Circuit and method for encoding an analog signal to a stream of bits at an Analog to Digital Converter (ADC) and subsequent reconstruction of the original signal from the bit stream at a Digital to Analog Converter (DAC), where the ADC module samples the analog signal at a sub-Nyquist rate and encodes the samples to a stream of bits. The bit steam is subsequently used to reconstruct the Nyquist-rate samples of the original analog signal at the DAC. The ADC samples the input signal in one of the two realizations of non-uniform sampling, namely, Random Sampling (RS) and Level Crossing (LC) sampling techniques, according to embodiments of the disclosed invention.