Bilinear Transformation Frequency 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%
✖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 [f_e]			+10% -10%

✖Bilinear Frequency is the result of a numerical integration of the analog transfer function into the digital domain.ⓘ Bilinear Transformation Frequency [f_b]

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Formula

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Bilinear Transformation Frequency

Formula

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

Example

`"76.81935Hz"=(2*pi*"4.52Hz")/tan(pi*"4.52Hz"/"40.1Hz")`

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Bilinear Transformation Frequency Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

Bilinear Frequency - (Measured in Hertz) - Bilinear Frequency is the result of a numerical integration of the analog transfer function into the digital domain.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Distortion Frequency: 4.52 Hertz --> 4.52 Hertz No Conversion Required
Sampling Frequency: 40.1 Hertz --> 40.1 Hertz No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

f_b = (2*pi*f_c)/tan(pi*f_c/f_e) --> (2*pi*4.52)/tan(pi*4.52/40.1)

Evaluating ... ...

f_b = 76.81935119988

STEP 3: Convert Result to Output's Unit

76.81935119988 Hertz --> No Conversion Required

FINAL ANSWER

76.81935119988 ≈ 76.81935 Hertz <-- Bilinear Frequency

(Calculation completed in 00.004 seconds)

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Created by Rahul Gupta

Chandigarh University (CU), Mohali, Punjab

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Chandigarh University (CU), Punjab

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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

Bilinear Transformation Frequency Formula

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

What are bilinear terms?

The bilinear term, which is the product of a non-negative continuous variable and a binary variable, can be linearized by introducing an auxiliary variable, a big-M parameter and auxiliary constraints.

How to Calculate Bilinear Transformation Frequency?

Bilinear Transformation Frequency calculator uses Bilinear Frequency = (2*pi*Distortion Frequency)/tan(pi*Distortion Frequency/Sampling Frequency) to calculate the Bilinear Frequency, The Bilinear Transformation Frequency formula is defined 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. Bilinear Frequency is denoted by f_b symbol.

How to calculate Bilinear Transformation Frequency using this online calculator? To use this online calculator for Bilinear Transformation Frequency, enter Distortion Frequency (f_c) & Sampling Frequency (f_e) and hit the calculate button. Here is how the Bilinear Transformation Frequency calculation can be explained with given input values -> 76.81935 = (2*pi*4.52)/tan(pi*4.52/40.1).

FAQ

What is Bilinear Transformation Frequency?

The Bilinear Transformation Frequency formula is defined 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_b = (2*pi*f_c)/tan(pi*f_c/f_e) or Bilinear Frequency = (2*pi*Distortion Frequency)/tan(pi*Distortion Frequency/Sampling 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 & 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.

How to calculate Bilinear Transformation Frequency?

The Bilinear Transformation Frequency formula is defined 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 Bilinear Frequency = (2*pi*Distortion Frequency)/tan(pi*Distortion Frequency/Sampling Frequency). To calculate Bilinear Transformation Frequency, you need Distortion Frequency (f_c) & Sampling Frequency (f_e). With our tool, you need to enter the respective value for Distortion Frequency & Sampling 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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