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Passive filters are utilized to shape the frequency spectrum of signals across a diverse array of applications. These filters, using only passive elements like resistors (R), inductors (L), and capacitors (C), are capable of selectively allowing or blocking certain frequency ranges without the need for external power sources.
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The innovation of touch-tone telephony revolutionized the telecommunications industry by replacing the traditional rotary dial with a dual-tone multi-frequency (DTMF) signaling system. This system uses a matrix-style keypad with buttons arranged in four rows and three columns, creating 12 distinct signals each assigned to a pair of frequencies. Each button press results in a simultaneous generation of two sinusoidal tones – one from a low-frequency group (697 to 941 Hz) and one from a...
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Frequency response analysis in electrical circuits provides vital insights into a circuit's behavior as the frequency of the input signal changes. The transfer function, a mathematical tool, is instrumental in understanding this behavior. It defines the relationship between phasor output and input and comes in four types: voltage gain, current gain, transfer impedance, and transfer admittance. The critical components of the transfer function are the poles and zeros.
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In signal processing, bandpass sampling is an effective technique for sampling signals that have most of their energy concentrated within a narrow frequency band. This type of signal is known as a bandpass signal. The key principle of bandpass sampling involves sampling the signal at a rate that is greater than twice the signal's bandwidth to prevent aliasing.
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Inductive circuits present intriguing challenges in electrical engineering, particularly during the transition from the time domain to the frequency domain. This transformation involves converting inductors into impedances and utilizing phasor representation.
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A unified approach for characterizing static/dynamic connectivity frequency profiles using filter banks.

Ashkan Faghiri1, Armin Iraji1, Eswar Damaraju1

  • 1Center for Translational Research in Neuroimaging and Data Science, Georgia State University, Georgia Institute of Technology, Emory University, Atlanta, GA, USA.

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Summary

Filter-banked connectivity (FBC) unifies static and dynamic brain network analysis. This novel approach reveals frequency-specific connectivity patterns missed by traditional methods, offering new insights into brain function in conditions like schizophrenia.

Keywords:
Dynamic connectivityFilter banksFrequencySchizophreniaStatic connectivityfMRI

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Area of Science:

  • Neuroscience
  • Functional Neuroimaging
  • Network Science

Background:

  • Static and dynamic functional network connectivity (FNC) are typically analyzed independently, limiting a comprehensive understanding of brain connectivity.
  • Existing methods, such as sliding-window approaches, may miss crucial frequency-dependent connectivity information.

Purpose of the Study:

  • To introduce filter-banked connectivity (FBC) as a unified method for analyzing both static and dynamic FNC across the full frequency spectrum.
  • To investigate the utility of FBC in identifying distinct network states and characterizing frequency profiles in brain activity.

Main Methods:

  • Developed and applied the FBC approach to estimate connectivity across multiple frequency bands.
  • Utilized a resting-state fMRI dataset from schizophrenia patients (SZ) and typical controls (TC).
  • Clustered FBC results into distinct network states and analyzed group differences in state occupancy based on frequency.

Main Results:

  • FBC successfully estimated connectivity across a wider frequency range compared to sliding-window methods.
  • Identified distinct network states, some characterized by low-frequency patterns not captured by traditional analyses.
  • Schizophrenia patients exhibited a tendency to occupy higher-frequency network states more than typical controls.

Conclusions:

  • FBC provides a novel, unified framework for analyzing static and dynamic functional network connectivity.
  • This approach offers valuable insights into the frequency-specific characteristics of brain connectivity patterns.
  • FBC can reveal group differences in dynamic connectivity, as demonstrated in the comparison between schizophrenia patients and typical controls.