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Related Concept Videos

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 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...
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]...
Characteristics of Series Resonant Circuit01:24

Characteristics of Series Resonant Circuit

Series resonance occurs in a circuit containing inductive (L), capacitive (C), and resistive (R) elements connected sequentially. At the resonance frequency, the inductive and capacitive reactances are equal in magnitude but opposite in sign, effectively canceling each other. This causes the circuit's impedance is minimal, primarily determined by the resistance R. The resonant frequency of an RLC circuit is defined as:
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...
Classification of Signals01:30

Classification of Signals

In signal processing, signals are classified based on various characteristics: continuous-time versus discrete-time, periodic versus aperiodic, analog versus digital, and causal versus noncausal. Each category highlights distinct properties crucial for understanding and manipulating signals.
A continuous-time signal holds a value at every instant in time, representing information seamlessly. In contrast, a discrete-time signal holds values only at specific moments, often denoted as x(n), where...

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Related Experiment Video

Updated: Jun 10, 2026

Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator
07:42

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Published on: December 15, 2021

Comparison of continuous and discrete frequency-versus-radius frequency-modulated reticles.

J S Taylor, R G Driggers, C E Halford

    Applied Optics
    |August 20, 2010
    PubMed
    Summary

    This study introduces a discrete frequency-versus-radius reticle, offering simplified electronic processing for imaging systems. While slightly limiting radial resolution, it remains effective for small targets.

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    Area of Science:

    • Optical Engineering
    • Image Processing

    Background:

    • Frequency-versus-radius reticles are crucial optical components for target detection and tracking.
    • Continuous reticles are widely used but can involve complex electronic processing.

    Purpose of the Study:

    • To present a general expression for the transmission function of a discrete frequency-versus-radius reticle.
    • To compare the performance and characteristics of discrete reticles against continuous ones.

    Main Methods:

    • Derivation of the transmission function for a discrete frequency-versus-radius reticle.
    • Comparative analysis of discrete and continuous reticle performance, focusing on resolution and signal processing.

    Main Results:

    • A general expression for the discrete reticle's transmission function was established.
    • The discrete reticle introduces a limitation in radial resolution, which is minimal for small-target images.
    • Simplified electronic processing due to the absence of phase reversal in the discrete design.

    Conclusions:

    • Discrete frequency-versus-radius reticles offer a viable alternative to continuous reticles, particularly when simplified processing is desired.
    • The trade-off between radial resolution and processing simplicity makes discrete reticles suitable for specific imaging applications.