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Who is Who
Manish Kumar Saini
has Published
491
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Signals and Systems – Common Z-Transform Pairs
Signals and Systems
Electronics & Electrical
Digital Electronics
Manish Kumar Saini
Published on 11-Jan-2022 06:44:41
Z-TransformZ-transform is a mathematical tool which is used to convert the difference equations in time domain into the algebraic equations in the frequency domain.Mathematically, if $\mathrm{\mathit{x\left ( n \right )}}$ is a discrete-time sequence, then its Z-transform is defined as −$$\mathrm{\mathit{X\left ( z \right )\mathrm{\, =\, }\sum_{n\mathrm{\, =\, }-\infty }^{\infty ...
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Laplace Transform of Periodic Functions (Time Periodicity Property of Laplace Transform)
Signals and Systems
Electronics & Electrical
Digital Electronics
Manish Kumar Saini
Published on 11-Jan-2022 06:36:33
Laplace TransformThe Laplace transform is a mathematical tool which is used to convert the differential equation in time domain into the algebraic equations in the frequency domain or s-domain.Mathematically, if $\mathrm{\mathit{x\left ( t \right )}}$ is a time domain function, then its Laplace transform is defined as, $$\mathrm{\mathit{L\left [ x\left ...
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Laplace Transform – Time Reversal, Conjugation, and Conjugate Symmetry Properties
Signals and Systems
Electronics & Electrical
Digital Electronics
Manish Kumar Saini
Published on 11-Jan-2022 06:31:36
Laplace TransformThe Laplace transform is a mathematical tool which is used to convert the differential equation in time domain into the algebraic equations in the frequency domain or s-domain.Mathematically, if $\mathrm{\mathit{x\left ( t \right )}}$ is a time domain function, then its Laplace transform is defined as −$$\mathrm{\mathit{L\left [ x\left ...
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Signals and Systems – Time Convolution and Multiplication Properties of Laplace Transform
Signals and Systems
Electronics & Electrical
Digital Electronics
Manish Kumar Saini
Published on 11-Jan-2022 06:18:31
Laplace TransformThe Laplace transform is a mathematical tool which is used to convert the differential equation in time domain into the algebraic equations in the frequency domain or s-domain.Mathematically, if $\mathrm{\mathit{x\left ( t \right )}}$ is a time domain function, then its Laplace transform is defined as −$$\mathrm{\mathit{L\left [ x\left ...
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Signals and Systems – What is Inverse Z-Transform?
Signals and Systems
Electronics & Electrical
Digital Electronics
Manish Kumar Saini
Published on 11-Jan-2022 06:10:19
The Inverse Z-TransformThe inverse Z-transform is defined as the process of finding the time domain signal $\mathrm{\mathit{x\left ( n \right )}}$ from its Z-transform $\mathrm{\mathit{X\left ( z \right )}}$. The inverse Z-transform is denoted as −$$\mathrm{\mathit{x\left ( n \right )\mathrm{\, =\, }Z^{-\mathrm{1}}\left [ X\left ( z \right ) \right ]}}$$Since ...
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Signals and Systems – Solving Differential Equations with Laplace Transform
Signals and Systems
Electronics & Electrical
Digital Electronics
Manish Kumar Saini
Published on 11-Jan-2022 05:36:14
Laplace TransformThe Laplace transform is a mathematical tool which is used to convert the differential equation in time domain into the algebraic equations in the frequency domain or sdomain.Mathematically, if $\mathit{x}\mathrm{\left(\mathit{t}\right)}$ is a time domain function, then its Laplace transform is defined as −$$\mathrm{\mathit{L}\mathrm{\left[\mathit{x}\mathrm{\left(\mathit{t}\right)}\right]}\:\mathrm{=}\:\mathit{X}\mathrm{\left(\mathit{s}\right)}\:\mathrm{=}\:\int_{-\infty }^{\infty }\mathit{x}\mathrm{\left(\mathit{t}\right)}\mathit{e^{-\mathit{st}}\:\mathit{dt}}}$$Solution of Differential Equations Using ...
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Signals and Systems – Properties of Z-Transform
Signals and Systems
Electronics & Electrical
Digital Electronics
Manish Kumar Saini
Published on 11-Jan-2022 05:31:15
Z-TransformThe Z-Transform is a mathematical tool which is used to convert the difference equations in time domain into the algebraic equations in the z-domain. Mathematically, the Z-transform of a discrete-time signal or a sequence $\mathit{x}\mathrm{\left(\mathit{n}\right)}$ is defined as −$$\mathrm{\mathit{X}\mathrm{\left(\mathit{z}\right)}\:\mathrm{=}\:\sum_{\mathit{n=-\infty }}^{\infty }\mathit{x}\mathrm{\left(\mathit{n}\right)}\mathit{z}^{-\mathit{n}}}$$Properties of Z-TransformThe following table highlights some of the important ...
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Signals and Systems – Properties of Laplace Transform
Signals and Systems
Electronics & Electrical
Digital Electronics
Manish Kumar Saini
Published on 11-Jan-2022 05:22:22
Laplace TransformThe Laplace transform is a mathematical tool which is used to convert the differential equations in time domain into the algebraic equations in the frequency domain or s-domain.Mathematically, the Laplace transform of a time-domain function $\mathit{x}\mathrm{\left(\mathit{t}\right)}$ is defined as −$$\mathrm{\mathit{L}\mathrm{\left[\mathit{x}\mathrm{\left(\mathit{t}\right)}\right]}\:\mathrm{=}\:\mathit{X}\mathrm{\left(\mathit{s}\right)}\:\mathrm{=}\:\int_{\mathrm{0} }^{\mathrm{\infty} }\mathit{x}\mathrm{\left(\mathit{t}\right)}\mathit{e^{-\mathit{st}}\:\mathit{dt}}}$$Where, s is a complex variable and it ...
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Signals and Systems – Properties of Discrete-Time Fourier Transform
Signals and Systems
Electronics & Electrical
Digital Electronics
Manish Kumar Saini
Published on 11-Jan-2022 05:16:23
Discrete Time Fourier TransformThe discrete time Fourier transform is a mathematical tool which is used to convert a discrete time sequence into the frequency domain. Therefore, the Fourier transform of a discrete time signal or sequence is called the discrete time Fourier transform (DTFT).Mathematically, if $\mathit{x}\mathrm{\left(\mathit{n}\right)}$ is a discrete time ...
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Signals and Systems – Partial Fraction Expansion Method for Inverse Z-Transform
Signals and Systems
Electronics & Electrical
Digital Electronics
Manish Kumar Saini
Published on 11-Jan-2022 05:03:17
Inverse Z-TransformThe inverse Z-transform is defined as the process of finding the time domain signal $\mathit{x}\mathrm{\left(\mathit{n}\right)}$ from its Z-transform $\mathit{X}\mathrm{\left(\mathit{z}\right)}$. The inverse Z-transform is denoted as −$$\mathrm{\mathit{x}\mathrm{\left(\mathit{n}\right)}\:\mathrm{=}\:\mathit{Z}^{-\mathrm{1}}\mathrm{\left[\mathit{X}\mathrm{\left(\mathit{z}\right)}\right]}}$$Partial Fraction Expansion Method to Find Inverse Z-TransformIn order to determine the inverse Z-transform of $\mathit{X}\mathrm{\left(\mathit{z}\right)}$ using partial fraction expansion method, the denominator of ...
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