A system for generating a sequence of sine wave output values separated by a fine time step, the system comprising: a fine time recursion block comprising a chain of fine phase propagation blocks, a plurality of the fine phase propagation blocks comprising: a slope input and a slope output; a frequency input and a frequency output; a phase input and a first phase output and a second phase output; a first adder, a second adder, each comprising a first input, a second input and an output; and a slope delay; wherein: the slope input is connected: through the slope delay to the slope output; and to a first input of the first adder; the frequency input is connected to the second input of the first adder; the output of the first adder is connected to the frequency output and to the first input of the second adder; the phase input is connected to the second input of the second adder; the output of the second adder is connected to the first phase output and to the second phase output; the slope output, a frequency output, and the first phase output of each of the plurality of fine phase propagation blocks connected to the slope input, the frequency input, and the phase input, respectively, of a subsequent fine phase propagation block in the chain; a plurality of sine generators, each sine generator having an input and an output, the inputs of the plurality of sine generators connected to the second phase outputs of the plurality of fine phase propagation blocks; and a plurality of delay blocks; each of the plurality of delay blocks having an input and an output, the inputs of the plurality of delay blocks being connected to the outputs of the plurality of sine generators. a fine time recursion block comprising a chain of fine phase propagation blocks, a plurality of the fine phase propagation blocks comprising: a slope input and a slope output; a frequency input and a frequency output; a phase input and a first phase output and a second phase output; a first adder, a second adder, each comprising a first input, a second input and an output; and a slope delay; wherein: the slope input is connected: through the slope delay to the slope output; and to a first input of the first adder; the frequency input is connected to the second input of the first adder; the output of the first adder is connected to the frequency output and to the first input of the second adder; the phase input is connected to the second input of the second adder; the output of the second adder is connected to the first phase output and to the second phase output; a slope input and a slope output; a frequency input and a frequency output; a phase input and a first phase output and a second phase output; a first adder, a second adder, each comprising a first input, a second input and an output; and a slope delay; wherein: the slope input is connected: through the slope delay to the slope output; and to a first input of the first adder; the frequency input is connected to the second input of the first adder; the output of the first adder is connected to the frequency output and to the first input of the second adder; the phase input is connected to the second input of the second adder; the output of the second adder is connected to the first phase output and to the second phase output; the slope input is connected: through the slope delay to the slope output; and to a first input of the first adder; through the slope delay to the slope output; and to a first input of the first adder; the frequency input is connected to the second input of the first adder; the output of the first adder is connected to the frequency output and to the first input of the second adder; the phase input is connected to the second input of the second adder; the output of the second adder is connected to the first phase output and to the second phase output; the slope output, a frequency output, and the first phase output of each of the plurality of fine phase propagation blocks connected to the slope input, the frequency input, and the phase input, respectively, of a subsequent fine phase propagation block in the chain; a plurality of sine generators, each sine generator having an input and an output, the inputs of the plurality of sine generators connected to the second phase outputs of the plurality of fine phase propagation blocks; and a plurality of delay blocks; each of the plurality of delay blocks having an input and an output, the inputs of the plurality of delay blocks being connected to the outputs of the plurality of sine generators.