correlation function based on a gain coefficient computed from an estimated signal transfer function of the multi-stage ADC.

7. The method of claim 1 , further comprising:

applying a moving average on a plurality of coefficient sets computed based on the cross-correlation function.

8. A system for tracking a transfer function for digital quantization noise cancellation in a multi-stage analog-to-digital converter (ADC), the system comprising:

a dither block for generating a maximum-length linear feedback shift registers (LFSR) sequence, said dither block coupled to a quantizer of a front end of the multi-stage ADC;

a cross-correlation hardware block receiving a digital output of the multi-stage ADC and the maximum-length LFSR sequence and generating coefficients of a cross-correlation function; and

a digital quantization noise cancellation filter programmable based on the coefficients of the cross-correlation function.

9. The system of claim 8 , wherein the cross-correlation hardware block comprises:

a multiplexer for (1) selecting a value among a plurality of values of the maximum-length sequence and providing the selected value to a correlator during a first time period and (2) selecting another value among a plurality of values of the maximum-length sequence and providing the selected value to the correlator during a second time period.

10. The system of claim 8 , wherein the cross-correlation hardware block comprises:

a multiplexer for (1) selecting an output of a first stage of the multi-stage ADC and providing the selected output of the first stage to a plurality of correlators during a first time period, and (2) selecting an output of a second stage of the multi-stage ADC and providing the selected output of the second stage to the plurality of correlators during a second time period.

11. The system of claim 8 , wherein the maximum-length LFSR sequence is a 2-level dither sequence.

12. The system of claim 8 , wherein the cross-correlation hardware block comprises:

an accumulator for receiving a value of the maximum-length LFSR sequence and the digital output of the multi-stage ADC, wherein a level of the value of the maximum-length LFSR sequence determines whether the digital output is subtracted or added to an accumulated value of the accumulator.

13. The system of claim 8 , further comprising:

a moving average filter for filtering coefficients of the cross-correlation function.

14. The system of claim 13 , wherein the moving average filter has a programmable moving window size.

15. The system of claim 8 , further comprising:

one or more decimation filters for filtering the cross-correlation function.

16. The system of claim 8 , further comprising:

one or more decimation filters for filtering the digital output of the multi-stage ADC and generating a decimated digital output;

wherein the digital quantization noise cancellation filter filters the decimated digital output.

17. The system of claim 8 , further comprising:

a normalization block for normalizing the coefficients of the cross-correlation function to a gain coefficient.

18. The system of claim 8 , further comprising:

a microprocessor on-chip with the multi-stage ADC for controlling the cross-correlation hardware block, reading the coefficients of the cross-correlation function from the cross-correlation hardware block, and programming the digital quantization noise cancellation filter.

19. The system of claim 8 , wherein the multi-stage ADC is a continuous time multi-stage noise shaping ADC.

20. An apparatus comprising:

a plurality of continuous-time analog-to-digital converters (ADCs) in cascade;

means for generating a sequence which approaches an impulse response and injecting the sequence to a quantizer of a first ADC of the plurality of ADCs;

means for computing coefficients of a cross-correlation function between the sequence and a given digital output of one of the plurality of ADCs; and

means for digital quantization noise cancellation which is programmable based on the coefficients of the cross-correlation function.