System and method for calibrating an analog-to-digital converter using a rational sampling frequency calibration digital-to-analog converter

An analog-to-digital conversion system, comprising:

• a clock generator configured to generate a first clock signal at a first frequency;
• an analog-to-digital converter (ADC) configured to convert an input analog signal to a digital signal, wherein the ADC operates based on the first clock signal at the first frequency;
• a calibration digital-to-analog converter (DAC) configured to generate an analog reference signal from digital reference data;
• a fractional rate clock generator configured to generate a second clock signal from the first clock signal or from a third clock signal, wherein the second clock signal is at a second frequency that is a fractional rate of the first frequency, and the calibration DAC operates at the second frequency, wherein the third clock signal is at a third frequency having an integer frequency relation with the first frequency;
• an equalizer configured to process an output of the ADC to remove a distortion incurred by the ADC;
• and
• an adaptation circuitry configured to generate coefficients for the equalizer based on the output of the ADC to the analog reference signal.