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Related Concept Videos

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...
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...
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...
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...
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.
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.

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Related Experiment Video

Updated: Jun 15, 2026

A Multimodal Wide-Field Fourier-Transform Raman Microscope
06:48

A Multimodal Wide-Field Fourier-Transform Raman Microscope

Published on: December 30, 2025

[Algorithm for restoring spectrogram with sub-pixel resolution].

Huai-Dong Yang1, Ke-Xin Chen, Qing-Sheng He

  • 1State Key Laboratory of Precision Measurement Technology and Instruments, Tsinghua University, Beijing 100084, China. yanghd@tsinghua.edu.cn

Guang Pu Xue Yu Guang Pu Fen Xi = Guang Pu
|March 10, 2010
PubMed
Summary
This summary is machine-generated.

This study introduces a new sub-pixel restoration algorithm to enhance spectral resolution. The method effectively restores high-resolution spectrograms from low-resolution inputs, overcoming detector limitations.

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Computer-based Multitaper Spectrogram Program for Electroencephalographic Data
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Computer-based Multitaper Spectrogram Program for Electroencephalographic Data

Published on: November 13, 2019

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Last Updated: Jun 15, 2026

A Multimodal Wide-Field Fourier-Transform Raman Microscope
06:48

A Multimodal Wide-Field Fourier-Transform Raman Microscope

Published on: December 30, 2025

Computer-based Multitaper Spectrogram Program for Electroencephalographic Data
04:13

Computer-based Multitaper Spectrogram Program for Electroencephalographic Data

Published on: November 13, 2019

Area of Science:

  • Spectroscopy
  • Image Processing
  • Signal Processing

Context:

  • Detector spatial resolution limits spectral analysis.
  • Sub-pixel restoration is crucial for high-resolution spectrograms.
  • Existing methods may not fully leverage sub-pixel information.

Purpose:

  • To propose a novel algorithm for sub-pixel restoration.
  • To improve the quality of spectrograms by increasing resolution.
  • To address the challenge of insufficient detector spatial resolution.

Summary:

  • A new sub-pixel restoration algorithm is presented.
  • The algorithm uses a bidirectional recursive relation to estimate sub-pixel values.
  • Averaging estimates from both directions refines the sub-pixel value.

Impact:

  • Enhances spectral resolution beyond detector limits.
  • Provides a more effective solution for high-resolution spectrogram reconstruction.
  • Validated through numerical experiments on Gaussian profiles.