Z-transform of quantized ramp signal

The z-transform of a ramp signal, with a rational slope, which is quantized by rounding down using the floor function, or rounding up using the ceiling function, is computed explicitly. The principles of rational sampling rate conversion are employed in modeling the signal. A multirate sample rate conversion system and a single-rate infinite impulse response (IIR) digital filter are also proposed for the division-free generation of the signal. The systems involve integer coefficients and operate using integer arithmetic. To produce a quantized ramp signal with a zero-valued intercept, the multirate system requires no form of multiplication.