Abstract: A digital phase-quadrature oscillator generates a series of sine values representative of a sine wave, and a series of cosine values representative of a cosine wave. In each iteration of the oscillator, a sum of the squares of past sine and cosine values is used as a negative feedback term in synthesizing next sine and cosine values, in order to stabilize the amplitudes of the sine and cosine values.

Abstract: A digital phase-quadrature oscillator generates a series of sine values representative of a sine wave, and a series of cosine values representative of a cosine wave. In each iteration of the oscillator, a sum of the squares of past sine and cosine values is used as a negative feedback term in synthesizing next sine and cosine values, in order to stabilize the amplitudes of the sine and cosine values.

Abstract: A system and method to locate electronic marker balls includes receiving a signal representative of a detected marker ball. The signal includes the resolved in-phase and quadrature-phase (I and Q) components, each centered about a first frequency. The I and Q components are filtered in order to shift the first frequency to a second frequency and match the second frequency I and Q components to exponential decay characteristics associated with the marker balls. The second frequency I and Q components phase integrated in order to distinguish the components from noise. The integrating is based upon predetermined gain coefficients and produces integrated I and Q components in accordance with the predetermined gain coefficients. Next, a magnitude of the integrated I and Q components is determined to produce an I and Q magnitude vector and a noise variance associated with the magnitude vector is determined. Finally, the recursive coefficients are adjusted in accordance with the determined noise variance.