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In this topic, you study the Causal, Anticausal & Non-Causal Signals theory, definition & solved examples.
A continuous-time signal $x(t)$ is said to be causal signal if $x(t)=0$ for $t$ < 0. The causal signal example is shown in Figure 1.
In this topic, you study the Energy and Power Signals theory, properties & solved examples.
Let us consider a circuit having resitance R supplied by a ac source voltage $v(t)$ as shown in Figure 1 is
$v(t) = {V_m}\sin \omega t$
The current passes throgh resistance R will be
In this topic, you study the Even and odd signals theory, properties & solved examples.
A continuous-time signal $x(t)$ is is said to be even signal if
$x(t)=x(-t)$
for all $t$. Figure 1 shows an even signal and it follows that
In this topic, you study the Periodic and Aperiodic Signals theory & solved examples.
A continuous-time signal $x(t)$ is called periodic if
$x(t+T)=x(t)$
for all $t$ and the time period $T$ of the signal $x(t)$ is non zero positive value.
In this topic, you study the Properties of Discrete Fourier Transform (DFT) as Linearity, Time Shifting, Frequency Shifting, Time Reversal, Conjugation, Multiplication in Time, and Circular Convolution.
if
\[a{x_1}[n]{\text{ }} \leftrightarrow a{X_1}[k]{\text{ }}\]
\[b{x_2}[n]{\text{ }} \leftrightarrow b{X_2}[k]{\text{ }}\]
Then
\[a{x_1}[n] + b{x_2}[n] \leftrightarrow a{X_1}[k] + b{X_2}[k]\]
In this topic, you study the Table of Z-Transform.
Definition: The inverse Z-transform of $X[z]$ is
\[{x_n} = \frac{1}{{2\pi j}}\oint\limits_C {X[z]{z^{n – 1}}dz} \]
Using above property, the inverse Z-transform of Basic Functions are
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
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.
if
\[a{x_1}[n]{\text{ }} \leftrightarrow a{X_1}[z]{\text{ }}\]
\[b{x_2}[n]{\text{ }} \leftrightarrow b{X_2}[z]{\text{ }}\]
Then
\[a{x_1}[n]{\text{ }}+b{x_2}[n]{\text{ }} \leftrightarrow a{X_1}[z]{\text{ }} + b{X_2}[z]{\text{ }}\]
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.
\[\sin {\omega _0}t.u(t) \rightleftarrows \frac{{{\omega _0}}}{{{s^2} + \omega _0^2}}\]
Region of convergence $\sigma$ :
\[\sigma > 0\]
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
\[a{f_1}(t){\text{ }}+{\text{ }}b{f_2}(t) \leftrightarrow a{F_1}(s){\text{ }} + {\text{ }}b{F_2}(s)\]