Abstract: An RF signal is processed by coupling an input signal into a signal loop, the signal loop comprising a resonator and a processing block, and filtering the input signal in the signal loop to produce an output signal by obtaining a plurality of resonator outputs from the resonator and processing the plurality of resonator outputs to generate feedback signals. The feedback signals are connected to a point upstream of the resonator. At least one of the plurality of resonator outputs is processed in the processing block. The signal loop is definable by a transfer function having poles, and the plurality of resonator outputs are processed such that the poles of the transfer function are independently controllable.

Abstract: A method and apparatus for generating an RF signal uses digital signal components to generate a synthesized RF signal having a plurality of frequency components. An analog filter is used to filter the synthesized RF signal. The analog filter is a tunable, active feedback circuit having one or more variable resonators and a variable gain block connected in a signal loop that is defined by a passband. The analog filter is tuned such that the passband of the analog filter overlaps one or more desired frequency components of the plurality of frequency components of the synthesized RF signal, and such that the passband has a relative bandwidth of about 1% or less.

Abstract: A method of stabilizing a variable filter for an analog electromagnetic signal against circuit oscillation includes the steps of: providing a signal loop comprising a signal input, a signal output, and a plurality of variable circuit elements connected in the signal loop, the plurality of variable circuit elements comprising an adjustable resonator and an adjustable gain block, the signal loop having a variable frequency response that is characterized by a central frequency, a frequency passband, a response Q, and an operating point and a resonator response curve that are plottable in a Cartesian s-plane having an origin, a real axis, and an imaginary axis; and maintaining stability of the variable filter within an operating range by controlling the adjustable resonator and the adjustable gain block such that, in the Cartesian s-plane, the resonator response curve satisfies an orthogonality stability condition.

Abstract: An oscillator has a feedback loop with a signal output, a multi-pole resonator, and a gain block. The gain block applies a gain sufficient to generate a stable oscillation signal at the signal output; and the multi-pole resonator is tunable between two or more resonance modes.

Abstract: A method and apparatus for generating an RF signal uses digital signal components to generate a synthesized RF signal having a plurality of frequency components. An analog filter is used to filter the synthesized RF signal. The analog filter is a tunable, active feedback circuit having one or more variable resonators and a variable gain block connected in a signal loop that is defined by a passband. The analog filter is tuned such that the passband of the analog filter overlaps one or more desired frequency components of the plurality of frequency components of the synthesized RF signal, and such that the passband has a relative bandwidth of about 1% or less.

Abstract: An RF signal is tuned by: producing a first signal at a first frequency using a digital sequence generator; filtering the first signal using a frequency-tunable tracking filter that is tuned to the first frequency, the tracking filter comprising one or more variable resonators; tuning the tracking filter from the first frequency to a second frequency over a transition period; and tuning the first signal to the second frequency by causing the digital sequence generator to transition between two or more states during the transition period. The two or more states are selected such that, immediately after the transition period, the analog signal substantially matches a desired steady state at the second frequency.

Abstract: An active feedback RF resonator has a signal loop having a signal input and a signal output. The signal loop has a variable gain stage and at least one variable resonator, each variable resonator comprising an inductance element and a variable capacitance element comprising a number of switched fixed value capacitors and a variable capacitor. A phase noise of the active feedback RF signal has a maximum value for an operating frequency of the variable resonator that is based on an operating range of the variable capacitor.

Abstract: An RF signal is processed by coupling an input signal into a signal loop, the signal loop comprising a resonator and a processing block, and filtering the input signal in the signal loop to produce an output signal by obtaining a plurality of resonator outputs from the resonator and processing the plurality of resonator outputs to generate feedback signals. The feedback signals are connected to a point upstream of the resonator. At least one of the plurality of resonator outputs is processed in the processing block. The signal loop is definable by a transfer function having poles, and the plurality of resonator outputs are processed such that the poles of the transfer function are independently controllable.

Abstract: A method and apparatus for modifying or controlling a resonator connected to a signal loop having an input, an output, and a closed loop frequency response. The signal loop has a primary resonator having a primary frequency response. There is at least one adjustable resonator having an adjustable frequency and a secondary Q-factor. An adjustable scaling block applies a gain factor. A controller is connected to the at least one adjustable resonator and the adjustable scaling block. The controller has instructions to adjust the closed loop frequency response toward a desired closed loop frequency response by controlling the adjustable frequency of the at least one adjustable resonator and the gain factor of the adjustable scaling block.

Abstract: A method and apparatus for modifying or controlling a resonator connected to a signal loop having an input (18828), an output (18822), and a closed loop frequency response. The signal loop has a primary resonator (18810) having a primary frequency response. There is at least one adjustable resonator (18812) having an adjustable frequency (f) and a secondary Q-factor. An adjustable scaling block (18824) applies a gain factor (g). A controller is connected to the at least one adjustable resonator (18812) and the adjustable scaling block (18824). The controller has instructions to adjust the closed loop frequency response toward a desired closed loop frequency response by controlling the adjustable frequency (f) of the at least one adjustable resonator (18812) and the gain factor (g) of the adjustable scaling block (18824).

Abstract: A variable filter and method of switching a resonant frequency of the variable filter from an initial frequency to a desired frequency, where the variable filter has a tunable frequency and a variable Q. With the variable filter operating at the initial frequency and an initial Q, the variable filter is Q-spoiled toward a low-Q state. The variable filter is tuned toward the desired frequency and the tunable resonator is Q-enhanced from the low-Q state to achieve a desired filter response.

Abstract: A method of stabilizing a variable filter for an analog electromagnetic signal against circuit oscillation includes the steps of: providing a signal loop comprising a signal input, a signal output, and a plurality of variable circuit elements connected in the signal loop, the plurality of variable circuit elements comprising an adjustable resonator and an adjustable gain block, the signal loop having a variable frequency response that is characterized by a central frequency, a frequency passband, a response Q, and an operating point and a resonator response curve that are plottable in a Cartesian s-plane having an origin, a real axis, and an imaginary axis; and maintaining stability of the variable filter within an operating range by controlling the adjustable resonator and the adjustable gain block such that, in the Cartesian s-plane, the resonator response curve satisfies an orthogonality stability condition.

Abstract: A variable filter for an RF circuit has a signal loop comprising a signal input port and a signal output port, and a plurality of circuit elements connected within the signal loop. The plurality of circuit elements comprise a multi-pole resonator comprising a plurality of frequency tunable resonators and an adjustable scaling block that applies a gain factor. Adjacent frequency tunable resonators within the multi-pole resonator are reciprocally coupled. A controller is connected to tune the multi-pole resonator and to adjust the gain factor of the adjustable scaling block such that the signal loop generates a desired bandpass response.

Abstract: A variable filter and method of switching a resonant frequency of the variable filter from an initial frequency to a desired frequency, where the variable filter has a tunable frequency and a variable Q. With the variable filter operating at the initial frequency and an initial Q, the variable filter is Q-spoiled toward a low-Q state. The variable filter is tuned toward the desired frequency and the tunable resonator is Q-enhanced from the low-Q state to achieve a desired filter response.

Abstract: A variable filter has a signal loop defined between a signal input and a signal output. A plurality of circuit elements connected in the signal loop, the plurality of circuit elements comprising a frequency tunable resonator, and an adjustable scaling block that applies a gain factor that is adjustable in a range that comprises a positive gain and a negative gain. A controller is connected to 1) tune the frequency tunable resonator; and to 2) adjust the gain factor of the adjustable scaling block between a negative gain factor to a positive gain factor providing for variable Q independent of frequency.

Abstract: A method and apparatus for modifying or controlling a resonator connected to a signal loop having an input (18828), an output (18822), and a closed loop frequency response. The signal loop has a primary resonator (18810) having a primary frequency response. There is at least one adjustable resonator (18812) having an adjustable frequency (f) and a secondary Q-factor. An adjustable scaling block (18824) applies a gain factor (g). A controller is connected to the at least one adjustable resonator (18812) and the adjustable scaling block (18824). The controller has instructions to adjust the closed loop frequency response toward a desired closed loop frequency response by controlling the adjustable frequency (f) of the at least one adjustable resonator (18812) and the gain factor (g) of the adjustable scaling block (18824).

Abstract: A variable filter has a signal loop defined between a signal input and a signal output. A plurality of circuit elements connected in the signal loop, the plurality of circuit elements comprising a frequency tunable resonator, and an adjustable scaling block that applies a gain factor that is adjustable in a range that comprises a positive gain and a negative gain. A controller is connected to 1) tune the frequency tunable resonator; and to 2) adjust the gain factor of the adjustable scaling block between a negative gain factor to a positive gain factor providing for variable Q independent of frequency.

Abstract: A method and system for tracking mobile objects in a site are disclosed. The system comprises a computer cloud communicating with one or more imaging devices and one or more tag devices. Each tag device is attached to a mobile object, and has one or more sensors for sensing the motion of the mobile object. The computer cloud visually tracks mobile objects in the site using image streams captured by the imaging devices, and uses measurements obtained from tag devices to resolve ambiguity occurred in mobile object tracking. The computer cloud uses an optimization method to reduce power consumption of tag devices.

Abstract: A variable filter has a signal loop defined between a signal input and a signal output. A plurality of circuit elements connected in the signal loop, the plurality of circuit elements comprising a frequency tunable resonator, and an adjustable scaling block that applies a gain factor that is adjustable in a range that comprises a positive gain and a negative gain. A controller is connected to 1) tune the frequency tunable resonator; and to 2) adjust the gain factor of the adjustable scaling block between a negative gain factor to a positive gain factor providing for variable Q independent of frequency.

Abstract: A variable filter has a signal loop defined between a signal input and a signal output. A plurality of circuit elements connected in the signal loop, the plurality of circuit elements comprising a frequency tunable resonator, and an adjustable scaling block that applies a gain factor that is adjustable in a range that comprises a positive gain and a negative gain. A controller is connected to 1) tune the frequency tunable resonator; and to 2) adjust the gain factor of the adjustable scaling block between a negative gain factor to a positive gain factor providing for variable Q independent of frequency.