A system for continuous-time signal processing comprising: a continuous-time analog-to-digital converter (CT ADC) that is configured to receive an analog input signal, determine time points at which the analog input signal crosses one of a plurality of quantization levels, and produce multiple digital signals representing the analog input signal, wherein the multiple digital signals include a first edge signal and a second edge signal associated with one of the plurality of quantization levels, the first edge signal changes being associated with an upward crossing of the quantization level and the second edge signal changes being associated with a downward crossing of the quantization level; and a continuous-time digital signal processor (CT DSP) coupled to the continuous-time analog-to-digital converter and configured to process the first edge signal and the second edge signal to provide a processed signal, wherein: the continuous-time digital signal processor further comprises: either a finite impulse filter (TTAP, b0,...,bM) configured to process each of the first edge signal and the second edge signal and sum the processed signals, and a continuous time DAC (CT DAC) configured to convert the summed processed signal to produce an analog output signal or, an analog summation filter (PULSE GEN, DELAY CELL,I0...I6) coupled to the continuous-time analog-to-digital converter, configured to convert each of the first edge signal and the second edge signal into analog signals and sum the analog signals to produce the analog output signal, wherein the analog summation circuit comprises a cascaded arrangement of delays (DELAY CELL) and charge pumps (PULSE GEN, I0...I6). a continuous-time analog-to-digital converter (CT ADC) that is configured to receive an analog input signal, determine time points at which the analog input signal crosses one of a plurality of quantization levels, and produce multiple digital signals representing the analog input signal, wherein the multiple digital signals include a first edge signal and a second edge signal associated with one of the plurality of quantization levels, the first edge signal changes being associated with an upward crossing of the quantization level and the second edge signal changes being associated with a downward crossing of the quantization level; and a continuous-time digital signal processor (CT DSP) coupled to the continuous-time analog-to-digital converter and configured to process the first edge signal and the second edge signal to provide a processed signal, wherein: the continuous-time digital signal processor further comprises: either a finite impulse filter (TTAP, b0,...,bM) configured to process each of the first edge signal and the second edge signal and sum the processed signals, and a continuous time DAC (CT DAC) configured to convert the summed processed signal to produce an analog output signal or, an analog summation filter (PULSE GEN, DELAY CELL,I0...I6) coupled to the continuous-time analog-to-digital converter, configured to convert each of the first edge signal and the second edge signal into analog signals and sum the analog signals to produce the analog output signal, wherein the analog summation circuit comprises a cascaded arrangement of delays (DELAY CELL) and charge pumps (PULSE GEN, I0...I6).