In this topic, you study the Table of inverse Z-Transform.
Definition: Z-transform of discrete time signal $x[n]$ is
\[X[z] = \sum\limits_{n = – \infty }^\infty {x[n]} {z^{ – n}}\]
Using above property, the Z-transform of Basic Functions are
Z-Transform Properties
In this topic, you study the Z-Transform Properties as Linearity, Time Scaling, Time Shifting, Multiplication by an Exponential Sequence, Differentiation in z-domain, Time Reversal, and Conjugate symmetry.
Linearity
if
\[a{x_1}[n]{\text{ }} \leftrightarrow a{X_1}[z]{\text{ }}\]
\[b{x_2}[n]{\text{ }} \leftrightarrow b{X_2}[z]{\text{ }}\]
Then
\[a{x_1}[n]{\text{ }}+b{x_2}[n]{\text{ }} \leftrightarrow a{X_1}[z]{\text{ }} + b{X_2}[z]{\text{ }}\]
Inverse Laplace Transform Table
In this topic, you study the Table of Inverse Laplace Transforms.
Definition: If Laplace transform $L[f(t)]=F(s)$ then inverse Laplace transform ${L^{ – 1}}[F(s)] = f(t)$. Using above property, the inverse Laplace transform of standard forms are
Laplace Transform Table
In this topic, you study the Table of Laplace Transforms.
Definition: Laplace transform of $f(t)$ is
\[L[f(t)] = F(s) = \int\limits_0^\infty {f(t){e^{ – st}}dt}\]
Using above property, the Laplace transform of Basic Functions are
Laplace Transform Pairs | Laplace Transform of Basic Signals
In this topic, you study the Laplace Transform Pairs of Basic Signals as Decaying Exponential, Impulse function, Cosine function, Sine function, Unit step function, etc.
Sine Function
\[\sin {\omega _0}t.u(t) \rightleftarrows \frac{{{\omega _0}}}{{{s^2} + \omega _0^2}}\]
Region of convergence $\sigma$ :
\[\sigma > 0\]
Laplace Transform Properties
In this topic, you study the Laplace Transform Properties as Linearity, Time Scaling, Time Shifting, Frequency Shifting, Time differentiation, Time integration, Time Reversal, Convolution in time and Multiplication in time.
Linearity
if
\[a{f_1}(t) \leftrightarrow a{F_1}(s)\]
\[b{f_2}(t) \leftrightarrow b{F_2}(s)\]
Then
\[a{f_1}(t){\text{ }}+{\text{ }}b{f_2}(t) \leftrightarrow a{F_1}(s){\text{ }} + {\text{ }}b{F_2}(s)\]
Fourier Transform Pairs | Fourier Transform of Basic Signals
In this topic, you study the Fourier Transform Pairs of Basic Signals as Decaying Exponential, Impulse function, DC, Cosine function, Sine function, Unit step function, Signum function, Complex Exponential, and, Exponential Pulse.
Sine Function
\[\sin {\omega _0}t \longleftrightarrow j\pi \left[ {\delta (\omega + {\omega _0}) {}- \delta ({}\omega {}- {\omega _0})} \right]\]
Fourier Transform Properties
In this topic, you study the Fourier Transform Properties as Linearity, Time Scaling, Time Shifting, Frequency Shifting, Time differentiation, Time integration, Frequency differentiation, Time Reversal, Duality, Convolution in time and Convolution in frequency.
Linearity
if
\[a{f_1}(t) \leftrightarrow a{F_1}(\omega )\]
\[b{f_2}(t) \leftrightarrow b{F_2}(\omega )\]
Then
\[a{f_1}(t){\text{ }}+{\text{ }}b{f_2}(t) \leftrightarrow a{F_1}(\omega ){\text{ }} + {\text{ }}b{F_2}(\omega )\]
Comparison between BJT and MOSFET
In this topic, you study the comparison of Power devices like BJT and MOSFET. Parameters BJT MOSFET Carriers type Bipolar device Majority carrier device Gate or base drive Current controlled Voltage Controlled Temperature coefficient of ON-state resistance Negative Positive Applications Inverters, Choppers, UPS, SMPS, induction motor drives. Choppers, low power UPS, SMPS, brushless DC motor … Read more
Comparison between MOSFET and IGBT
In this topic, you study the comparison of Power devices like MOSFET and IGBT. Parameters MOSFET IGBT Carriers type Majority carrier device Bipolar device Gate or base drive Voltage Controlled Voltage Controlled Temperature coefficient of ON-state resistance Positive Positive Applications Choppers, low power UPS, SMPS, brushless DC motor drives. Inverters, UPS, SMPS, AC motor drives. … Read more