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Related Concept Videos

Passive Filters01:27

Passive Filters

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.
Low-Pass Filters
Low-pass filters are designed to transmit signals with frequencies lower than the cutoff frequency, ωc, and attenuate those above it. The cutoff frequency...
Wave Parameters01:10

Wave Parameters

The simplest mechanical waves are associated with simple harmonic motion and repeat themselves for several cycles. These simple harmonic waves can be modeled using a combination of sine and cosine functions. Consider a simplified surface water wave that moves across the water's surface. Unlike complex ocean waves, in surface water waves, water moves vertically, oscillating up and down, whereas the disturbance of the wave moves horizontally through the medium. If a seagull is floating on the...
Basic signals of Fourier Transform01:07

Basic signals of Fourier Transform

The Fourier Transform is a pivotal mathematical tool in signal processing, enabling the transformation of time-domain signals into their frequency-domain representations. Among the numerous elements within this domain, certain functions like the sinc function, delta function, and exponential signals hold significant importance due to their unique properties and implications.
The sinc function, defined as sinc(x) = sin(πx)/(πx), is particularly notable for its symmetry and behavior at zero. It...
Intensity and Pressure of Sound Waves01:05

Intensity and Pressure of Sound Waves

The intensity of sound waves can be related to displacement and pressure amplitudes by using their wave expressions and the definition of intensity. The critical step to achieve this is to write the power delivered by the particles on the wave as the product of force and velocity and simplify the force per unit area as the pressure. The velocity of the medium's particles can be derived from the displacement.
Unlike the time average of a sinusoidal term, which is zero since it is positive and...
Active Filters01:25

Active Filters

Active filters are electronic circuits that use operational amplifiers (op-amps), resistors, and capacitors to filter out unwanted frequency components from a signal. A first-order low-pass active filter is designed to pass signals with a frequency lower than a certain cutoff frequency and attenuate frequencies higher than that cutoff frequency. The transfer function for a first-order low-pass active filter is:
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...

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Related Experiment Video

Updated: Jun 6, 2026

Using Fiberless, Wearable fNIRS to Monitor Brain Activity in Real-world Cognitive Tasks
10:07

Using Fiberless, Wearable fNIRS to Monitor Brain Activity in Real-world Cognitive Tasks

Published on: December 2, 2015

Wavelet filter: pure-intensity spatial filters that implement wavelet transforms.

Z P Jiang, M Ni, Q S Lu

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

    This study introduces novel optical filters with wavelet point-spread functions, enabling manipulation of both phase and amplitude for optical waves. These filters facilitate optical wavelet transforms, demonstrated through simulations for edge and corner detection.

    Related Experiment Videos

    Last Updated: Jun 6, 2026

    Using Fiberless, Wearable fNIRS to Monitor Brain Activity in Real-world Cognitive Tasks
    10:07

    Using Fiberless, Wearable fNIRS to Monitor Brain Activity in Real-world Cognitive Tasks

    Published on: December 2, 2015

    Area of Science:

    • Optics and Photonics
    • Signal Processing

    Background:

    • Mirrors with wavelet-related point-spread functions were previously proposed.
    • Existing optical systems may have limitations in manipulating both phase and amplitude of optical waves.

    Purpose of the Study:

    • To propose novel optical filters with wavelet point-spread functions.
    • To enable manipulation of both phase and amplitude of optical waves.
    • To facilitate optical wavelet transforms for image processing tasks.

    Main Methods:

    • Designing filters with specific transmittance functions (real and positive under certain conditions).
    • Implementing optical wavelet transforms using the proposed filters.
    • Conducting computer simulations for edge and corner extraction.

    Main Results:

    • Demonstrated the feasibility of filters with wavelet point-spread functions.
    • Showcased the ability to reform both phase and amplitude of optical waves.
    • Successfully performed edge and corner extractions using optical wavelet transforms via simulations.

    Conclusions:

    • The proposed filters offer a new approach for optical wave manipulation.
    • These filters are effective for implementing optical wavelet transforms.
    • The method shows promise for applications in image analysis and feature extraction.