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Related Concept Videos

Bandpass Sampling01:17

Bandpass Sampling

In signal processing, bandpass sampling is an effective technique for sampling signals that have most of their energy concentrated within a narrow frequency band. This type of signal is known as a bandpass signal. The key principle of bandpass sampling involves sampling the signal at a rate that is greater than twice the signal's bandwidth to prevent aliasing.
A bandpass signal has a spectrum with a lower frequency limit, denoted as ω1, and an upper frequency limit, denoted as ω2. The spectrum...
Upsampling01:22

Upsampling

Managing signal sampling rates is essential in digital signal processing to maintain signal integrity. A decimated signal, characterized by a reduced frequency range due to its lower sampling rate, can be upsampled by inserting zeros between each sample. This upsampling process expands the original spectrum and introduces repeated spectral replicas at intervals dictated by the new Nyquist frequency. To refine this zero-inserted sequence, it is passed through a lowpass filter with a cutoff...
Sampling Theorem01:15

Sampling Theorem

In signal processing, the analysis of continuous-time signals, denoted as x(t), often involves sampling techniques to convert these signals into discrete-time signals. This process is essential for digital representation and manipulation. A critical component in sampling is the train of impulses, characterized by the sampling interval and the sampling frequency. The relationship between these parameters and the original signal's properties dictates the success of the sampling process.
Downsampling01:20

Downsampling

When considering a sampled sequence with zero values between sampling instants, one can replace it by taking every N-th value of the sequence. At these integer multiples of N, the original and sampled sequences coincide. This process, known as decimation, involves extracting every N-th sample from a sequence, thereby creating a more efficient sequence.
The Fourier transform of the decimated sequence reveals a combination of scaled and shifted versions of the original spectrum. This...
NMR Spectrometers: Resolution and Error Correction01:14

NMR Spectrometers: Resolution and Error Correction

When magnetic nuclei in a sample achieve resonance and undergo relaxation, the signal detected in NMR is an approximately exponential free induction decay. Fourier transform of an exponential decay yields a Lorentzian peak in the frequency domain. Lorentzian peaks in an NMR spectrum are defined by their amplitude, full width at half maximum, and position, where the peak width is governed by the spin-spin relaxation time alone. In real experiments, however, the applied magnetic field is rendered...
Parallel Resonance01:23

Parallel Resonance

The parallel RLC circuit is an arrangement where the resistor (R), inductor (L), and capacitor (C) are all connected to the same nodes and, as a result, share the same voltage across them. The parallel RLC circuit is analyzed in terms of admittance (Y), which reflects the ease with which current can flow. The admittance is given by:

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Related Experiment Video

Updated: Jun 16, 2026

Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping
09:43

Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping

Published on: March 20, 2017

Minimax spectrum shaping with a bandwidth constraint.

J P Allebach, B Liu

    Applied Optics
    |February 16, 2010
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces a novel spectrum shaping technique to minimize spectral peaks within bandwidth constraints. The findings offer practical methods for digital holography and spectral optimization.

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    Quasi-light Storage for Optical Data Packets
    07:45

    Quasi-light Storage for Optical Data Packets

    Published on: February 6, 2014

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    Last Updated: Jun 16, 2026

    Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping
    09:43

    Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping

    Published on: March 20, 2017

    Quasi-light Storage for Optical Data Packets
    07:45

    Quasi-light Storage for Optical Data Packets

    Published on: February 6, 2014

    Area of Science:

    • Optics and Photonics
    • Signal Processing

    Background:

    • Spectrum shaping is crucial for various optical and digital communication systems.
    • Minimizing spectral peaks while constraining bandwidth is a persistent challenge.

    Purpose of the Study:

    • To introduce and analyze a new minimax spectrum shaping approach.
    • To develop practical methods for achieving this optimized spectrum.
    • To evaluate the effectiveness of these methods in digital holography.

    Main Methods:

    • Formulating a minimax optimization problem for spectrum shaping.
    • Deriving a lower bound for the spectral maximum.
    • Developing and simulating practical spectrum shaping algorithms.

    Main Results:

    • A lower bound for the spectral maximum was established.
    • A new figure of merit for spectrum shaping was introduced.
    • Computer simulations confirmed the tightness of the lower bound and the efficacy of the proposed methods.

    Conclusions:

    • The proposed minimax spectrum shaping approach is effective.
    • The derived lower bound and figure of merit provide valuable benchmarks.
    • The methods show promise for applications in digital holography and beyond.