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Related Concept Videos

Discrete-time Fourier transform01:26

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...
Discrete-Time Fourier Series01:20

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]...
Basic Discrete Time Signals01:16

Basic Discrete Time Signals

The unit step sequence is defined as 1 for zero and positive values of the integer n. This sequence can be graphically displayed using a set of eight sample points, showing a step function starting from n=0 and remaining constant thereafter.
The unit impulse or sample sequence is mathematically expressed as zero for all n values except at n=0, where it is one. The unit impulse sequence, denoted by δ(n), is the first difference of the unit step sequence, while the unit step sequence u(n) is the...
Sampling Continuous Time Signal01:11

Sampling Continuous Time Signal

In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
In the...
Discrete Fourier Transform01:15

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...
Reconstruction of Signal using Interpolation01:10

Reconstruction of Signal using Interpolation

Signal processing techniques are essential for accurately converting continuous signals to digital formats and vice versa. When a continuous signal is sampled with a period T, the resulting sampled signal exhibits replicas of the original spectrum in the frequency domain, spaced at intervals equal to the sampling frequency. To handle this sampled signal, a zero-order hold method can be applied, which creates a piecewise constant signal by retaining each sample's value until the next sampling...

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Related Experiment Video

Updated: May 11, 2026

DNA-Tethered RNA Polymerase for Programmable In vitro Transcription and Molecular Computation
09:26

DNA-Tethered RNA Polymerase for Programmable In vitro Transcription and Molecular Computation

Published on: December 29, 2021

Discrete-time signal processing with DNA.

Hua Jiang1, Sayed Ahmad Salehi, Marc D Riedel

  • 1Department of Electrical Engineering, University of Minnesota, Minneapolis, MN 55455, United States.

ACS Synthetic Biology
|May 10, 2013
PubMed
Summary
This summary is machine-generated.

This study introduces molecular reactions for signal processing, enabling filters and transforms like the Fast Fourier Transform (FFT) using DNA. These molecular computations are robust and have potential in biochemical sensing and drug delivery.

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Last Updated: May 11, 2026

DNA-Tethered RNA Polymerase for Programmable In vitro Transcription and Molecular Computation
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Published on: December 29, 2021

Plasmid-derived DNA Strand Displacement Gates for Implementing Chemical Reaction Networks
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Published on: November 25, 2015

Automated Robotic Liquid Handling Assembly of Modular DNA Devices
11:22

Automated Robotic Liquid Handling Assembly of Modular DNA Devices

Published on: December 1, 2017

Area of Science:

  • Biochemistry
  • Molecular Biology
  • Computational Biology

Background:

  • Discrete-time signal processing is crucial in many fields.
  • Implementing complex computations using molecular reactions remains a significant challenge.
  • Existing molecular computing approaches often lack robustness or require precise reaction rate control.

Purpose of the Study:

  • To develop a methodology for implementing discrete-time signal processing operations using molecular reactions.
  • To demonstrate the feasibility of molecular filters and transforms.
  • To explore robust computation independent of precise reaction rates.

Main Methods:

  • Designing molecular reaction networks to perform signal processing functions.
  • Implementing two approaches: clock-synchronized (using chemical oscillations) and self-timed (asynchronous).
  • Translating abstract molecular reactions into DNA strand displacement reactions and validating through mass-action simulations.

Main Results:

  • Successful synthesis of molecular moving-average filters, biquad filters, and Fast Fourier Transforms (FFTs).
  • Demonstrated robustness of molecular computations, independent of reaction rates within coarse categories.
  • Validated computational accuracy through DNA kinetics simulations.

Conclusions:

  • Molecular reactions can be reliably used to implement discrete-time signal processing operations.
  • This proof-of-concept opens avenues for molecular computing in biochemical sensing and targeted drug delivery.
  • The developed methodology offers a robust and scalable approach for future molecular signal processing applications.