Fourier Transform of Rectangular Window Calculator

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Discrete Time Signals

Continuous Time Signals

✖Unlimited Time Signal is one that is both zero and nonzero for a infinite length time interval.ⓘ Unlimited Time Signal [T_o]			+10% -10%
✖Input Periodic Frequency is the number of complete cycles of a periodic phenomenon that occur in one second.ⓘ Input Periodic Frequency [f_inp]			+10% -10%

✖Rectangular Window provides the minimum mean square error estimate of the Discrete-time Fourier transform, at the cost of other issues discussed.ⓘ Fourier Transform of Rectangular Window [W_rn]

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Formula

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Fourier Transform of Rectangular Window

Formula

`"W"_{"rn"} = sin(2*pi*"T"_{"o"}*"f"_{"inp"})/(pi*"f"_{"inp"})`

Example

`"0.037345"=sin(2*pi*"40"*"5.01Hz")/(pi*"5.01Hz")`

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Fourier Transform of Rectangular Window Solution

STEP 0: Pre-Calculation Summary

Formula Used

Rectangular Window = sin(2*pi*Unlimited Time Signal*Input Periodic Frequency)/(pi*Input Periodic Frequency)
W_rn = sin(2*pi*T_o*f_inp)/(pi*f_inp)
This formula uses 1 Constants, 1 Functions, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)

Variables Used

Rectangular Window - Rectangular Window provides the minimum mean square error estimate of the Discrete-time Fourier transform, at the cost of other issues discussed.
Unlimited Time Signal - Unlimited Time Signal is one that is both zero and nonzero for a infinite length time interval.
Input Periodic Frequency - (Measured in Hertz) - Input Periodic Frequency is the number of complete cycles of a periodic phenomenon that occur in one second.

STEP 1: Convert Input(s) to Base Unit

Unlimited Time Signal: 40 --> No Conversion Required
Input Periodic Frequency: 5.01 Hertz --> 5.01 Hertz No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

W_rn = sin(2*pi*T_o*f_inp)/(pi*f_inp) --> sin(2*pi*40*5.01)/(pi*5.01)

Evaluating ... ...

W_rn = 0.0373448815883735

STEP 3: Convert Result to Output's Unit

0.0373448815883735 --> No Conversion Required

FINAL ANSWER

0.0373448815883735 ≈ 0.037345 <-- Rectangular Window

(Calculation completed in 00.004 seconds)

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Home » Engineering » Electronics » Signal and Systems » Discrete Time Signals » Fourier Transform of Rectangular Window

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Created by Rahul Gupta

Chandigarh University (CU), Mohali, Punjab

Rahul Gupta has created this Calculator and 25+ more calculators!

Verified by Ritwik Tripathi

Vellore Institute of Technology (VIT Vellore), Vellore

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< 14 Discrete Time Signals Calculators

Triangular Window

Go Triangular Window = 0.42-0.52*cos((2*pi*Number of Samples)/(Sample Signal Window-1))-0.08*cos((4*pi*Number of Samples)/(Sample Signal Window-1))

Damping Coefficient of Second Order Transmittance

Go Damping Coefficient = (1/2)*Input Resistance*Initial Capacitance*sqrt((Transmittance Filtering*Input Inductance)/(Sample Signal Window*Initial Capacitance))

Fourier Transform of Rectangular Window

Go Rectangular Window = sin(2*pi*Unlimited Time Signal*Input Periodic Frequency)/(pi*Input Periodic Frequency)

Sampling Frequency of Bilinear

Go Sampling Frequency = (pi*Distortion Frequency)/arctan((2*pi*Distortion Frequency)/Bilinear Frequency)

Bilinear Transformation Frequency

Go Bilinear Frequency = (2*pi*Distortion Frequency)/tan(pi*Distortion Frequency/Sampling Frequency)

Natural Angular Frequency of Second Order Transmittance

Go Natural Angular Frequency = sqrt((Transmittance Filtering*Input Inductance)/(Sample Signal Window*Initial Capacitance))

Cutoff Angular Frequency

Go Cutoff Angular Frequency = (Maximal Variation*Central Frequency)/(Sample Signal Window*Clock Count)

Maximal Variation of Cutoff Angular Frequency

Go Maximal Variation = (Cutoff Angular Frequency*Sample Signal Window*Clock Count)/Central Frequency

Inverse Transmittance Filtering

Go Inverse Transmittance Filtering = (sinc(pi*Input Periodic Frequency/Sampling Frequency))^-1

Hanning Window

Go Hanning Window = 1/2-(1/2)*cos((2*pi*Number of Samples)/(Sample Signal Window-1))

Hamming Window

Go Hamming Window = 0.54-0.46*cos((2*pi*Number of Samples)/(Sample Signal Window-1))

Transmittance Filtering

Go Transmittance Filtering = sinc(pi*(Input Periodic Frequency/Sampling Frequency))

Initial Frequency of Dirac Comb Angle

Go Initial Frequency = (2*pi*Input Periodic Frequency)/Signal Angle

Frequency Dirac Comb Angle

Go Signal Angle = 2*pi*Input Periodic Frequency*1/Initial Frequency

Fourier Transform of Rectangular Window Formula

Rectangular Window = sin(2*pi*Unlimited Time Signal*Input Periodic Frequency)/(pi*Input Periodic Frequency)
W_rn = sin(2*pi*T_o*f_inp)/(pi*f_inp)

What is a window transform?

A window transformation performs calculations on a row based on row values that are related to it. Windowing functions can perform calculations based on time, relative row positions, and rolling windows.

How to Calculate Fourier Transform of Rectangular Window?

Fourier Transform of Rectangular Window calculator uses Rectangular Window = sin(2*pi*Unlimited Time Signal*Input Periodic Frequency)/(pi*Input Periodic Frequency) to calculate the Rectangular Window, The Fourier Transform of Rectangular Window formula is defined as the minimum mean square error estimate of the Discrete-time Fourier transform, at the cost of other issues discussed. In general, the transform is applied to the product of the waveform and a window function. Rectangular Window is denoted by W_rn symbol.

How to calculate Fourier Transform of Rectangular Window using this online calculator? To use this online calculator for Fourier Transform of Rectangular Window, enter Unlimited Time Signal (T_o) & Input Periodic Frequency (f_inp) and hit the calculate button. Here is how the Fourier Transform of Rectangular Window calculation can be explained with given input values -> 0.037345 = sin(2*pi*40*5.01)/(pi*5.01).

FAQ

What is Fourier Transform of Rectangular Window?

The Fourier Transform of Rectangular Window formula is defined as the minimum mean square error estimate of the Discrete-time Fourier transform, at the cost of other issues discussed. In general, the transform is applied to the product of the waveform and a window function and is represented as W_rn = sin(2*pi*T_o*f_inp)/(pi*f_inp) or Rectangular Window = sin(2*pi*Unlimited Time Signal*Input Periodic Frequency)/(pi*Input Periodic Frequency). Unlimited Time Signal is one that is both zero and nonzero for a infinite length time interval & Input Periodic Frequency is the number of complete cycles of a periodic phenomenon that occur in one second.

How to calculate Fourier Transform of Rectangular Window?

The Fourier Transform of Rectangular Window formula is defined as the minimum mean square error estimate of the Discrete-time Fourier transform, at the cost of other issues discussed. In general, the transform is applied to the product of the waveform and a window function is calculated using Rectangular Window = sin(2*pi*Unlimited Time Signal*Input Periodic Frequency)/(pi*Input Periodic Frequency). To calculate Fourier Transform of Rectangular Window, you need Unlimited Time Signal (T_o) & Input Periodic Frequency (f_inp). With our tool, you need to enter the respective value for Unlimited Time Signal & Input Periodic Frequency 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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