Sampling Frequency of Bilinear Calculator

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Discrete Time Signals

Continuous Time Signals

✖Distortion Frequency refers to the frequency which occurs when a circuit or device causes the voltage/current of different frequency components in an input signal to be modified by different amounts.ⓘ Distortion Frequency [f_c]			+10% -10%
✖Bilinear Frequency is the result of a numerical integration of the analog transfer function into the digital domain.ⓘ Bilinear Frequency [f_b]			+10% -10%

✖Sampling Frequency defines the number of samples per second (or per other unit) taken from a continuous signal to make a discrete or digital signal.ⓘ Sampling Frequency of Bilinear [f_e]

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Formula

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Sampling Frequency of Bilinear

Formula

`"f"_{"e"} = (pi*"f"_{"c"})/arctan((2*pi*"f"_{"c"})/"f"_{"b"})`

Example

`"40.09552Hz"=(pi*"4.52Hz")/arctan((2*pi*"4.52Hz")/"76.81Hz")`

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Sampling Frequency of Bilinear Solution

STEP 0: Pre-Calculation Summary

Formula Used

Sampling Frequency = (pi*Distortion Frequency)/arctan((2*pi*Distortion Frequency)/Bilinear Frequency)
f_e = (pi*f_c)/arctan((2*pi*f_c)/f_b)
This formula uses 1 Constants, 3 Functions, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

tan - The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle., tan(Angle)
ctan - Cotangent is a trigonometric function that is defined as the ratio of the adjacent side to the opposite side in a right triangle., ctan(Angle)
arctan - Inverse trigonometric functions are usually accompanied by the prefix - arc. Mathematically, we represent arctan or the inverse tangent function as tan-1 x or arctan(x)., arctan(Number)

Variables Used

Sampling Frequency - (Measured in Hertz) - Sampling Frequency defines the number of samples per second (or per other unit) taken from a continuous signal to make a discrete or digital signal.
Distortion Frequency - (Measured in Hertz) - Distortion Frequency refers to the frequency which occurs when a circuit or device causes the voltage/current of different frequency components in an input signal to be modified by different amounts.
Bilinear Frequency - (Measured in Hertz) - Bilinear Frequency is the result of a numerical integration of the analog transfer function into the digital domain.

STEP 1: Convert Input(s) to Base Unit

Distortion Frequency: 4.52 Hertz --> 4.52 Hertz No Conversion Required
Bilinear Frequency: 76.81 Hertz --> 76.81 Hertz No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

f_e = (pi*f_c)/arctan((2*pi*f_c)/f_b) --> (pi*4.52)/arctan((2*pi*4.52)/76.81)

Evaluating ... ...

f_e = 40.0955166184122

STEP 3: Convert Result to Output's Unit

40.0955166184122 Hertz --> No Conversion Required

FINAL ANSWER

40.0955166184122 ≈ 40.09552 Hertz <-- Sampling Frequency

(Calculation completed in 00.020 seconds)

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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

Sampling Frequency of Bilinear Formula

Sampling Frequency = (pi*Distortion Frequency)/arctan((2*pi*Distortion Frequency)/Bilinear Frequency)
f_e = (pi*f_c)/arctan((2*pi*f_c)/f_b)

What is meant by frequency warping?

Frequency warping transformation is a process where one spectral representation on a certain frequency scale (e.g., Hz, f-domain) and with a certain frequency resolution (most often uniform) is transformed to another representation on a new frequency scale (e.g., Bark or ERB-rate scale, v-domain).

How to Calculate Sampling Frequency of Bilinear?

Sampling Frequency of Bilinear calculator uses Sampling Frequency = (pi*Distortion Frequency)/arctan((2*pi*Distortion Frequency)/Bilinear Frequency) to calculate the Sampling Frequency, The Sampling Frequency of Bilinear formula is defined as in digital signal processing and discrete-time control theory to transform continuous-time system representations to discrete-time and vice versa with first order all-pass filters. Sampling Frequency is denoted by f_e symbol.

How to calculate Sampling Frequency of Bilinear using this online calculator? To use this online calculator for Sampling Frequency of Bilinear, enter Distortion Frequency (f_c) & Bilinear Frequency (f_b) and hit the calculate button. Here is how the Sampling Frequency of Bilinear calculation can be explained with given input values -> 40.09552 = (pi*4.52)/arctan((2*pi*4.52)/76.81).

FAQ

What is Sampling Frequency of Bilinear?

The Sampling Frequency of Bilinear formula is defined as in digital signal processing and discrete-time control theory to transform continuous-time system representations to discrete-time and vice versa with first order all-pass filters and is represented as f_e = (pi*f_c)/arctan((2*pi*f_c)/f_b) or Sampling Frequency = (pi*Distortion Frequency)/arctan((2*pi*Distortion Frequency)/Bilinear Frequency). Distortion Frequency refers to the frequency which occurs when a circuit or device causes the voltage/current of different frequency components in an input signal to be modified by different amounts & Bilinear Frequency is the result of a numerical integration of the analog transfer function into the digital domain.

How to calculate Sampling Frequency of Bilinear?

The Sampling Frequency of Bilinear formula is defined as in digital signal processing and discrete-time control theory to transform continuous-time system representations to discrete-time and vice versa with first order all-pass filters is calculated using Sampling Frequency = (pi*Distortion Frequency)/arctan((2*pi*Distortion Frequency)/Bilinear Frequency). To calculate Sampling Frequency of Bilinear, you need Distortion Frequency (f_c) & Bilinear Frequency (f_b). With our tool, you need to enter the respective value for Distortion Frequency & Bilinear 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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