Signals and Systems is one of the most important topics in both EEE and ECE GATE exams as it always has a consistently good weightage and also because of simple and very less number of topics in Signals and Systems, this can easily be converted to one of the most scoring topics in GATE. Also the problems from Signals and Systems are not very much tricky and mostly all are straight forward.
The best way to prepare for Signals and Systems is to filter out the necessary information and make very short notes which can include properties of Transforms and other formulas that help in Problem Solving.
The most important thing to take care while preparing Signals and Systems is to solve a large number of problems that will teach you a number of tricks regarding GATE problems. For Problem Solving you can refer Oppenheim and Wilsky book. Otherwise, you can try solving our Question Bank in Koncept 2018 which has good problems that too fully solved.
Now coming to the topics that are covered in Signals and Systems, the following topics constitute Signals and Systems curriculum:
Continuous and Discrete Time Signals
This topic is not very important for GATE and we just need to study here the impact of shifting and scaling operations on the waveform of the signals, it may be continuous and discrete and you can easily find several examples of these sort of operations on signals in Oppenheim book.
One more thing that is covered here is the classifications of signals based on different criteria like:
- Periodic and Aperiodic Signal
- Even and Odd Signal
- Power and Energy Signals
So the classification criterion needs to be carefully studied as it is a small concept but can be directly asked.
Linear Time Invariant Systems
This probably is the most important part in Signals and Systems as all the systems are studied here only and the most important concept here is that of impulse response and Convolution. The impulse response is useful when there is a connection of more than one systems may be in cascade configuration or parallel one but we need to remember what will be the equivalent impulse response of entire system.
Also convolution methodology needs to be remembered though one can argue that we can take some transform like Laplace Transform and multiply two such transforms and take the inverse to find the output of the system and thus avoiding the convolution altogether but reality is that this process is time consuming and by the help of convolution we can compute output at some points only and verify with the options given and save time.
The next important thing the properties of Systems like Causality, Time-Invariance, Stability, Linearity and we need to study the criterion to determine each of these properties for a system because many times we may be given a system and asked which of these properties does that particular system exhibit.
Basically there are two types of Fourier Series and Transforms as one exists for Continuous Time Signals and other for Discrete Time Signals and both are very similar but for EEE GATE course discrete time Fourier Series is not included and hence they only need to prepare only continuous time fourier series.
The approach towards preparing any transform and any series is to have two pronged approach that is you need to remember two things or rather three things which are:
- Analysis and Synthesis Equations
- Properties of Transforms
- Common Transform Pairs
The thing with the GATE exam is most of the questions are directly based upon the properties of transforms and if you will calculate them completely, a lot of time will be wasted and if you apply some property, it may be done in a short time but to apply properties you need to remember some transform pairs so that you can represent a signal in terms of some known signal and apply a property, so try to prepare all the transforms in this fashion only.
Here also the approach remains same and we just need to remember that Fourier Transform exists for Aperiodic Signals and Fourier Series for Periodic Signals and Fourier Transform approaches Fourier Series for periodic Signals.
Also there is one very important duality that a signal discrete in one domain is periodic in other and vice versa so a periodic signal in time domain is discrete in frequency domain which means fourier series exists as fourier series exists only for periodic signals and that too provided Drichlet Conditions are satisfied.
Also, one more important thing is the fourier transform of rectangular and triangular functions and the converse also which can easily be computed by duality property.
Laplace Transforms only exist for Continuous Time signals and is the most important transform as it is used in Engineering Mathematics and Control Systems as well and the only additional thing that comes here is the concept of Region of Convergence (ROC) as the same transform may have different inverses based on different ROCs. So please remember no Laplace Transform is complete without ROC and rest of the approach remains same as we need to follow three pronged approach.
One more thing that is introduced here is the concept of Initial Value and Final Value Theorem and one must always remember that final value only exists subject to the condition that the system is stable and sometime students may be fooled by this, so before applying final value theorem, please verify the stability.
Z-Transform is the analogue of Fourier Transform but for the discrete time signals and hence the properties are very similar but there are some striking differences also like in case of Final Value Theorem so such differences must be clearly remembered but rest of the things and even concept of ROC remains the same.
One thing to be noticed in Laplace and Z Transform is the concept of Stability and Causality as sometimes that may come in handy if pole-zero plot is given and system properties need to be identified.
The only important concept in Sampling is for the Nyquist Rate and Nyquist Frequency and you must practice drawing one or two waveforms where sampling frequency is less than Nyquist Frequency and that will result in aliasing as sometimes waveforms may also be asked and you may come across many weird kind of problems , please ignore them as they are not important for GATE but please also read about Band-Pass Sampling Theorem as that may also be asked.
So guys, I believe that if you follow whatever I wrote above then all topics will be covered without much pain and effort and also it will be easy to remember as this is most confusing subject but at the same time most scoring one. So, please let me know if this post was helpful in you shortlisting the topics that need to be studied and if so please share it with your friends and let me know the queries and responses in comments.
If you feel the need of classes to understand the concepts then I would suggest that you try out our free demo plan of Kapsule which is a complete GATE online preparation portal, Here you would find demo content for Signals and Systems and Control Systems. Click on link below to register for free: