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In this topic, you study the Causal & Non-Causal Systems theory, definition & solved examples.
Let $x(t)$ and $y(t)$ be the input and output signals, respectively, of a system shown in Figure 1. Then the transformation of $x(t)$ into $y(t)$ is represented by the mathematical notation
In this topic, you study the Time Variant & Time-Invariant Systems theory, definition & solved examples.
Let $x(t)$ and $y(t)$ be the input and output signals, respectively, of a system shown in Figure 1. Then the transformation of $x(t)$ into $y(t)$ is represented by the mathematical notation
In this topic, you study the Stable and Unstable Systems theory, definition & solved examples.
Let $x(t)$ and $y(t)$ be the input and output signals, respectively, of a system shown in Figure 1. Then the transformation of $x(t)$ into $y(t)$ is represented by the mathematical notation
In this topic, you study the Bounded and Unbounded Signals theory, definition & solved examples.
A continuous-time signal $x(t)$ having finite value at any instant of time is said to be bounded signal i.e. if $x(t) < M$ ; where $M$ is the finite value for all time $t$. The bounded signal example with $M=1$ shown in Figure 1.
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