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Related Concept Videos

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...
Fast Fourier Transform01:10

Fast Fourier Transform

The Fast Fourier Transform (FFT) is a computational algorithm designed to compute the Discrete Fourier Transform (DFT) efficiently. By breaking down the calculations into smaller, manageable sections, the FFT significantly reduces the computational complexity involved. Direct computation of an N-point DFT requires N2 complex multiplications, whereas the FFT algorithm needs only (N/2)log⁡2N multiplications, offering a much faster performance.
The computational efficiency of the FFT becomes...
Continuous -time Fourier Transform01:11

Continuous -time Fourier Transform

The Fourier series is instrumental in representing periodic functions, offering a powerful method to decompose such functions into a sum of sinusoids. This technique, however, necessitates modification when applied to nonperiodic functions. Consider a pulse-train waveform consisting of a series of rectangular pulses. When these pulses have a finite period, they can be accurately represented by a Fourier series. Yet, as the period approaches infinity, resulting in a single, isolated pulse, the...
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]...
Relation of DFT to z-Transform01:20

Relation of DFT to z-Transform

The Discrete Fourier Transform (DFT) is a crucial tool for analyzing the frequency content of discrete-time signals. It converts a sequence of N samples from the time domain into its corresponding sequence in the frequency domain, where each sample represents a specific frequency component.
To understand how the DFT works, it's helpful to consider the z-transform, which is a method for representing discrete sequences in the complex frequency domain. The z-transform involves summing the terms of...

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Updated: Jun 16, 2026

A Multimodal Wide-Field Fourier-Transform Raman Microscope
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Digital fourier transforms as means for scanner evaluation.

H C Andrews

    Applied Optics
    |February 4, 2010
    PubMed
    Summary
    This summary is machine-generated.

    Fourier transforms can evaluate digital image scanner performance by analyzing frequency axes. Perfectly aligned energy often indicates human influence, while windowing and jitter effects are also identifiable in scanned imagery.

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    Area of Science:

    • Digital Image Processing
    • Signal Analysis

    Background:

    • Evaluating digital image scanner performance is crucial for accurate data acquisition.
    • Traditional methods may not fully capture subtle performance degradations.
    • Understanding artifacts in scanned imagery is essential for reliable analysis.

    Purpose of the Study:

    • To illustrate the application of Fourier transforms for digital image scanner performance evaluation.
    • To identify and interpret man-induced artifacts in scanned imagery.
    • To demonstrate image enhancement techniques using a priori knowledge.

    Main Methods:

    • Analysis of Fourier energy distribution along horizontal and vertical frequency axes.
    • Examination of windowing, scanner jitter, and aperture effects in laser scanner systems.
    • Application of a nonlinear space domain transformation for noise reduction.

    Main Results:

    • Fourier energy alignment along frequency axes suggests man-induced artifacts.
    • Specific examples demonstrate the impact of windowing and jitter on scanned imagery.
    • A priori knowledge-based nonlinear transformation effectively reduces noise.

    Conclusions:

    • Fourier transform analysis provides a valuable tool for assessing digital image scanner performance.
    • Identifying artifact sources like jitter and windowing is critical for image quality.
    • Image enhancement using a priori knowledge offers a practical approach to noise reduction.