A navigation device including a digital filter configured to smooth tracking is provided. The digital filter is configured to sequentially receive input data and output a tap sum, and calculate a quotient and a remainder by dividing an accumulation value with an average number, wherein the remainder is feedback to the tap sum for updating the accumulation value and the quotient is configured as output data.

A zero-insertion FIR filter architecture for filtering a signal with a target band and a secondary band. Digital filter circuitry includes an L-tap FIR (finite impulse response) filter, with a number L filter tap elements (L=0, 1, 2, . . . (L1)), each with an assigned coefficient from a defined coefficient sequence. The L-tap FIR filter is configurable with a defined zero-insertion coefficient sequence of a repeating sub-sequence of a nonzero coefficient followed by one or more zero-inserted coefficients, with a number Nj of nonzero coefficients, and a number Nk of zero-inserted coefficients, so that L=Nj+Nk. The L-tap FIR filter is configurable as an M-tap FIR filter with a nonzero coefficient sequence in which each of the L filter tap elements is assigned a non-zero coefficient, the M-tap FIR filter having an effective length of M=(Nj+Nk) non-zero coefficients.

A navigation device including a digital filter configured to smooth tracking is provided. The digital filter is configured to sequentially receive input data and output a tap sum, and calculate a quotient and a remainder by dividing an accumulation value with an average number, wherein the remainder is feedback to the tap sum for updating the accumulation value and the quotient is configured as output data.

A method includes receiving an input digital signal and applying the input digital signal to digital filter processing with a corner frequency to produce a filtered output digital signal. The digital filter processing includes a set of multiplication operations using a set of filter multiplication coefficients. The set of multiplication operations is performed by alternately using a first set of approximate multiplication coefficients and a second set of approximate multiplication coefficients different from the first set of approximate multiplication coefficients. The approximate multiplication coefficients in the first set of approximate multiplication coefficients and the second set of approximate multiplication coefficients approximate multiplication coefficients in the set of filter multiplication coefficients as a function of negative power-of-two values. The alternating of multiplication operations results in digital filter processing with average corner frequency approximating the corner frequency.

Provided is a digital filter circuit in which a filter coefficient can be easily changed, for which circuit scale and power consumption can be reduced, and which carries out digital filter processing in a frequency domain. This digital filter circuit includes: a separating circuit for separating a first complex number signal, of a frequency domain that was subjected to Fourier transform, into a real number portion and an imaginary number portion; a filter coefficient generating circuit for generating a first frequency domain filter coefficient from a first input filter coefficient and a third input filter coefficient, and for generating a second frequency domain filter coefficient from a second input filter coefficient and the third input filter coefficient; a first filter that filters the separated real number portion using the first frequency domain filter coefficient; a second filter that filters the separated imaginary number portion using the second frequency domain filter coefficient; and a combining circuit for combining the output from the two filters.

A system and method for representing quasi-periodic waveforms, for example, representing a plurality of limited decompositions of the quasi-periodic waveform. Each decomposition includes a first and second amplitude value and at least one time value. In some embodiments, each of the decompositions is phase adjusted such that the arithmetic sum of the plurality of limited decompositions reconstructs the quasi-periodic waveform. Data-structure attributes are created and used to reconstruct the quasi-periodic waveform. Features of the quasi-periodic wave are tracked using pattern-recognition techniques. The fundamental rate of the signal (e.g., heartbeat) can vary widely, for example by a factor of 2-3 or more from the lowest to highest frequency. To get quarter-phase representations of a component (e.g., lowest frequency rate component) that varies over time (by a factor of two to three) many overlapping filters use bandpass and overlap parameters that allow tracking the component's frequency version on changing quarter-phase basis.

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 method for setting a filter frequency response includes: dividing a target frequency band into multiple first partial bands at a frequency corresponding to an intersection between a first line representative of a target spectrum envelope and a second line representative of a first spectrum envelope derived from smoothing a measured frequency spectrum; and setting a frequency response of a filter corresponding to a first partial band specified by an operator from among the multiple first partial bands, in accordance with a setting operation for setting an adjustment amount performed by the operator with respect to the specified first partial band.

A method of designing a digital filter for example for use in an FBMC/OQAM telecommunications system, with a target overlapping factor and meeting a specified signal to interference ratio is described, whereby a candidate filter design defined by an impulse response, satisfying the Nyquist criterion and having an overlapping factor higher than the target is selected, and the time and frequency coefficients of its impulse response inverted to define a new filter design; and truncating the impulse response defining said new filter design to the minimum number of coefficients achieving said specified signal to interference ratio.

Systems and methods are provided for de-noising seismic data recorded by seismic receivers. A first portion of the seismic data having a first signal-to-noise ratio (SNR) to is processed to generate a de-noising operator or function. The de-noising operator is applied to a second portion of seismic data having a second SNR to remove noise from the second portion of the seismic data, where the first SNR is greater than the second SNR.