Method and system for a multi-rate analog finite impulse response filter

A modulator comprising:

• a first adder configured to receive an input signal and produce a first adder output therefrom;
• a quantizer configured to receive the first adder output and produce a quantized output;
• a second adder configured to receive the first adder output and the quantized output and produce a second adder output based upon the first adder output and the quantized output;
• a first two-unit delay configured to receive the second adder output as an input and produce a delayed output therefrom, the delayed output being provided as one input to the first adder forming a first feedback path;
• and
• a second two-unit delay configured to receive the delayed output and provide a second two unit-delay output to another input of the first adder, forming a second feedback path.

A method for modulating a signal, comprising:

• quantizing a first added signal to produce a quantized signal;
• adding the quantized signal and the first added signal to produce a second added signal;
• delaying the second added signal two clock cycles along a first feedback path to produce a first delayed signal;
• delaying the second added signal by four clock cycles alone a second feedback path to produce a second delayed signal;
• and
• substantially simultaneously adding the first delayed signal, the second delayed signal, and an input digital signal.