- Digital Signal Processing Tutorial
- DSP - Home
- DSP - Signals-Definition
- DSP - Basic CT Signals
- DSP - Basic DT Signals
- DSP - Classification of CT Signals
- DSP - Classification of DT Signals
- DSP - Miscellaneous Signals
- Operations on Signals
- Operations Signals - Shifting
- Operations Signals - Scaling
- Operations Signals - Reversal
- Operations Signals - Differentiation
- Operations Signals - Integration
- Operations Signals - Convolution
- Basic System Properties
- DSP - Static Systems
- DSP - Dynamic Systems
- DSP - Causal Systems
- DSP - Non-Causal Systems
- DSP - Anti-Causal Systems
- DSP - Linear Systems
- DSP - Non-Linear Systems
- DSP - Time-Invariant Systems
- DSP - Time-Variant Systems
- DSP - Stable Systems
- DSP - Unstable Systems
- DSP - Solved Examples
- Z-Transform
- Z-Transform - Introduction
- Z-Transform - Properties
- Z-Transform - Existence
- Z-Transform - Inverse
- Z-Transform - Solved Examples
- Discrete Fourier Transform
- DFT - Introduction
- DFT - Time Frequency Transform
- DTF - Circular Convolution
- DFT - Linear Filtering
- DFT - Sectional Convolution
- DFT - Discrete Cosine Transform
- DFT - Solved Examples
- Fast Fourier Transform
- DSP - Fast Fourier Transform
- DSP - In-Place Computation
- DSP - Computer Aided Design
- Digital Signal Processing Resources
- DSP - Quick Guide
- DSP - Useful Resources
- DSP - Discussion
Digital Signal Processing - Basic DT Signals
We have seen that how the basic signals can be represented in Continuous time domain. Let us see how the basic signals can be represented in Discrete Time Domain.
Unit Impulse Sequence
It is denoted as δ(n) in discrete time domain and can be defined as;
$$\delta(n)=\begin{cases}1, & for \quad n=0\\0, & Otherwise\end{cases}$$Unit Step Signal
Discrete time unit step signal is defined as;
$$U(n)=\begin{cases}1, & for \quad n\geq0\\0, & for \quad n<0\end{cases}$$The figure above shows the graphical representation of a discrete step function.
Unit Ramp Function
A discrete unit ramp function can be defined as −
$$r(n)=\begin{cases}n, & for \quad n\geq0\\0, & for \quad n<0\end{cases}$$The figure given above shows the graphical representation of a discrete ramp signal.
Parabolic Function
Discrete unit parabolic function is denoted as p(n) and can be defined as;
$$p(n) = \begin{cases}\frac{n^{2}}{2} ,& for \quad n\geq0\\0, & for \quad n<0\end{cases}$$In terms of unit step function it can be written as;
$$P(n) = \frac{n^{2}}{2}U(n)$$The figure given above shows the graphical representation of a parabolic sequence.
Sinusoidal Signal
All continuous-time signals are periodic. The discrete-time sinusoidal sequences may or may not be periodic. They depend on the value of ω. For a discrete time signal to be periodic, the angular frequency ω must be a rational multiple of 2π.
A discrete sinusoidal signal is shown in the figure above.
Discrete form of a sinusoidal signal can be represented in the format −
$$x(n) = A\sin(\omega n + \phi)$$Here A,ω and φ have their usual meaning and n is the integer. Time period of the discrete sinusoidal signal is given by −
$$N =\frac{2\pi m}{\omega}$$Where, N and m are integers.