BM661 - Module 1: Introduction to Signals and Systems
Lecture 1C
2-Dimensional signals - flat pictures or images
- Two independent variables - in the case of a picture, the two variables are along the length (X) and breadth (Y) of the image.
- The light intensity, or colour varies with the position on the image - colour is a function of the X and Y variables.
- Examples: (a) light intensity reflected from a black & white photograph, (b) the elevation of terrain above sea-level.
- The signal is usually represented as, p(x,y), where "x" and "y" are the independent variables (along the length and breadth in the case of flat pictures) and "p" is the dependent variable (the amplitude or strength of the signal).
3-Dimensional signals
- Three independent variables - in the case of a solid object, the three variables are along the length (X) and breadth (Y) and height (Z) of the object.
- The density of the material varies with the position within the object - the mass density is a function of the X and Y variables.
- A motion picture is also an example of a 3-D signal. The three independent variables are the screen length (X) and breadth (Y) and time (Z).
Multi-dimensional signals
The same properties and operations discussed for 1-D signals can be extended to multi-dimensional signals.
- Similar to time shifts, we can have X-shifts and Y-shifts which will move the picture in the horizontal or
vertical direction. If g(x,y) is a 2-D signal, then it can be shifted to give g(x-u, y-v).
- Scaling in the X or Y direction, g(ax, by) will result in magnification (a<1, b<1) or shrinking (a>1, b>1).
- Reversal on both axes will give, g(-x, -y)
- We can have systems that operate on multidimensional signals. Usually, a multi-dimensional signal will have
a single dependent variable, denoted by "g" in the above discussion.
Combinations of systems
A number of individual systems can be combined. These systems may operate simultaneously (in parallel) or
sequentially (in series) on any signal.
Self-Quiz
In the following three questions, the signal on the left is x(t). What is the expression for the signal on the
right in each case?
A
- x(t-1)
- x(t+1)
- x(1-t)
- x(t+2)
- x(2t)
B
- x(t/2)
- x(2t)
- x(2t-1)
- x(2t+1)
- x(t/2-1)
C
- x(-t-1)
- x(-t+1)
- x(2-t)
- x(-2-t)
- x(t-3)
D Consider the system: y(t)=x(t-5)+x(t+2). Which of the following statements is/are true?
- Linear
- Causal
- Invertible
- Stable
© Suresh Devasahayam
