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Bilinear Transformation Frequency Formula

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Bilinear Frequency is the result of a numerical integration of the analog transfer function into the digital domain. Check FAQs

f b = \frac{2 \cdot π \cdot f c}{\tan (π \cdot \frac{f c}{f e})}

f_b - Bilinear Frequency?f_c - Distortion Frequency?f_e - Sampling Frequency?π - Archimedes' constant?

Bilinear Transformation Frequency Example

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Here is how the Bilinear Transformation Frequency equation looks like with Values.

Here is how the Bilinear Transformation Frequency equation looks like with Units.

Here is how the Bilinear Transformation Frequency equation looks like.

76.8194 = \frac{2 \cdot 3.1416 \cdot 4.52}{\tan (3.1416 \cdot \frac{4.52}{40.1})}

76.8194Hz = \frac{2 \cdot 3.1416 \cdot 4.52Hz}{\tan (3.1416 \cdot \frac{4.52Hz}{40.1Hz})}

76.8194 = \frac{2 \cdot 3.1416 \cdot 4.52}{\tan (3.1416 \cdot \frac{4.52}{40.1})}

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Bilinear Transformation Frequency Solution

Follow our step by step solution on how to calculate Bilinear Transformation Frequency?

FIRST Step Consider the formula

f b = \frac{2 \cdot π \cdot f c}{\tan (π \cdot \frac{f c}{f e})}

Next Step Substitute values of Variables

∴

f b = \frac{2 \cdot π \cdot 4.52Hz}{\tan (π \cdot \frac{4.52Hz}{40.1Hz})}

Next Step Substitute values of Constants

∴

f b = \frac{2 \cdot 3.1416 \cdot 4.52Hz}{\tan (3.1416 \cdot \frac{4.52Hz}{40.1Hz})}

Next Step Prepare to Evaluate

∴

f b = \frac{2 \cdot 3.1416 \cdot 4.52}{\tan (3.1416 \cdot \frac{4.52}{40.1})}

Next Step Evaluate

∴

f b = 76.81935119988Hz

LAST Step Rounding Answer

∴

f b = 76.8194Hz

Bilinear Transformation Frequency Formula Elements

Variables

Constants

Functions

Bilinear Frequency

Bilinear Frequency is the result of a numerical integration of the analog transfer function into the digital domain.

Symbol: f_b

Measurement: FrequencyUnit: Hz

Note: Value should be greater than 0.

Formulas to find Bilinear Frequency

Distortion 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.

Symbol: f_c

Measurement: FrequencyUnit: Hz

Note: Value should be greater than 0.

Formulas to find Distortion Frequency

Sampling Frequency

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.

Symbol: f_e

Measurement: FrequencyUnit: Hz

Note: Value should be greater than 0.

Formulas to find Sampling Frequency

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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.

Syntax: tan(Angle)

Other formulas in Discrete Time Signals category

Go Cutoff Angular Frequency

ω co = \frac{M \cdot f ce}{W ss \cdot K}

Go Hanning Window

W hn = \frac{1}{2} - (\frac{1}{2}) \cdot \cos (\frac{2 \cdot π \cdot n}{W ss - 1})

Go Hamming Window

W hm = 0.54 - 0.46 \cdot \cos (\frac{2 \cdot π \cdot n}{W ss - 1})

Go Triangular Window

W tn = 0.42 - 0.52 \cdot \cos (\frac{2 \cdot π \cdot n}{W ss - 1}) - 0.08 \cdot \cos (\frac{4 \cdot π \cdot n}{W ss - 1})

How to Evaluate Bilinear Transformation Frequency?

Bilinear Transformation Frequency evaluator uses Bilinear Frequency = (2*pi*Distortion Frequency)/tan(pi*Distortion Frequency/Sampling Frequency) to evaluate 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 evaluate Bilinear Transformation Frequency using this online evaluator? To use this online evaluator for Bilinear Transformation Frequency, enter Distortion Frequency (f_c) & Sampling Frequency (f_e) and hit the calculate button.

FAQs on Bilinear Transformation Frequency

What is the formula to find Bilinear Transformation Frequency?

The formula of Bilinear Transformation Frequency is expressed as Bilinear Frequency = (2*pi*Distortion Frequency)/tan(pi*Distortion Frequency/Sampling Frequency). Here is an example- 76.81935 = (2*pi*4.52)/tan(pi*4.52/40.1).

How to calculate Bilinear Transformation Frequency?

With Distortion Frequency (f_c) & Sampling Frequency (f_e) we can find Bilinear Transformation Frequency using the formula - Bilinear Frequency = (2*pi*Distortion Frequency)/tan(pi*Distortion Frequency/Sampling Frequency). This formula also uses Archimedes' constant and Tangent (tan) function(s).

Can the Bilinear Transformation Frequency be negative?

No, the Bilinear Transformation Frequency, measured in Frequency cannot be negative.

Which unit is used to measure Bilinear Transformation Frequency?

Bilinear Transformation Frequency is usually measured using the Hertz[Hz] for Frequency. Petahertz[Hz], Terahertz[Hz], Gigahertz[Hz] are the few other units in which Bilinear Transformation Frequency can be measured.

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Bilinear Transformation Frequency Formula

Bilinear Transformation Frequency Example

Bilinear Transformation Frequency Solution

Bilinear Transformation Frequency Formula Elements

Other formulas in Discrete Time Signals category

How to Evaluate Bilinear Transformation Frequency?

FAQs on Bilinear Transformation Frequency

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