Discrete-Time Fourier TransformA discrete-time signal can be represented in the frequency domain using discrete-time Fourier transform. Therefore, the Fourier transform of a discretetime sequence is called the discrete-time Fourier transform (DTFT).Mathematically, if $\mathit{x}\mathrm{\left(\mathit{n}\right)}$ is a discrete-time sequence, then its discrete-time Fourier transform is defined as −$$\mathrm{\mathit{F}\mathrm{\left[\mathit{x}\mathrm{\left(\mathit{n }\right)}\right]}\:\mathrm{=}\:\mathit{X}\mathrm{\left(\mathit{\omega}\right)}\:\mathrm{=}\:\sum_{\mathit{n=-\infty}}^{\infty}\mathit{x}\mathrm{\left(\mathit{n}\right)}\mathit{e^{-\mathit{j\omega n}}}}$$The discrete-time Fourier ... Read More

Discrete-Time Fourier TransformThe Fourier transform of a discrete-time sequence is known as the discrete-time Fourier transform (DTFT).Mathematically, the discrete-time Fourier transform (DTFT) of a discrete-time sequence $\mathit{x}\mathrm{\left(\mathit{n}\right)}$ is defined as −$$\mathrm{\mathit{F}\mathrm{\left[\mathit{x}\mathrm{\left(\mathit{n }\right)}\right]}\:\mathrm{=}\:\mathit{X}\mathrm{\left(\mathit{\omega}\right)}\:\mathrm{=}\:\sum_{\mathit{n=-\infty}}^{\infty}\mathit{x}\mathrm{\left(\mathit{n}\right)}\mathit{e^{-\mathit{j\omega n}}}}$$Time Shifting Property of Discrete-Time Fourier TransformStatement - The time-shifting property of discrete-time Fourier transform states that if ... Read More

Z-TransformThe Z-transform is a mathematical tool which is used to convert the difference equations in discrete time domain into the algebraic equations in z-domain.Mathematically, if $\mathit{x}\mathrm{\left(\mathit{n}\right)}$ is a discrete time function, then its Z-transform is defined as, $$\mathrm{\mathit{Z}\mathrm{\left[\mathit{x}\mathrm{\left(\mathit{n}\right)}\right]}\:\mathrm{=}\:\mathit{X}\mathrm{\left(\mathit{z}\right)}\:\mathrm{=}\:\sum_{\mathit{n=-\infty}}^{\infty}\mathit{x}\mathrm{\left(\mathit{n}\right)}\mathit{z^{-\mathit{n}}}}$$Differentiation in z-Domain Property of Z-TransformStatement - The differentiation in z-domain property of ... Read More

Discrete-Time Fourier TransformThe Fourier transform of a discrete-time sequence is known as the discrete-time Fourier transform (DTFT).Mathematically, the discrete-time Fourier transform (DTFT) of a discrete-time sequence $\mathit{x}\mathrm{\left(\mathit{n}\right)}$is defined as −$$\mathrm{\mathit{F}\mathrm{\left[\mathit{x}\mathrm{\left(\mathit{n}\right)}\right]}\:\mathrm{=}\:\mathit{X}\mathrm{\left(\mathit{\omega }\right)}\:\mathrm{=}\:\sum_{\mathit{n=-\infty}}^{\infty}\mathit{x}\mathrm{\left(\mathit{n}\right)}\mathit{e^{-\mathit{j\omega n}}}}$$Differentiation in Frequency Domain Property of DTFTStatement - The differentiation in frequency domain property of discrete-time Fourier transform states ... Read More

Z-TransformThe Z-transform is a mathematical tool which is used to convert the difference equations in discrete time domain into the algebraic equations in z-domain.Mathematically, if $\mathit{x}\mathrm{\left(\mathit{n}\right)}$ is a discrete time function, then its Z-transform is defined as, $$\mathrm{\mathit{Z}\mathrm{\left[\mathit{x}\mathrm{\left(\mathit{n}\right)}\right]}\:\mathrm{=}\:\mathit{X}\mathrm{\left(\mathit{z}\right)}\:\mathrm{=}\:\sum_{\mathit{n=-\infty}}^{\infty}\mathit{x}\mathrm{\left(\mathit{n}\right)}\mathit{z^{-\mathit{n}}}}$$Correlation Property of Z-TransformStatement - The correlation property of Z-transform states that if, ... Read More

Z-TransformThe Z-transform is a mathematical tool which is used to convert the difference equations in discrete time domain into the algebraic equations in z-domain.Mathematically, if $\mathit{x}\mathrm{\left(\mathit{n}\right)}$ is a discrete time function, then its Z-transform is defined as, $$\mathrm{\mathit{Z}\mathrm{\left[\mathit{x}\mathrm{\left(\mathit{n}\right)}\right]}\:\mathrm{=}\:\mathit{X}\mathrm{\left(\mathit{z}\right)}\:\mathrm{=}\:\sum_{\mathit{n=-\infty}}^{\infty}\mathit{x}\mathrm{\left(\mathit{n}\right)}\mathit{z^{-\mathit{n}}}}$$Convolution in Time Domain Property of Z-TransformStatement - The convolution in time domain ... Read More

System RealizationThe realization of a continuous-time system means obtaining a network corresponding to the differential equation or transfer function of the system.Block DiagramA diagram of a system in which the main parts or functions are represented by blocks connected by the lines that show the relationship of the blocks is ... Read More

Z-TransformThe Z-transform is a mathematical tool which is used to convert the difference equations in discrete time domain into the algebraic equations in z-domain. Mathematically, if $\mathit{x}\mathrm{\left(\mathit{n}\right)}$ is a discrete time function, then its Z-transform is defined as, $$\mathrm{\mathit{Z}\mathrm{\left[\mathit{x}\mathrm{\left(\mathit{n}\right)}\right]}\:\mathrm{=}\:\mathit{X}\mathrm{\left(\mathit{z}\right)}\:\mathrm{=}\:\sum_{\mathit{n=-\infty}}^{\infty}\mathit{x}\mathrm{\left(\mathit{n}\right)}\mathit{z^{-\mathit{n}}}}$$Transform Analysis of Discrete-Time SystemThe Z-transform plays a vital role in the ... Read More

Realization of Continuous-Time SystemRealisation of a continuous-time LTI system means obtaining a network corresponding to the differential equation or transfer function of the system.The transfer function of the system can be realised either by using integrators or differentiators. Due to certain drawbacks, the differentiators are not used to realise the ... Read More

Realization of Continuous-Time SystemRealisation of a continuous-time LTI system means obtaining a network corresponding to the differential equation or transfer function of the system.The transfer function of the system can be realised either by using integrators or differentiators. Due to certain drawbacks, the differentiators are not used to realise the ... Read More