Mathematics · Complex and Fourier

Fourier Quadrature Mode Energy Calculator

Calculate mode energy index from cosine coefficient and sine coefficient.

Runs locally
Your numbers

Inputs and results stay in this browser. Change one value at a time to explore the relationship.

Your inputCalculatedPassed forward in chains
mode energy index25

Calculation steps

  1. Use c=a²+b² with cosine coefficient=3 and sine coefficient=4.
  2. mode energy index=25.

Understand Fourier Quadrature Mode Energy

One idea, three depths

Choose how deeply to explain Fourier Quadrature Mode Energy

Fourier Quadrature Mode Energy: Calculate mode energy index from cosine coefficient and sine coefficient.

Age 5Explain it to a 5-year-oldStart with a picture

Imagine using Fourier Quadrature Mode Energy to answer this question: calculate mode energy index from cosine coefficient and sine coefficient? Enter cosine coefficient and sine coefficient; the calculator shows mode energy index. For example: cosine coefficient=3 and sine coefficient=4 produce mode energy index=25. The answer tells you mode energy index.

Age 15Explain it to a 15-year-oldConnect it to the formula

A real Fourier mode's cosine and sine coefficients contribute a squared-amplitude sum. This page evaluates the relationship directly. The rule is c=a²+b². Its input values are cosine coefficient, sine coefficient, and the main result is mode energy index. For example: cosine coefficient=3 and sine coefficient=4 produce mode energy index=25.

CollegeExplain it at college levelState the model precisely

This calculator evaluates the stated fourier quadrature mode energy relation over the valid real-number domain stated below. The implemented relation is c=a²+b², evaluated from cosine coefficient, sine coefficient to produce mode energy index. A real Fourier mode's cosine and sine coefficients contribute a squared-amplitude sum. This page evaluates the relationship directly. Normalization conventions determine whether an additional factor belongs in physical energy.

Inputs and valid domain

  • cosine coefficient must be a finite real number.
  • sine coefficient must be a finite real number.

Important boundary: Normalization conventions determine whether an additional factor belongs in physical energy.

The formula

c=a²+b²

How the calculator works through it

It substitutes cosine coefficient, sine coefficient into the formula and exposes every numerical step above. The main output is mode energy index.

Read the result correctly

The mode energy index is the direct answer to “calculate mode energy index from cosine coefficient and sine coefficient.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.

A worked check

cosine coefficient=3 and sine coefficient=4 produce mode energy index=25.

Where this model stops being reliable

Normalization conventions determine whether an additional factor belongs in physical energy.

Learn it by changing one value

Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.

Dictionary terms behind this calculator

Before studying the codeWhat you should know firstUse the calculator immediately, or check the foundations before reading the implementation.

These foundations help you understand why Fourier Quadrature Mode Energy works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.

Hard requirements

  • Reading formulas and substituting values

    Fourier Quadrature Mode Energy uses c=a²+b². You need to recognise what each side represents before substituting the stated inputs or rearranging the relationship.

    Review this foundation about 4 min

Strong support

Optional enrichment

Learn the missing foundationsI already know these — show the code

Mathematics → algorithm → program

Implement this calculation in code

These are direct reference implementations of the calculator's principal relationship and first output. They run locally and include a small known-answer check where the language supports it.

Algorithm

  1. Read cosine coefficient, sine coefficient.
  2. Evaluate the principal relationship: c=a²+b².
  3. Return mode energy index and check the domain conditions described above.
Python
            from math import *

def fourier_quadrature_mode_energy_calculator(a, b) -> float:
    return ((a * a) + (b * b))

assert abs(fourier_quadrature_mode_energy_calculator(3, 4) - 25) < 1e-6 * max(1.0, abs(25))
          
Current calculator valuesUpdates when you change an input above.
              
            
C
            #include <assert.h>
#include <math.h>

double fourier_quadrature_mode_energy_calculator(double a, double b) {
    return ((a * a) + (b * b));
}

int main(void) {
    const double expected = 25;
    const double actual = fourier_quadrature_mode_energy_calculator(3, 4);
    assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
          
Current calculator valuesUpdates when you change an input above.
              
            
C++
            #include <cassert>
#include <cmath>
#include <numbers>

double fourier_quadrature_mode_energy_calculator(double a, double b) {
    return ((a * a) + (b * b));
}

int main() {
    constexpr double expected = 25;
    const double actual = fourier_quadrature_mode_energy_calculator(3, 4);
    assert(std::fabs(actual - expected) < 1e-6 * std::fmax(1.0, std::fabs(expected)));
}
          
Current calculator valuesUpdates when you change an input above.
              
            
Linux x86-64 assembly

x86-64 NASM · System V ABI · Linux · SSE2 with libm where required

            ; double fourier_quadrature_mode_energy_calculator(double a, double b)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global fourier_quadrature_mode_energy_calculator
section .text

fourier_quadrature_mode_energy_calculator:
    push rbp
    mov rbp, rsp
    sub rsp, 48
    movsd [rbp-8], xmm0
    movsd [rbp-16], xmm1
    movsd xmm0, [rbp-8]
    mulsd xmm0, [rbp-8]
    movsd [rbp-32], xmm0
    movsd xmm0, [rbp-16]
    mulsd xmm0, [rbp-16]
    movsd [rbp-40], xmm0
    movsd xmm0, [rbp-32]
    addsd xmm0, [rbp-40]
    movsd [rbp-24], xmm0
    movsd xmm0, [rbp-24]
    leave
    ret
          
Current calculator valuesUpdates when you change an input above.
              
            
MATLAB
            function result = fourier_quadrature_mode_energy_calculator(a, b)
    result = ((a * a) + (b * b));
end
          
Current calculator valuesUpdates when you change an input above.
              
            
Wolfram Language
            ClearAll[mwCalculate];
mwCalculate[a_, b_] := ((a * a) + (b * b));
          
Current calculator valuesUpdates when you change an input above.
              
            

Continue in mathematical software

The downloaded file includes your current inputs and first calculated result. It is created locally.

Floating-point answers can differ slightly by language, compiler and processor. Compare within a suitable tolerance rather than assuming every decimal representation will be identical.

Reuse the page responsiblyCite this pageAPA, MLA, Chicago, Harvard, BibTeX and RIS

These formats cite this calculator page itself. They are separate from the academic references above, which support the mathematical method and terminology.

APA 7

MW SysArc. (2026, July 21). Fourier Quadrature Mode Energy Calculator. MW SysArc Tools. https://math.mwsysarc.com/complex-fourier/fourier-quadrature-mode-energy-calculator

MLA 9

MW SysArc. “Fourier Quadrature Mode Energy Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/complex-fourier/fourier-quadrature-mode-energy-calculator. Accessed 31 Aug. 2026.

Chicago 17

MW SysArc. “Fourier Quadrature Mode Energy Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/complex-fourier/fourier-quadrature-mode-energy-calculator.

Harvard

MW SysArc (2026) ‘Fourier Quadrature Mode Energy Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/complex-fourier/fourier-quadrature-mode-energy-calculator (Accessed: 31 August 2026).

BibTeX and RIS records

BibTeX

@misc{mwsysarc_fourier_quadrature_mode_energy_calculator_2026,
  author = {{MW SysArc}},
  title = {Fourier Quadrature Mode Energy Calculator},
  howpublished = {MW SysArc Tools},
  year = {2026},
  url = {https://math.mwsysarc.com/complex-fourier/fourier-quadrature-mode-energy-calculator},
  note = {Published July 21, 2026; accessed August 31, 2026}
}

RIS

TY  - ELEC
AU  - MW SysArc
TI  - Fourier Quadrature Mode Energy Calculator
T2  - MW SysArc Tools
PY  - 2026
DA  - 2026-07-21
Y2  - 2026-08-31
UR  - https://math.mwsysarc.com/complex-fourier/fourier-quadrature-mode-energy-calculator
N1  - Published July 21, 2026
ER  -

Clear answers

Frequently asked questions

What does the Fourier Quadrature Mode Energy do?

Calculate mode energy index from cosine coefficient and sine coefficient.

How does the Fourier Quadrature Mode Energy work?

The calculator applies c=a²+b². A real Fourier mode's cosine and sine coefficients contribute a squared-amplitude sum. This page evaluates the relationship directly.

What can I learn from the Fourier Quadrature Mode Energy?

It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.

Does MW SysArc receive or store what I enter?

No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.

How should I use the result?

Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.

Last reviewed . Calculations tested .

MW SysArc Certified