Questions tagged [wavelet]

A wavelet is a wave-like oscillation with an amplitude that starts out at zero, increases, and then decreases back to zero.

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77 views

Why does MATLAB's dualtree3 function not return the lowpass subband of the imaginary tree?

MATLAB has a function named dualtree3 which computes 3-D dual-tree complex wavelet transform. This function only retains the last low-pass coefficients/subband of ...
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1answer
1k views

Adaptive Piecewise Constant Approximation (APCA) with wavelets/DWT

I am trying to approximate a vector or a time series, in order to have as little changes as possible. To do so, I pretend to apply the Adaptive piecewise constant approximation (APCA) algorithm. ...
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15 views

How can a thresholding method in discrete wavelet transform be adaptive and denoising is performed level independent?

I am a bit confused regarding the thresholding methods and noise estimation options found in Matlab regarding Discrete Wavelet Transform. Please correct me if I am wrong. I am understanding that noise ...
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1answer
917 views

Filter ECG signal with Wavelet and Python

I have to filter the signal of an ECG with the wavelet method with Python. The data is in a txt file. I can create my dataframe with pandas, display that with seaborn, but can not find a way to apply ...
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22 views

Is convolving a signal by a wavelet (in time domain) equivalent to wavelet filtering?

I am a noob in signal processing. Please help me understand if the following relation is true or not: ...
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0answers
26 views

What does voices per octave means?

I was studying the description of continuous wavelet transform in Matlab and I came across this term '**cwt uses 10 voices per octave**' ...
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1answer
152 views

Continuous wavelet transform subsampling at lower frequencies?

I am not completely confident in my understanding of wavelet theory, but since I am currently in the process of creating a CWT scalogram tool, I have to ask: Is there a theorem allowing us to ...
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18 views

Morlet wavelet: DFT vs Fourier Transform

I find what seem to be contradictions between the two. "Morlet" defined here, and its Fourier Transform (FT) below it. DFT's imaginary component zeroes with large ...
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2answers
62 views

Determine the haar wavelet function is linear or nonlinear

I'm looking for analytical justification of linearity or non linearity of the wavelet transform with the real Haar mother wavelet function. I have googling already. But I can't find and understand ...
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15 views

Fbank back to wav

Here's my problem. I have some wav files. I use the wavs as input to compute the fbanks. Then I want to do some stuff with the fbanks and then I want to recreate a wav file associated to the new fbank....
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462 views

Detection of Troughs and Notches in a PPG Signal

I'm working a project which tries to determine Blood Pressure from PPG signals.I'm trying to extract the features as shown below... I'm having problem in finding the troughs and dicrotic notch for ...
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How well can discrete wavelet packet transform reduce noises that are similar to the input signal in the same frequency band?

If I had 50Hz noise coming from power line, and signals in the same frequency range (EEG for example 0.1Hz to 100Hz). If my sampling frequency is 30kHz but I downsample my signal to 937kHz and use the ...
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23 views

What are the wavelet packet functions and how are they different from the wavelet and scaling functions?

I understand that in the decomposition process, wavelet and scaling functions are used to split the signal to approximation and detail coefficients. Most of the time I saw the wavelet and scaling ...
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1answer
368 views

Discrete Wavelet Transform (DWT) Filter Bank

I have some stumbling block in my thesis writing. Do we use the same filter pair while implementing DWT filter bank with downsampling of the filter output, or filters do change also from level to ...
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1answer
366 views

Programming the IDWT for image processing

I want to program the 2D inverse discrete wavelet transform (only 1 level) in the case of image processing. In the matlab website there's this diagram: now, I want to program the IDWT with haar ...
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1answer
1k views

Issues with the smoothing operator in coherence estimation using the complex Morlet (Gabor) wavelet

The goal I wish to compute the coherence estimate using the continuous wavelet transform (CWT) of a real-valued signal with the complex Morlet (a.k.a. Gabor) wavelet. I compute the cwt of the signal ...
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1answer
43 views

EEG signal processing with wavelet or fft?

I have confusion about signal processing related with EEG signal. I have done some of my research and that made me more confused about processing and filtering the signal. Let me jump into the problem ...
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1answer
155 views

Please help me understand this paper about Discrete Wavelet Transform!

I am trying to understand this paper says. I have found this paragraph to be vague: (a) Preprocessing Stage. The first step in this stage was to apply the Discrete Wavelet Transform (DWT). This ...
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1answer
105 views

Non-Linear, Non-Stationary spectral analysis methods! When and where?

I have been reading about non-linear non-stationary signal analysis methods and it seems to do this type of analysis the go-to method is the Empirical Mode Decomposition (EMD), then Hilbert Transform (...
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2answers
1k views

Fourier Transform of Morlet wavelet Function?

One definition of the Morlet wavelet function is given by: $$\frac{1}{\sqrt{\pi f_b}}e^{\frac{-t^2}{f_b}}e^{j2\pi f_c t}$$ The Fourier transform of this equation is: $e^{-\pi^2 f_b(f-f_c)^2}$ (is it ...
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1answer
889 views

Getting frequency content at different times from discrete wavelet transform coeffs

After being away from DSP for a long time, I am trying to familiarize myself with wavelet transform. Here is what I (think) have understood so far: Wavelet transform provides you high time resolution ...
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1answer
44 views

At what stage do we compute the approximations and details while performing a DWT?

$$ \int_{-\infty}^{+\infty}{f(t)\psi_{j,k}^\ast(t)dt}\ \textrm{with}\ \psi_{j,k}(t)\ =\ a_0^{-j/2}\psi(a_0^{-j}t\ -\ b_0k) $$ If this is the expression for the wavelet transform, how does this lead to ...
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1answer
263 views

What's the similarities and differences between Wigner transform and wavelet transform?

Wigner transform and continuous wavelet transform are both some kind of time-frequency representation of a signal. What are the similarities and differences between them? Could you give some ...
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1answer
582 views

Wavelet transform of a spatial convolution

Does anyone know if there exist a kind of convolution theorem for the discrete wavelet transform (decimated or undecimated)? In other words can I find a simple form of $W\left[ \int f(t) g(x-t) \, ...
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10 views

Energy of coefficients of wavelet decomposition?

I have recently been working with a dataset associated with the paper Human Activity Recognition from Accelerometer Data Using a Wearable Device. In Section 3.1 - Feature Selection for Motion Data, ...
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1answer
442 views

Wavelet filter coefficients from the Morlet wavelet

How can I obtain the wavelet filter coefficients ( i.e. lowpass decomposition filter, highpass decomposition filter, lowpass reconstruction filter, highpass reconstruction ...
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1answer
141 views

Wavelets and bank filters

The wavelet transform has a problem as it gives poor time resolution for low frequencies and poor frequency resolution for high frequencies according to uncertainty conditions. This appears well ...
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1answer
263 views

change the central frequency of a wavelet

I am using the discrete meyer wavelet in MATLAB for time series decomposition. I would like to change the central frequency of this wavelet but I do not know if this is possible or if I would need to ...
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1answer
680 views

MATLAB: Generating and Visualizing Mother Wavelet of different scale

In MATLAB, there is a function wavefun that outputs both the scaling and wavelet functions. To generate a Daubechies, the following command can be used: ...
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1answer
231 views

Extract approximation and detail coefficients

I am a student and would like to know how to extract the approximation and detail coefficients (A5, D5, D4, D3, D2 and D1) after an applied DWT decomposition dB5 (Daubechies 5, level = 5)?
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31 views

Why should wavelet re-synthesis produce an output when the main component is suppressed and what does this mean for denoising?

I understand that aliasing occurs in DWPT if the wavelet used is of low order since the "filters" are not perfect and the combination of down sampling and overlapping between bands causes ...
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1answer
234 views

2D DWT computation order

In 2D the discrete wavelet transform (DWT) of an image using lifting based 5/3 filter, if I perform a row-wise operation first then perform column-wise operation then I will get 4 sub-band LL, LH and ...
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1answer
39 views

How do wavelet levels depend on one another?

I am working with wavelets for my thesis, and I would like to know if there is an intuitive dependency between the levels of a DWT. To make it clear: The DWT performs a convolution, and then the ...
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18 views

Discrete wavelet center frequency

I am understanding that mother wavelets have a center frequency. Wavelets are limited in duration and oscillate then decay, so the center frequency is the mid pulse of the wavelet or so. But my ...
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1answer
65 views

Is it possible to extract peak locations in the time domain using help from fourier/wavelet analysis?

The signal I'm studying has fundamental frequencies of 20 and 60 cycles per minute (shown in the Periodogram graph). It is straight forward to extract the peaks in the time domain belonging to the 20 ...
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2answers
283 views

What is the normalization factor for the quincunx lattice wavelet transform, and how do you find it?

On pages 57-60 (preview was available last I checked, images here in case), there is a quincunx lattice transform described. Lattice: ...
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1answer
65 views

Time location of the DWT detail coefficients using MATLAB

When performing the Discrete Wavelet Transform in MATLAB using the command DWT or WAVEDEC, what it the exact time or pseudo-time location of the DWT coefficients? At each level the time series is ...
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0answers
26 views

Best way to measure effectiveness of discrete wavelet denoising?

I am using matlab wavelet toolbox to denoise physiological signals, I am plotting the denoised signal on top of the original noisy signal and making sure spikes were not removed as a measure of ...
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1answer
52 views

Faded line in spectrogram for a chirp

I've generated this spectrogram using wavelet convolution. The chirp is generated like so: ...
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1answer
63 views

Understanding Parseval's Theorem with Discrete Wavelet Transform

I have difficulty to understand the results I get with implementing Parseval's Theorem in Python to DWT. I have the good results getting the Energy with Fourier transform and the time series in python:...
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1answer
30 views

Plotting a Time Frequency contour/colormesh plot of a Discrete Wavelet Transform

I have a pressure vs time data of a noise on which I wish to perform discrete wavelet transform. I have divided my frequency range into 1/3rd Octave Bands and have calculated sound pressure level at ...
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1answer
32 views

Some questions about the intuition of the DWT

Assuming a DWT of a signal of length 8 with Haar filter taps. At the lowest level, I end up with a3 and d3 both of length 1, d2 of length 2 and d1 of length 4 which is the same number of coefficients ...
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16 views

How does the band pass wavelet act as a high pass filter in DWT

I am understanding that wavelets have a bandpass filter response due to their compact support, and when doing decomposition they are used as a high pass filter along with the scaling function as a low ...
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2answers
52 views

Can discrete wavelet transform for denoising purposes be implemented in real time? [closed]

I have been researching effective algorithms for denoising biomedical signals (non-stationary) that can be implemented in real time either using FPGA or DSP. I can across many suggestions for ...
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1answer
287 views

Wavelet transform and FFT using to extract feature power bands with EEG signals

I am using 5 channels [ fz , cz , c3 , c4 , pz] to detect drowsiness of driver My First Question is, what is the right input to get feature power band ( Theta , alpha , gamma , beta ) to wavelet ...
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24 views

Filtering out symmetric noise from an oscilloscope reading

I have a signal that looks like this: The data is readings from two oscilloscope channels, one color coded blue, the other color coded orange. I would like to filter out the supply noise (all the ...
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9 views

How to choose the appropriate number of samples for discrete wavelet transform denoising?

I want to make sure I am understanding the filter bank frequencies correctly in DWT decomposition. If my sampling frequency is 30kHz, then would I need to input data with 30k samples which later will ...
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2answers
208 views

Down sampling an EEG signal

I have a set of 10 minute EEG signals that were sampled at 400 Hz and have 16 channels which corresponds to a 16x240000 matrix. These EEG signals belong to two different classes. I am trying to ...
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1answer
31 views

Does Discrete Wavelet Consider Sampling Frequency or Cutoff Frequency of Bandpass Filter?

I have EEG signal with a sampling frequency of 128 Hz, and filtered from 1-30 Hz using a bandpass filter. Now I want to know ...
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0answers
15 views

Can thresholding in wavelet transform be implemented on the approximation coefficients?

Sorry as it might be a silly question since I am a beginner in wavelets. I have been using the matlab wavelet toolbox for denoising purposes and saw that thresholding is only applied on the detail (...

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