Trans-filter/Detectors are extremely sensitive circuits that recover exponentially modulated signals buried in noise. They can be used wherever Matched Filter/Coherent Detectors are used and operate at negative input signal-to-noise ratios to recover RADAR, SONAR, communications, or data signals, as well as reduce phase noise of precision oscillators. Input signal and noise is split into two paths where complementary derivatives are extracted. Outputs of the two paths are equal in amplitude and 180 degrees relative to each other at the band center frequency. The outputs are summed, causing stationary in-band noise to be reduced by cancellation while exponentially modulated signals are undiminished. Trans-filters are Linear Time Invariant circuits, have no noise x noise threshold and can be cascaded, increasing output signal-to-noise ratio prior to detection. Trans-filters are most sensitive to all types of digital modulation, producing easily detected polarized pulses synchronous with data transitions. Trans-filters do not require coherent conversion oscillators and complex synchronizing circuits.

Trans-filter/Detectors are extremely sensitive circuits that recover exponentially modulated signals buried in noise. They can be used wherever Matched Filter/Coherent Detectors are used and operate at negative input signal-to-noise ratios to recover RADAR, SONAR, communications, or data signals, as well as reduce phase noise of precision oscillators. Input signal and noise is split into two paths where complementary derivatives are extracted. Outputs of the two paths are equal in amplitude and 180 degrees relative to each other at the band center frequency. The outputs are summed, causing stationary in-band noise to be reduced by cancellation while exponentially modulated signals are undiminished. Trans-filters are Linear Time Invariant circuits, have no noise x noise threshold and can be cascaded, increasing output signal-to-noise ratio prior to detection. Trans-filters are most sensitive to all types of digital modulation, producing easily detected polarized pulses synchronous with data transitions. Trans-filters do not require coherent conversion oscillators and complex synchronizing circuits.

A digital control circuitry for a MEMS gyroscope is provided. The digital control circuitry comprises a digital primary loop circuitry configured to process a digitized primary signal, a digital secondary loop circuitry configured to process a digitized secondary signal and a digital phase shifting filter circuitry configured to generate two phase shifted demodulation signals from the digitized primary signal. The digital secondary loop is configured to demodulate the digitized secondary signal using the two phase shifted demodulation signals.

A transmitter that reduces 3.sup.rd order harmonic (HD3) and inter modulation distortion (IMD3) for a gm stage of a mixer while reducing flicker noise is disclosed. The transmitter may include a balanced mixer, a transconductance stage connected to the mixer, and a bias circuit. The bias circuit may include a programmable current source configured to provide a reference current. Further, the bias circuit may include a replica circuit configured to replicate a DC signal of the transconductance stage. The bias circuit may also include a bias transistor configured to level shift a bias signal obtained from a signal source based on the reference current and the DC signal of the transconductance stage as determined from the replica circuit.

A transmitter that reduces 3.sup.rd order harmonic (HD3) and inter modulation distortion (IMD3) for a gm stage of a mixer while reducing flicker noise is disclosed. The transmitter may include a balanced mixer, a transconductance stage connected to the mixer, and a bias circuit. The bias circuit may include a programmable current source configured to provide a reference current. Further, the bias circuit may include a replica circuit configured to replicate a DC signal of the transconductance stage. The bias circuit may also include a bias transistor configured to level shift a bias signal obtained from a signal source based on the reference current and the DC signal of the transconductance stage as determined from the replica circuit.

Trans-filter/Detectors are extremely sensitive circuits that recover exponentially modulated signals buried in noise. They can be used wherever Matched Filter/Coherent Detectors are used and operate at negative input signal-to-noise ratios to recover RADAR, SONAR, communications, or data signals, as well as reduce phase noise of precision oscillators. Input signal and noise is split into two paths where complementary derivatives are extracted. Outputs of the two paths are equal in amplitude and 180 degrees relative to each other at the band center frequency. The outputs are summed, causing stationary in-band noise to be reduced by cancellation while exponentially modulated signals are undiminished. Trans-filters are Linear Time Invariant circuits, have no noise×noise threshold and can be cascaded, increasing output signal-to-noise ratio prior to detection. Trans-filters are most sensitive to all types of digital modulation, producing easily detected polarized pulses synchronous with data transitions. Trans-filters do not require coherent conversion oscillators and complex synchronizing circuits.

Trans-filter/Detectors are extremely sensitive circuits that recover exponentially modulated signals buried in noise. They can be used wherever Matched Filter/Coherent Detectors are used and operate at negative input signal-to-noise ratios to recover RADAR, SONAR, communications or data signals. Input signal and noise is split into two paths where complementary derivatives are extracted. Outputs of the two paths are equal in amplitude and 180 degrees relative to each other at the band center frequency. The outputs are summed, causing stationary in-band noise to be reduced by cancellation while exponentially modulated signals are increased by addition. Trans-filters are Linear Time Invariant circuits, have no noise×noise threshold and can be cascaded, increasing in-band signal-to-noise ratio prior to detection. Trans-filters are most sensitive to all types of digital modulation, producing easily detected polarized pulses synchronous with data transitions. Trans-filters do not require coherent conversion oscillators and complex synchronizing circuits.

A universal nonlinear variable delay filter includes a first mixer configured to convert an input signal to an up-converted signal including a frequency corresponding to a selected time delay. The input signal includes an original frequency. The variable delay filter also includes a nonlinear filter that filters the up-converted signal and generates a delayed signal that is delayed by the selected time delay. The variable delay filter further includes a second mixer configured to convert the delayed signal to a down-converted signal including a frequency substantially equal to the original frequency.

Trans-filter/Detectors are extremely sensitive circuits that recover exponentially modulated signals buried in noise. They can be used wherever Matched Filter/Coherent Detectors are used and operate at negative input signal-to-noise ratios to recover RADAR, SONAR, communications or data signals. Input signal and noise is split into two paths where complementary derivatives are extracted. Outputs of the two paths are equal in amplitude and 180 degrees relative to each other at the band center frequency. The outputs are summed, causing stationary in-band noise to be reduced by cancellation while exponentially modulated signals are increased by addition. Trans-filters are Linear Time Invariant circuits, have no noise x noise threshold and can be cascaded, increasing in-band signal-to-noise ratio prior to detection. Trans-filters are most sensitive to all types of digital modulation, producing easily detected polarized pulses synchronous with data transitions. Trans-filters do not require coherent conversion oscillators and complex synchronizing circuits.

A digital control circuitry for a MEMS gyroscope is provided. The digital control circuitry comprises a digital primary loop circuitry configured to process a digitized primary signal, a digital secondary loop circuitry configured to process a digitized secondary signal and a digital phase shifting filter circuitry configured to generate two phase shifted demodulation signals from the digitized primary signal. The digital secondary loop is configured to demodulate the digitized secondary signal using the two phase shifted demodulation signals.