Time-Shifting of Signals
Time shifting is the shifting of the entire signal along the time axis. By applying this operation, shape of the signal remains the same, only the position of the signal changes. It is nothing but the shifting of the origin of the signal.
supposing we have a signal x(t), we modify the time axis of the signal by adding/subtracting a finite value from its independent variable time denoted as ‘ t ‘.
For a continuous time signal
Time shifting by t0 can be denoted as x( t – t0 ).
x( t – t0 ) represents a right shift of the signal along the time axis or we can say x( t – t0 ) is the delayed version of x(t) by t0 where t0 is the positive and real value.
x( t + t0 ) represents a left shift of the signal along the time axis or we can say x( t + t0 ) is the advanced version of x(t) by t0 where t0 is the positive and real value.
For discrete time signals : same concept as for continuous time signal.
Time shifting by n0 can be denoted as x[n – n0] where n0 is an integer value.
Example: x(t) be a signal shown below. find x( t-2 ) and x( t+1 ).
x(t) = 1 ; [Tex]-4 \leq t \leq 4[/Tex]
0 ; otherwise
put t = t-2 then we get x(t -2)
x(t-2) = 1 ; [Tex] -4 \leq (t-2) \leq 4 \space or -2 \leq t \leq 6[/Tex]
0 ; otherwise
put t = t+1 then we get x(t +1)
x(t+1) = 1 ; [Tex] -4 \leq (t+1) \leq 4 \space or -5 \leq t \leq 3[/Tex]
0 ; otherwise
graphically,
Basic Signal Operations
Basic signal operations are nothing but signal manipulation or modification tools that are used in signal processing and analysis. It helps to understand the signals in different situations. These operations allow the modification and enhancement of signals for specific applications.
In this article, we will discuss the basic signal operations and understand different operations related to the time and amplitude of the signal. In time transformations, we will cover time scaling, time shifting, and time reversal, and in amplitude transformations amplitude scaling of signals, amplitude reversal of signals, addition of signals, multiplication of signals, differentiation of signals and integration of signals. We also cover various advantages, disadvantages and applications of time and amplitude transformations.
Table of Content
- What are Basic Signal Operations?
- Classification
- Basic Signal Operations on Independent Variable Time
- Basic Signal Operations on Dependent Variable Amplitude
- Addition
- Multiplication
- Differentiation
- Integration