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Related Concept Videos

Aliasing01:18

Aliasing

Accurate signal sampling and reconstruction are crucial in various signal-processing applications. A time-domain signal's spectrum can be revealed using its Fourier transform. When this signal is sampled at a specific frequency, it results in multiple scaled replicas of the original spectrum in the frequency domain. The spacing of these replicas is determined by the sampling frequency.
If the sampling frequency is below the Nyquist rate, these replicas overlap, preventing the original signal...
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...
IR Spectrum Peak Splitting: Symmetric vs Asymmetric Vibrations01:08

IR Spectrum Peak Splitting: Symmetric vs Asymmetric Vibrations

Identical bonds within a polyatomic group can stretch symmetrically (in-phase) or asymmetrically (out-of-phase). Similar to hydrogen bonding, these vibrations also influence the shape of the IR peak. Generally, asymmetric stretching frequencies are higher than symmetric stretching frequencies. For example, primary amines exhibit two distinct IR peaks between 3300–3500 cm−1 corresponding to the symmetric and asymmetric N-H stretching, while secondary amines exhibit a single stretching vibration...
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...
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...
Mass Spectrometry: Complex Analysis01:21

Mass Spectrometry: Complex Analysis

Mass spectrometry is an important technique for the identification of pure compounds. However, it has some limitations for the analysis of complex mixtures, often due to excessive fragmentation making the spectrum too complicated to decipher. Mass spectrometry can be combined with suitable separation methods in sequence, forming hyphenated methods, which are useful in the analysis of complex mixtures.
GC–MS is a powerful hyphenated method commonly used in forensics and environmental...

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Related Experiment Video

Updated: Jun 6, 2026

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis
07:11

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis

Published on: August 19, 2021

Spectral recovery by analytic continuation in crossing-based spectrum analysis.

C M Blanca, V R Daria, C Saloma

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

    Analytic continuation recovers the true spectrum of undersampled analog signals from aliased Fourier spectra. This method reconstructs accurate signal bandwidth from sinusoid-crossing data, even with noise.

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    Area of Science:

    • Signal Processing
    • Fourier Analysis
    • Analog-to-Digital Conversion

    Background:

    • Undersampling analog signals leads to aliasing, corrupting the Fourier spectrum.
    • Sinusoid-crossing detection offers an alternative data acquisition method.
    • Accurate crossing localization is crucial for reliable spectrum reconstruction.

    Purpose of the Study:

    • To recover the true spectrum of an undersampled analog signal.
    • To overcome limitations of traditional aliasing in Fourier spectrum analysis.
    • To demonstrate a novel spectrum recovery technique using analytic continuation.

    Main Methods:

    • Utilizing analytic continuation to reconstruct the original signal spectrum.
    • Computing aliased Fourier spectra from sinusoid-crossing locations.
    • Employing a reference sinusoid for signal intersection detection.

    Main Results:

    • Successfully recovered the true spectrum of an undersampled signal.
    • Demonstrated robustness of the method with an interferogram test signal.
    • Showed effectiveness in both noise-free and noisy conditions (additive Gaussian noise).

    Conclusions:

    • Analytic continuation enables accurate spectrum recovery from undersampled signals.
    • The technique is viable even with low-accuracy crossing detection if the signal has compact support.
    • This method offers a potential solution for signal analysis when traditional sampling is not feasible.