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 $\mathit{x}\mathrm{\left(\mathit{t}\right)}$ is a time domain function, then its Laplace transform is defined as −$$\mathrm{\mathit{L}\mathrm{\left[\mathit{x}\mathrm{\left(\mathit{t}\right)}\right]}\:\mathrm{=}\:\mathit{X}\mathrm{\left(\mathit{s}\right)}\:\mathrm{=}\:\int_{-\infty}^{\infty}\mathit{x}\mathrm{\left(\mathit{t}\right)}\mathit{e^{-st}}\:\mathit{dt}\:\:\:\:\:\:...(1)}$$Equation (1) gives the bilateral Laplace ... Read More

Power Spectral DensityThe distribution of average power of a signal $x\mathrm{\left(\mathit{t}\right)}$ in the frequency domain is called the power spectral density (PSD) or power density (PD) or power density spectrum. The PSD function is denoted by $\mathit{S\mathrm{\left({\mathit{\omega }}\right)}}$ and is given by, $$\mathrm{\mathit{S}\mathrm{\left(\mathit{\omega}\right)}\mathrm{=}\displaystyle\lim_{\tau \to \infty }\frac{\left| \mathit{X\mathrm{\left ( \mathit{\omega}\right)}}\right|^{2}}{\tau}\:\:\:\:\:\:...(1)}$$ExplanationIn order ... Read More

What is Data Reconstruction?Data reconstruction is defined as the process of obtaining the analog signal $x\mathrm{\left(\mathit{t}\right)}$ from the sampled signal $x_{\mathit{s}}\mathrm{\left ( \mathit{t}\right)}$. The data reconstruction is also known as interpolation.The sampled signal is given by, $$\mathrm{\mathit{x}_{\mathit{s}}\mathrm{\left ( \mathit{t}\right)}\:\mathrm{=}\:\mathit{x}\mathrm{\left(\mathit{t}\right)}\sum_{\mathit{n}=-\infty}^{\infty}\:\delta \mathrm{\left ( \mathit{t-nT} \right )}}$$$$\mathrm{\Rightarrow \mathit{x}_{\mathit{s}}\mathrm{\left ( \mathit{t}\right)}\:\mathrm{=}\sum_{\mathit{n}=-\infty}^{\infty}\:\mathit{x}\mathrm{\left(\mathit{nT}\right )}\delta\mathrm{\left(\mathit{t-nT}\right)}}$$Where, $\mathit{\delta}\mathrm{\left(\mathit{t-nT} \right)}$ ... Read More

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 ... Read More

What is Region of Convergence?Region of Convergence (ROC) is defined as the set of points in s-plane for which the Laplace transform of a function $\mathrm{\mathit{x\left ( t \right )}}$ converges. In other words, the range of 𝑅𝑒(𝑠) (i.e., 𝜎) for which the function 𝑋(𝑠) converges is called the region ... Read More

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 ... Read More

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 $\mathrm{\mathit{x\left ( \mathit{t} \right )}}$ is a time domain function, then its Laplace transform is defined as −$$\mathrm{\mathit{L\left [ x\left ... Read More

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 $x\mathrm{\left ( \mathit{t}\right)}$ 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 ... Read More

What is Correlation?The correlation of two functions or signals or waveforms is defined as the measure of similarity between those signals. There are two types of correlations −Cross-correlationAutocorrelationCross-correlationThe cross-correlation between two different signals or functions or waveforms is defined as the measure of similarity or coherence between one signal and ... Read More

What is Sampling?The process of converting a continuous-time signal into a discrete-time signal is called sampling. Once the sampling is done, the signal is defined at discrete instants of time and the time interval between two successive sampling instants is called the sampling period.Nyquist Rate of SamplingThe Nyquist rate of ... Read More