No item in cart
Transformation on Independent Variables | Signals & Systems | GATE Preparation | EC
Real Life Application
This concept finds application in data transmission and reception in TV signals, internet and various signal processing applications. Ultra slow motion is one application area of time scaling operation.
Transformation on Independent Variable (time) is a very important concept in Signals and Systems. It finds its application in Convolution, Periodic signals, Symmetric signals, to verify systems as time invariant systems and also in various transformation techniques like Fourier series, Fourier Transform, Laplace and Z transform.
There are three operations that are performed as part of transformation on time. They are
- Time Shifting
- Time Scaling
- Time Reversal
Time shifting has two subparts: Time-Advance and Time Delay. For a signal f(t), f(t+t’) is time advanced signal and f(t-t’) is time delayed signal where t’ >0. Relation between Signals at transmitter and receiver have a relation of time shift provided the signal is noise free.
Time Scaling also has two Subparts: Time-Compression and Time-Expansion. For a signal f(t), f(at) is time scaled version of it where ‘a’ is scaling parameter, a>0. f(at) represents the time-compressed version when a>1 and time expanded version when a By means of time-scaling, information is not distorted.
Time- Reversal of a signal represented by f(-t) is the reflected version of original signal f(t). After learning all the three operations one by one, now its time to apply all the three operations simultaneously on the signal. For example, On the signal f (t), we have to apply transformations to form f(-at±b). The best way of doing it is to apply Shift then Scale and reversal at last. The reason why it is best is because the chance of doing a mistake to get final transformed signal is less. Having said that, its also important to learn about other permutations of doing it. i.e. Scale, reversal and Shift or reversal, shift and scale etc. But the care to be taken is whenever shift is done after reversal or scale or both. This has been explained clearly in the class.
Whatever transformation has been done to time, the same can be applied to frequency as well as in frequency domain the independent variable is frequency.
I am Praveen. I got AIR 1 in Instrumentation stream. I want to dedicate this to my parents and to the Gate Academy faculty. Gate Academy coaching helped me tremendously to update myself continuously.I was very impressed with the way they taught each topic in different sessions with separate material for each session.
To begin with, it gives me immense pleasure to Thank,Thank the institute THE GATE ACADEMY for all their help and support.Its a place to learn, explore, grow and succeed.Well it helps you brush-up your engineering knowledge and learn new things and clears your concept in such great details
In one year’s time, I was able to prepare for GATE exam with the help of THE GATE ACADEMY and faculties. GATE Focused study materials and online mock tests helped me know my strengthen & weakness to prepare accordingly. I wish all the best to all GATE aspirants and suggest them to go through GATE coaching in case the basics are not clear.
E Lectures helped me a lot in making a head start in the right direction. It helped whenever I got stuck in any topic. Mock Tests across 50 centers helped me judge my progress both on individual and comparative basis.
I took up mechanical coaching at THE GATE ACADEMY as there is no separate coaching for Engineering Sciences in India and Mechanical and Engineering sciences have more or less common topics.I feared that cracking GATE would be very difficult because I started my preparations very late but the counsellors and teachers guided me
THE GATE Academy questions covered a wide variety of topics and were similar to GATE paper standard. The online platform replicated the actual GATE test environment and the detailed and video solutions were sufficient to clear all doubts regarding the question. Thanks to THE GATE Academy team to provide such wonderful tests & platform.
GATE Success Story
- Our students get all India rank 1, 1, 1, 1, 4 and 4
- More than 142 students in top 100.