Linear Combination of Expansion Calculator

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Digital Image Fundamentals

Intensity Transformation

✖Integer Index For Linear Expansion is an integer index of a finite or infinite sum.ⓘ Integer Index For Linear Expansion [k]			+10% -10%
✖Real Valued Expansion Coefficients are the coefficients for the respective expansion functions.ⓘ Real Valued Expansion Coefficients [α_k]			+10% -10%
✖Real Valued Expansion Functions are the functions which are used to calculate linear combination of expansion.ⓘ Real Valued Expansion Functions [φ[x]]			+10% -10%

✖Linear Combination of expansion functions is the signal f(x) used to evaluate.ⓘ Linear Combination of Expansion [f[x]]

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Formula

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Linear Combination of Expansion

Formula

`"f[x]" = sum(x,0,"k","α"_{"k"}*"φ[x]")`

Example

`"50"=sum(x,0,"4","2"*"5")`

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Linear Combination of Expansion Solution

STEP 0: Pre-Calculation Summary

Formula Used

Linear Combination of expansion functions = sum(x,0,Integer Index For Linear Expansion,Real Valued Expansion Coefficients*Real Valued Expansion Functions)
f[x] = sum(x,0,k,α_k*φ[x])
This formula uses 1 Functions, 4 Variables

Functions Used

sum - Summation or sigma (∑) notation is a method used to write out a long sum in a concise way., sum(i, from, to, expr)

Variables Used

Linear Combination of expansion functions - Linear Combination of expansion functions is the signal f(x) used to evaluate.
Integer Index For Linear Expansion - Integer Index For Linear Expansion is an integer index of a finite or infinite sum.
Real Valued Expansion Coefficients - Real Valued Expansion Coefficients are the coefficients for the respective expansion functions.
Real Valued Expansion Functions - Real Valued Expansion Functions are the functions which are used to calculate linear combination of expansion.

STEP 1: Convert Input(s) to Base Unit

Integer Index For Linear Expansion: 4 --> No Conversion Required
Real Valued Expansion Coefficients: 2 --> No Conversion Required
Real Valued Expansion Functions: 5 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

f[x] = sum(x,0,k,α_k*φ[x]) --> sum(x,0,4,2*5)

Evaluating ... ...

f[x] = 50

STEP 3: Convert Result to Output's Unit

50 --> No Conversion Required

FINAL ANSWER

50 <-- Linear Combination of expansion functions

(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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Linear Combination of Expansion Formula

Linear Combination of expansion functions = sum(x,0,Integer Index For Linear Expansion,Real Valued Expansion Coefficients*Real Valued Expansion Functions)
f[x] = sum(x,0,k,α_k*φ[x])

What is the purpose of calculating the Linear Combination of Expansion?

Linear combination of expansion means in the context of MRA involves combining information from different resolution levels using linear weights, followed by an expansion operation to reconstruct the image at a higher resolution. This approach allows for the integration of multi-scale information and can be valuable in various image processing tasks such as denoising, compression, or feature extraction.

How to Calculate Linear Combination of Expansion?

Linear Combination of Expansion calculator uses Linear Combination of expansion functions = sum(x,0,Integer Index For Linear Expansion,Real Valued Expansion Coefficients*Real Valued Expansion Functions) to calculate the Linear Combination of expansion functions, The Linear Combination of Expansion formula is refer to a method of combining information from different resolution levels or scales, followed by an expansion operation. Linear Combination of expansion functions is denoted by f[x] symbol.

How to calculate Linear Combination of Expansion using this online calculator? To use this online calculator for Linear Combination of Expansion, enter Integer Index For Linear Expansion (k), Real Valued Expansion Coefficients (α_k) & Real Valued Expansion Functions (φ[x]) and hit the calculate button. Here is how the Linear Combination of Expansion calculation can be explained with given input values -> 50 = sum(x,0,4,2*5).

FAQ

What is Linear Combination of Expansion?

The Linear Combination of Expansion formula is refer to a method of combining information from different resolution levels or scales, followed by an expansion operation and is represented as f[x] = sum(x,0,k,α_k*φ[x]) or Linear Combination of expansion functions = sum(x,0,Integer Index For Linear Expansion,Real Valued Expansion Coefficients*Real Valued Expansion Functions). Integer Index For Linear Expansion is an integer index of a finite or infinite sum, Real Valued Expansion Coefficients are the coefficients for the respective expansion functions & Real Valued Expansion Functions are the functions which are used to calculate linear combination of expansion.

How to calculate Linear Combination of Expansion?

The Linear Combination of Expansion formula is refer to a method of combining information from different resolution levels or scales, followed by an expansion operation is calculated using Linear Combination of expansion functions = sum(x,0,Integer Index For Linear Expansion,Real Valued Expansion Coefficients*Real Valued Expansion Functions). To calculate Linear Combination of Expansion, you need Integer Index For Linear Expansion (k), Real Valued Expansion Coefficients (α_k) & Real Valued Expansion Functions (φ[x]). With our tool, you need to enter the respective value for Integer Index For Linear Expansion, Real Valued Expansion Coefficients & Real Valued Expansion Functions 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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