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Related Concept Videos

Downsampling01:20

Downsampling

133
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...
133
Upsampling01:22

Upsampling

206
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...
206
Reconstruction of Signal using Interpolation01:10

Reconstruction of Signal using Interpolation

177
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...
177
Deconvolution01:20

Deconvolution

137
Deconvolution, also known as inverse filtering, is the process of extracting the impulse response from known input and output signals. This technique is vital in scenarios where the system's characteristics are unknown, and they must be inferred from the observable signals.
Deconvolution involves several mathematical techniques to derive the impulse response. One common approach is polynomial division. In this method, the input and output sequences are treated as coefficients of...
137
Sampling Continuous Time Signal01:11

Sampling Continuous Time Signal

211
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...
211
Bandpass Sampling01:17

Bandpass Sampling

164
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....
164

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Optimal Wavelet Selection for Signal Denoising.

Gyana Ranjan Sahoo1, Jack H Freed1,2, Madhur Srivastava1,2,3

  • 1Department of Chemistry and Chemical Biology, Cornell University, Ithaca, NY 14853, USA.

IEEE Access : Practical Innovations, Open Solutions
|October 18, 2024
PubMed
Summary
This summary is machine-generated.

Selecting the right wavelet is crucial for effective signal denoising. This study introduces a novel, empirical method to objectively identify optimal wavelets by analyzing the sparsity of signal components, improving accuracy and efficiency.

Keywords:
Wavelet selectiondecomposition level selectiondetail componentssignal denoisingsparsitywavelet denoisingwavelet transform

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Area of Science:

  • Signal Processing
  • Data Analysis
  • Spectroscopy

Background:

  • Wavelet denoising is essential for noise reduction in signals across various applications.
  • Current mother wavelet selection methods are often heuristic, time-consuming, and prone to human bias.
  • Optimal wavelet selection maximizes noise and signal coefficient separation for effective thresholding.

Purpose of the Study:

  • To introduce a universal, empirical method for selecting optimal mother wavelets for signal denoising.
  • To address the limitations of current heuristic and trial-and-error wavelet selection approaches.
  • To provide an objective and efficient method for wavelet selection based on signal characteristics.

Main Methods:

  • A novel parameter, mean of sparsity change (MSC), is defined to quantify the variation in noisy Detail components.
  • The method analyzes the sparsity of Detail components in the wavelet domain.
  • The efficacy of the MSC parameter is validated using simulated and experimental Electron Spin Resonance (ESR) spectroscopy data at varying Signal-to-Noise Ratios (SNRs).

Main Results:

  • Signal components exhibit abrupt changes in MSC values across different wavelets, while noise components show similar MSC values.
  • The change in MSC between the highest and second-highest values is approximately 8-10% for low SNR data and around 5% for high SNR data.
  • MSC increases with signal SNR, indicating that more wavelets are suitable for denoising high SNR signals, while low SNR signals benefit from a limited selection.

Conclusions:

  • The proposed empirical method offers a universal approach to optimal wavelet selection for denoising.
  • Selecting wavelets with the highest MSC values, individually or as a group (top five), ensures effective noise reduction.
  • This method enhances denoising efficiency and objectivity, particularly for signals like those in ESR spectroscopy.