Fractional Fourier Transform (FrFT)-based spectrum analyzers and spectrum analysis techniques are disclosed. Rather than using the standard Fast Fourier Transform (FFT), the FrFT may be used to view the signal content contained in a particular bandwidth. Usage of the FrFT in place of the frequency or time domain allows viewing of the signal in different dimensions, where “spectral” features of interest, or signal content, may appear where they were not visible in these domains before. This may allow signals to be identified and viewed in any domain within the continuous time-frequency plane, and may significantly enhance the ability to detect and extract signals that were previously hidden under interference and/or noise, provide or enhance the ability to extract signals from a congested environment, and enable operation in a signal-dense environment.

An infinite impulse response filter includes a plurality of lower order filter stages and a random number generator circuit. The plurality of lower order filter stages include a first filter stage coupled to a second filter stage. The random number generator circuit includes a first output coupled to the first filter stage and a second output coupled to the second filter stage. The random number generator circuit is configured to generate the same random value at both the first output and the second output. The infinite impulse response filter is an n.sup.th-order filter. The respective order of each of the lower order filter stages is less than n.

An analysis filter bank corresponding to a plurality of sub-bands, comprising: multiple sub-filters with different center frequencies which perform multiple complex-type first-order infinite impulse response filtering operations on an audio input signal to generate multiple sub-filter signals; a first set of binomial combiners, each of which performs a weighted-sum operation on a first number of the sub-filter signals with a first set of binomial weights to generate one of multiple sub-band signals; a second set of binomial combiners, each of which performs a weighted-sum operation on a second number of the sub-filter signals with a second set of binomial weights to generate one of multiple lower sub-band-edge signals or one of multiple higher sub-band-edge signals; and multiple envelope detection with decimation devices, which perform multiple envelope detection with decimation operations on the sub-band signals, the lower sub-band-edge signals, and the higher sub-band-edge signals to generate multiple fine spectrums.

An infinite impulse response filter includes a plurality of lower order filter stages and a random number generator circuit. The plurality of lower order filter stages include a first filter stage coupled to a second filter stage. The random number generator circuit includes a first output coupled to the first filter stage and a second output coupled to the second filter stage. The random number generator circuit is configured to generate the same random value at both the first output and the second output. The infinite impulse response filter is an n.sup.th-order filter. The respective order of each of the lower order filter stages is less than n.

An electric digital received signal obtained from a received optical signal is segmented into blocks of a certain length with an overlap of a length determined in advance with an adjacent block. Fourier transformation is performed for each of the blocks. The blocks subjected to the Fourier transformation are stored consecutively in time series, a coefficient determined based on a wavelength dispersion compensation amount according to one of frequency positions and a delay amount according to one of the frequency positions and one of time positions is applied to each of frequency component values included in a plurality of the stored blocks, and the blocks to which the coefficient has been applied and which are obtained by adding up the frequency component values to which the coefficient has been applied for each of the frequency positions are generated. Inverse Fourier transformation is performed on the generated blocks to which the coefficient has been applied. A part of the overlap subjected to the inverse Fourier transformation is removed.

A method for acquiring a fingerprint image through a fingerprint image acquisition apparatus is provided. The method includes recognizing a finger of an user through a sensor included in the apparatus to generate an initial input fingerprint image when the finger contacts with a biometric recognition area of the display unit, acquiring a converted fingerprint image by converting the initial input fingerprint image in a pre-determined manner to reveal a characteristic of a pattern, included within the initial input fingerprint image, corresponding to a pattern signal reflected from at least a part of the display unit. The method further includes selecting a pattern removal fingerprint image, if a learned pattern image is stored in a memory, from the learned pattern image based on similarity. The similarity is calculated between the converted fingerprint image and a converted reference image.

An audio processing system and method of operating the system are provided. The system includes a memory storing a plurality of frequency domain sound recording samples represented and stored in a frequency domain and being previously converted from a plurality of sound recording samples represented in a time domain. The system also includes at least one processing unit coupled to the memory and is configured to read the plurality of frequency domain sound recording samples from the memory. The at least one processing unit is also configured to process the plurality of frequency domain sound recording samples.

A method and an apparatus for signal processing: implementing step-by-step orthogonal decomposition of an original signal to be inputted; on the basis of the number of layers of orthogonal decomposition and the edge high frequency bandwidth of the original signal after orthogonal decomposition, generating a finite-length unit impulse response FIR filter; using the FIR filter to filter the edge high-frequency signal of the original signal; and, after passing the signal obtained after filtering and the low frequency signal obtained at each stage of orthogonal decomposition through an orthogonal filter bank, implementing signal synthesis processing.

An example process includes reducing a quality factor of a first tunable bandpass filter, used, for example, in a low-noise amplifier stage of a polar receiver. A first wideband test signal centered at a desired center frequency of a second tunable bandpass filter is received. A frequency response of the second tunable bandpass filter to the first wideband test signal is estimated using a Fast Fourier Transform (FFT) signal processor. At least a resonant frequency or a quality factor of the second tunable bandpass filter are calibrated based at least in part on a portion of the estimated frequency response of the second tunable bandpass filter obtained from the FFT signal processor. Frequency response characteristics of the first tunable bandpass filter may be similarly tuned in accordance with the example process.

This application relates to a signal filtering device. The device includes a memory and a processor. The processor may generate one or more matrices based on a size of a digital filter bank that generates an output signal by dividing an input signal into a plurality of channels and store in the memory each of the generated one or more matrices to which a plurality of digital filter bank coefficients or a plurality of input signals are assigned. The processor may also partially calculate the stored plurality of digital filter bank coefficients and the plurality of signals based on a number of at least some of the plurality of channels, and calculate the calculated digital filter bank coefficients and signals. The processor may further perform a discrete Fourier transform (DFT) on the calculated signal and compensate for a phase of the discrete Fourier transformed signal according to a preset reference.