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Related Concept Videos

Upsampling01:22

Upsampling

668
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...
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Bandpass Sampling01:17

Bandpass Sampling

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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....
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Aliasing01:18

Aliasing

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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...
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Downsampling01:20

Downsampling

724
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...
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Sampling Methods: Overview01:06

Sampling Methods: Overview

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A sample refers to a smaller subset representative of a larger population. In analytical chemistry, studying or analyzing an entire population is often impractical or impossible. Therefore, samples are used to draw inferences and generalize the whole population. The sampling method selects individuals or items from a population to create a sample. Standard sampling methods include random, judgemental, systematic, stratified, and cluster sampling. 
In analytical chemistry, the choice of...
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Sampling Continuous Time Signal01:11

Sampling Continuous Time Signal

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In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
In the...
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Unmixing hyperspectral data by using signal subspace sampling.

Jakob Spiegelberg1, Shunsuke Muto2, Masahiro Ohtsuka3

  • 1Department of Physics and Astronomy, Uppsala University, Box 516, S-751 20 Uppsala, Sweden.

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Summary
This summary is machine-generated.

Signal Subspace Sampling (SSS) effectively pre-processes data for Non-negative Matrix Factorization (NMF) and Vertex Component Analysis (VCA). This method uniquely extracts orthogonal source signals, improving hyperspectral image analysis and spectroscopy data processing.

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Area of Science:

  • Data Science
  • Spectroscopy
  • Microscopy

Background:

  • Non-negative Matrix Factorization (NMF) and Vertex Component Analysis (VCA) are crucial for source signal extraction.
  • Processing hyperspectral images and emission spectroscopy data presents unique challenges.
  • Existing methods may not always guarantee unique extraction of non-negative source components.

Purpose of the Study:

  • To introduce and validate Signal Subspace Sampling (SSS) as a pre-processing technique for NMF and VCA.
  • To demonstrate SSS's ability to uniquely extract orthogonal non-negative source signals.
  • To enhance the processing of hyperspectral and spectroscopic data.

Main Methods:

  • Signal Subspace Sampling (SSS) resamples data to meet NMF/VCA conditions.
  • The proposed method is applied to both simulated and experimental datasets.
  • Evaluation involves assessing the uniqueness and non-negativity of extracted source components.

Main Results:

  • SSS significantly improves the performance of NMF and VCA.
  • Unique extraction of orthogonal non-negative source signals is achieved.
  • Successful application to hyperspectral X-ray microscopy and electron microscopy data.

Conclusions:

  • Signal Subspace Sampling is a powerful pre-processing step for NMF and VCA.
  • The method enhances the analysis of complex spectroscopic and imaging data.
  • SSS offers a robust approach for non-negative source component separation.