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Bandpass Sampling01:17

Bandpass Sampling

599
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....
599
Aliasing01:18

Aliasing

732
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...
732
Upsampling01:22

Upsampling

679
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...
679
Properties of Fourier Transform II01:24

Properties of Fourier Transform II

872
The Fourier Transform (FT) is an essential mathematical tool in signal processing, transforming a time-domain signal into its frequency-domain representation. This transformation elucidates the relationship between time and frequency domains through several properties, each revealing unique aspects of signal behavior.
The Frequency Shifting property of Fourier Transforms highlights that a shift in the frequency domain corresponds to a phase shift in the time domain. Mathematically, if x(t) has...
872
Time and frequency -Domain Interpretation of Phase-lag Control01:21

Time and frequency -Domain Interpretation of Phase-lag Control

433
Phase-lag controllers are widely used in control systems to improve stability and reduce steady-state errors. A dimmer switch controlling the brightness of a light bulb serves as a practical example of phase-lag control, gradually adjusting the bulb's brightness. Mathematically, phase-lag control or low-pass filtering is represented when the factor 'a' is less than 1.
Phase-lag controllers do not place a pole at zero, but instead influence the steady-state error by amplifying any...
433
Sampling Theorem01:15

Sampling Theorem

1.5K
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.
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Related Experiment Video

Updated: Mar 12, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Frequency domain tailoring for intra-pulse frequency mixing.

G Ernotte, P Lassonde, F Légaré

    Optics Express
    |November 10, 2016
    PubMed
    Summary

    Researchers developed a novel all-inline inter-pulse difference frequency generation (DFG) method using a 4-f setup. This technique offers independent control over mid-infrared (MIR) pulse parameters with high stability and 20 attosecond jitter.

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    Area of Science:

    • Optics and Photonics
    • Nonlinear Optics
    • Ultrafast Lasers

    Background:

    • Difference frequency generation (DFG) for mid-infrared (MIR) pulse generation typically involves a trade-off between stability (intra-pulse) and control (inter-pulse).
    • Existing methods often require complex feedback stabilization for precise parameter control.

    Purpose of the Study:

    • To combine the stability of intra-pulse DFG with the independent parameter control of inter-pulse DFG.
    • To achieve carrier-envelope-phase (CEP) stabilized MIR pulses with high energy and short duration.

    Main Methods:

    • An all-inline inter-pulse DFG scheme was implemented using a 4-f optical setup.
    • A supercontinuum source, generated after filamentation in air from a Ti:Sa laser, was spectrally tailored.
    • The 4-f setup enabled independent manipulation of amplitude, delay, and polarization of spectral sidebands.

    Main Results:

    • Tunable MIR pulses were generated in a single DFG stage.
    • Achieved pulses had a central wavelength of 2 µm, energy of 4.8 µJ, and duration of 26.5 fs.
    • Demonstrated 20 attosecond jitter without feedback stabilization, maintaining CEP stability.

    Conclusions:

    • The proposed 4-f based all-inline inter-pulse DFG scheme successfully merges stability and control.
    • This method provides a robust platform for generating high-quality, tunable MIR pulses for various applications.