Signal window coherent gain calculator

Calculate coherent gain and equivalent noise bandwidth with your own figures.

Your numbers

Use the units shown. Results update as you change valid inputs.

Use coherent gain and equivalent noise bandwidth to compare changes to your inputs. The method and limits below explain the scope.

Examples

Examples

Try the starting example

Window sample count
32
Window: 0 rectangular, 1 periodic Hann, 2 periodic Hamming
1
Coherent gain
0.5
Equivalent noise bandwidth (bins)
1.5
Window coefficients
[0,0.00960735979838,0.0380602337444,0.0842651938487,0.146446609407,0.22221488349,0.308658283817,0.402454838992,0.5,0.597545161008,0.691341716183,0.77778511651,0.853553390593,0.915734806151,0.961939766256,0.990392640202,1,0.990392640202,0.961939766256,0.915734806151,0.853553390593,0.77778511651,0.691341716183,0.597545161008,0.5,0.402454838992,0.308658283817,0.22221488349,0.146446609407,0.0842651938487,0.0380602337444,0.00960735979838]

Try another scenario

Window sample count
33
Window: 0 rectangular, 1 periodic Hann, 2 periodic Hamming
1
Coherent gain
0.5
Equivalent noise bandwidth (bins)
1.5
Window coefficients
[0,0.00903565136865,0.035816033492,0.0793732335844,0.138132980947,0.209971545214,0.292292493499,0.382120532245,0.476209042088,0.571157419137,0.663533981659,0.75,0.827430366973,0.893026547371,0.944417724327,0.979746486807,0.997735961287,0.997735961287,0.979746486807,0.944417724327,0.893026547371,0.827430366973,0.75,0.663533981659,0.571157419137,0.476209042088,0.382120532245,0.292292493499,0.209971545214,0.138132980947,0.0793732335844,0.035816033492,0.00903565136865]
Calculation method

Calculation method

Coherent gain

Mean of window coefficients.

Equivalent noise bandwidth (bins)

N × sum(window²)/sum(window)².

Window coefficients

Periodic sampled window, endpoint N excluded.

Symbols and units
a
Window sample count
b
Window: 0 rectangular, 1 periodic Hann, 2 periodic Hamming

Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.

Calculation steps and notation

sum(list) adds all entries in the list.

Assumptions & limits

Assumptions & limits

  • Window type-length. Returns Coherent gain and noise bandwidth. All coefficients and observations are user supplied; results describe only the stated mathematical model. Quantities are deterministic calculations from supplied observations and assumptions; no external data is fetched. Supported limits: Finite inputs only; numeric fields bounded as labelled. Lists and JSON records are limited to 256 entries unless a stricter tool bound is stated. No automatic design approval, legal conclusion, treatment recommendation or safety certification. Window sample count: minimum 3, maximum 256. Window: 0 rectangular, 1 periodic Hann, 2 periodic Hamming: minimum 0, maximum 2.
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These calculations run in your browser. A shared link contains the values you choose to share. Only questions submitted to the separate AI finder are sent to OpenAI.

Further reading

Method reference ↗

Background reading; this does not imply endorsement or independent review of SumFizz.

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