Wavelet Coefficient Calculator

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Digital Image Fundamentals

Intensity Transformation

✖Scaling Function Expansion is the scaling function expansion refers to the representation of a signal or an image using a series of scaled and translated versions of a base or fundamental function.ⓘ Scaling Function Expansion [f_s[x]]			+10% -10%
✖Wavelet Expansion Function refers to the representation of a signal or an image as a linear combination of wavelet functions at different scales and positions.ⓘ Wavelet Expansion Function [ψ _j,k[x]]			+10% -10%
✖Integer Index For Linear Expansion is an integer index of a finite or infinite sum.ⓘ Integer Index For Linear Expansion [k]			+10% -10%

✖Detail Wavelet Coefficient refers to the component of the signal or image that represents the high-frequency details captured by the wavelet transform.ⓘ Wavelet Coefficient [d_j[k]]

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Formula

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Wavelet Coefficient

Formula

`("d"_{"j"}"[k]") = int(("f"_{"s"}"[x]")*("ψ "_{"j,k"}"[x]")*x,x,0,"k")`

Example

`"160"=int("2.5"*"8"*x,x,0,"4")`

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Wavelet Coefficient Solution

STEP 0: Pre-Calculation Summary

Formula Used

Detail Wavelet Coefficient = int(Scaling Function Expansion*Wavelet Expansion Function*x,x,0,Integer Index For Linear Expansion)
d_j[k] = int(f_s[x]*ψ _j,k[x]*x,x,0,k)
This formula uses 1 Functions, 4 Variables

Functions Used

int - The definite integral can be used to calculate net signed area, which is the area above the x -axis minus the area below the x -axis., int(expr, arg, from, to)

Variables Used

Detail Wavelet Coefficient - Detail Wavelet Coefficient refers to the component of the signal or image that represents the high-frequency details captured by the wavelet transform.
Scaling Function Expansion - Scaling Function Expansion is the scaling function expansion refers to the representation of a signal or an image using a series of scaled and translated versions of a base or fundamental function.
Wavelet Expansion Function - Wavelet Expansion Function refers to the representation of a signal or an image as a linear combination of wavelet functions at different scales and positions.
Integer Index For Linear Expansion - Integer Index For Linear Expansion is an integer index of a finite or infinite sum.

STEP 1: Convert Input(s) to Base Unit

Scaling Function Expansion: 2.5 --> No Conversion Required
Wavelet Expansion Function: 8 --> No Conversion Required
Integer Index For Linear Expansion: 4 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d_j[k] = int(f_s[x]*ψ _j,k[x]*x,x,0,k) --> int(2.5*8*x,x,0,4)

Evaluating ... ...

d_j[k] = 160

STEP 3: Convert Result to Output's Unit

160 --> No Conversion Required

FINAL ANSWER

160 <-- Detail Wavelet Coefficient

(Calculation completed in 00.004 seconds)

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Created by Zaheer Sheik

Seshadri Rao Gudlavalleru Engineering College (SRGEC), Gudlavalleru

Zaheer Sheik has created this Calculator and 10+ more calculators!

Verified by Dipanjona Mallick

Heritage Insitute of technology (HITK), Kolkata

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Wavelet Coefficient Formula

Detail Wavelet Coefficient = int(Scaling Function Expansion*Wavelet Expansion Function*x,x,0,Integer Index For Linear Expansion)
d_j[k] = int(f_s[x]*ψ _j,k[x]*x,x,0,k)

What is Wavelet Coefficient?

Wavelet coefficients are the numerical values obtained from the wavelet transform of a signal or an image. When a signal or an image is processed using wavelet analysis, it is decomposed into different frequency components and spatial details. Wavelet coefficients represent the contribution of each wavelet function to the decomposition at different scales and positions.

How to Calculate Wavelet Coefficient?

Wavelet Coefficient calculator uses Detail Wavelet Coefficient = int(Scaling Function Expansion*Wavelet Expansion Function*x,x,0,Integer Index For Linear Expansion) to calculate the Detail Wavelet Coefficient, The Wavelet Coefficient formula is used to calculate the numerical values obtained from the wavelet transform of a signal or an image and it represents the strength or magnitude of the high-frequency components present in the image at different scales and orientations. Detail Wavelet Coefficient is denoted by d_j[k] symbol.

How to calculate Wavelet Coefficient using this online calculator? To use this online calculator for Wavelet Coefficient, enter Scaling Function Expansion (f_s[x]), Wavelet Expansion Function (ψ _j,k[x]) & Integer Index For Linear Expansion (k) and hit the calculate button. Here is how the Wavelet Coefficient calculation can be explained with given input values -> 160 = int(2.5*8*x,x,0,4).

FAQ

What is Wavelet Coefficient?

The Wavelet Coefficient formula is used to calculate the numerical values obtained from the wavelet transform of a signal or an image and it represents the strength or magnitude of the high-frequency components present in the image at different scales and orientations and is represented as d_j[k] = int(f_s[x]*ψ _j,k[x]*x,x,0,k) or Detail Wavelet Coefficient = int(Scaling Function Expansion*Wavelet Expansion Function*x,x,0,Integer Index For Linear Expansion). Scaling Function Expansion is the scaling function expansion refers to the representation of a signal or an image using a series of scaled and translated versions of a base or fundamental function, Wavelet Expansion Function refers to the representation of a signal or an image as a linear combination of wavelet functions at different scales and positions & Integer Index For Linear Expansion is an integer index of a finite or infinite sum.

How to calculate Wavelet Coefficient?

The Wavelet Coefficient formula is used to calculate the numerical values obtained from the wavelet transform of a signal or an image and it represents the strength or magnitude of the high-frequency components present in the image at different scales and orientations is calculated using Detail Wavelet Coefficient = int(Scaling Function Expansion*Wavelet Expansion Function*x,x,0,Integer Index For Linear Expansion). To calculate Wavelet Coefficient, you need Scaling Function Expansion (f_s[x]), Wavelet Expansion Function (ψ _j,k[x]) & Integer Index For Linear Expansion (k). With our tool, you need to enter the respective value for Scaling Function Expansion, Wavelet Expansion Function & Integer Index For Linear Expansion and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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