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Discrete-Time Fourier Series

Discrete-Time Fourier Series

The Discrete-Time Fourier Series (DTFS) is a fundamental concept in signal processing, serving as the discrete-time counterpart to the continuous-time Fourier series. It allows for the representation and analysis of discrete-time periodic signals in terms of their frequency components. Unlike its continuous counterpart, which utilizes integrals, the calculation of DTFS expansion coefficients involves summations due to the discrete nature of the signal.
For a discrete-time periodic signal x[n]...

Discrete Fourier Transform

Discrete Fourier Transform

The Discrete Fourier Transform (DFT) is a fundamental tool in signal processing, extending the discrete-time Fourier transform by evaluating discrete signals at uniformly spaced frequency intervals. This transformation converts a finite sequence of time-domain samples into frequency components, each representing complex sinusoids ordered by frequency. The DFT translates these sequences into the frequency domain, effectively indicating the magnitude and phase of each frequency component present...

Discrete-time Fourier transform

Discrete-time Fourier transform

The Discrete-Time Fourier Transform (DTFT) is an essential mathematical tool for analyzing discrete-time signals, converting them from the time domain to the frequency domain. This transformation allows for examining the frequency components of discrete signals, providing insights into their spectral characteristics. In the DTFT, the continuous integral used in the continuous-time Fourier transform is replaced by a summation to accommodate the discrete nature of the signal.
One of the notable...

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Related Experiment Video

Updated: Mar 28, 2026

High Content Screening Analysis to Evaluate the Toxicological Effects of Harmful and Potentially Harmful Constituents HPHC

High Content Screening Analysis to Evaluate the Toxicological Effects of Harmful and Potentially Harmful Constituents HPHC

Published on: May 10, 2016

Predicting GHS toxicity using RTCA and discrete-time Fourier transform.

Jiao Chen^1,2, Tianhong Pan¹, Tianqing Pu¹

¹* School of Electrical & Information Engineering, Jiangsu University, Zhenjiang, Jiangsu 212013, China.

Journal of Bioinformatics and Computational Biology

|December 29, 2015

Summary

This summary is machine-generated.

A new in vitro toxicity testing method uses discrete-time Fourier transform (DTFT) to analyze dynamic cell data. This approach, using the DC component, accurately predicts rodent oral toxicity, reducing animal use in studies.

Keywords:

Discrete-time Fourier transform (DTFT)globally harmonized system (GHS)high-throughput screening (HTS)in vitro toxicity assay registry of cytotoxicity (RC)time-dependent cellular response curve (TCRC)

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Developmental Toxicity Assay Based on Real-Time Monitoring of Fibroblast Growth Factor Signal Disruption in Human Induced Pluripotent Stem Cells

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Published on: October 10, 2025

Area of Science:

Toxicology
Cell Biology
Biotechnology

Background:

Traditional cytotoxicity assays like LC50 can be time-dependent and lack accuracy.
Technological advancements allow for dynamic data collection on cell health and proliferation.
Validating in vitro methods against in vivo results is crucial for regulatory acceptance.

Purpose of the Study:

To develop and validate a novel in vitro method for assessing cytotoxicity.
To establish a reliable toxicity index using dynamic cell data analysis.
To compare the accuracy of the new method with established in vivo toxicity data.

Main Methods:

Utilized discrete-time Fourier transform (DTFT) to analyze time-domain cell index data.
Extracted the direct current (DC) component of the DTFT as a cytotoxicity feature.
Calculated a novel toxicity index (DC50) based on the DC component.
Validated results against data from The Interagency Coordinating Committee on the Validation of Alternative Method (ICCVAM) report.

Main Results:

The novel DC50 index effectively reflects cytotoxicity intensity.
Results showed favorable agreement with ICCVAM data for predicting rodent acute systemic toxicity.
The method demonstrated accuracy in estimating acute rodent oral toxicity.

Conclusions:

The DTFT-based in vitro toxicity assessment method provides an accurate alternative to traditional assays.
The DC50 index offers a reliable measure of cytotoxicity, correlating well with in vivo outcomes.
This method supports higher throughput screening and reduces the need for animal testing in toxicity studies.