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Sampling Frequency of Bilinear Formula

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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. Check FAQs

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

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

Sampling Frequency of Bilinear Example

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

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

Here is how the Sampling Frequency of Bilinear equation looks like.

40.0955 = \frac{3.1416 \cdot 4.52}{\arctan (\frac{2 \cdot 3.1416 \cdot 4.52}{76.81})}

40.0955Hz = \frac{3.1416 \cdot 4.52Hz}{\arctan (\frac{2 \cdot 3.1416 \cdot 4.52Hz}{76.81Hz})}

40.0955 = \frac{3.1416 \cdot 4.52}{\arctan (\frac{2 \cdot 3.1416 \cdot 4.52}{76.81})}

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Sampling Frequency of Bilinear Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

f e = \frac{π \cdot 4.52Hz}{\arctan (\frac{2 \cdot π \cdot 4.52Hz}{76.81Hz})}

Next Step Substitute values of Constants

∴

f e = \frac{3.1416 \cdot 4.52Hz}{\arctan (\frac{2 \cdot 3.1416 \cdot 4.52Hz}{76.81Hz})}

Next Step Prepare to Evaluate

∴

f e = \frac{3.1416 \cdot 4.52}{\arctan (\frac{2 \cdot 3.1416 \cdot 4.52}{76.81})}

Next Step Evaluate

∴

f e = 40.0955166184122Hz

LAST Step Rounding Answer

∴

f e = 40.0955Hz

Sampling Frequency of Bilinear Formula Elements

Variables

Constants

Functions

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

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

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

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)

ctan

Cotangent is a trigonometric function that is defined as the ratio of the adjacent side to the opposite side in a right triangle.

Syntax: 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).

Syntax: arctan(Number)

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 Sampling Frequency of Bilinear?

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

FAQs on Sampling Frequency of Bilinear

What is the formula to find Sampling Frequency of Bilinear?

The formula of Sampling Frequency of Bilinear is expressed as Sampling Frequency = (pi*Distortion Frequency)/arctan((2*pi*Distortion Frequency)/Bilinear Frequency). Here is an example- 40.09552 = (pi*4.52)/arctan((2*pi*4.52)/76.81).

How to calculate Sampling Frequency of Bilinear?

With Distortion Frequency (f_c) & Bilinear Frequency (f_b) we can find Sampling Frequency of Bilinear using the formula - Sampling Frequency = (pi*Distortion Frequency)/arctan((2*pi*Distortion Frequency)/Bilinear Frequency). This formula also uses Archimedes' constant and , Tangent (tan), Cotangent (ctan), Inverse Tangent (arctan) function(s).

Can the Sampling Frequency of Bilinear be negative?

No, the Sampling Frequency of Bilinear, measured in Frequency cannot be negative.

Which unit is used to measure Sampling Frequency of Bilinear?

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

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Sampling Frequency of Bilinear Formula

Sampling Frequency of Bilinear Example

Sampling Frequency of Bilinear Solution

Sampling Frequency of Bilinear Formula Elements

Other formulas in Discrete Time Signals category

How to Evaluate Sampling Frequency of Bilinear?

FAQs on Sampling Frequency of Bilinear

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