Gate Signal and System Preparation Strategy
In this post I am going to share with you the preparation strategy of Signal and System subject. I have already shared the preparation strategy of EM Theory for Gate.
Signal and System is an easy subject compared to other subjects if you practice lots of questions from this subject. You need to clear thoroughly the first two introductory chapters . Then it will be must easier for you to understand the remaining chapters. If you practice hard you may score full marks from this subject in GATE examination.
The syllabus of Signal and System for gate is given under Networks, Signal and Systems and is as follows:
Continuous-time signals: Fourier series and Fourier transform representations, sampling theorem and applications; Discrete-time signals: discrete-time Fourier transform (DTFT), DFT, FFT, Z-transform, interpolation of discrete-time signals; LTI systems: definition and properties, causality, stability, impulse response, convolution, poles and zeros, parallel and cascade structure, frequency response, group delay, phase delay, digital filter design techniques.
From the syllabus it is clear that the syllabus constitutes basic understanding of the subject. ‘Digital filter design techniques’ was introduced in GATE 2016 and you can expect a question from this topic in GATE 2017.
Before explaining the procedure to prepare this subject let me tell you the best books and study material for this subject. This subject can be prepared from standard reference books or from class notes of various coaching institutes. The main funda in preparing this subject lies in practice. The more you practice the more you have the chances to apply formulas in right place.
Books and Study Materials to refer:
- Signal and Systems by Oppenheim
- Signal and Systems by Schaum’s Series
- Digital Signal Processing by John G. Proakis
- Made Easy Handwritten Class Note- Signals and Systems
- The best book for siganl and sytem is Signal and Systems by Oppenheim. You need to learn the first introductory chapter very well.
Start with some basic signals like delta function, step function, ramp signal, sinc function, sampling function. You should read and make note all the properties of these signals. Best way to prepare a note for this is you write delta function in a page then write down all properties that you are getting from the book after that leave some blank space of one or two pages. While solving problems you will find more properties of delta function that you can write in the blank space.
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- Then you need to learn different signals like causal signal, anti-causal signal, non-causal signal, left sided signal, right sided signal etc. Different signal properties like odd even signal, conjugate symmetry, conjugate anti-symmetry, scaling, periodic and aperiodic signal, amplitude and time reversal should be practiced. Also in the mean time different systems like linear system, time invarient system, causal system, invertible system, memory system should be learnt. These are all basic concepts that have to be crystal clear to you. In any exam this properties of signals and systems will be embedded in the given question.
- Convolution is one of the most important topic for gate as well as for all psus. First point to learn from this chapter is convolution is valid only for linear time-invariant system. If you go through the proof of convolution formula you will understand this. Write down all properties of convolution in a notebook. You should be familiar with some common convolution conversions like convolution of two rectangular pulses, two sinc pulses, two Gaussian pulses etc. Commenting on stability, causality etc from system impulse response should be learnt.
- Fourier Series is a bit tough chapter as here is more calculation. But in gate they mainly asks the symmetry of a given signal and which harmonics will be there in Fourier series expansion. The exponential Fourier series formula, Parseval’s theorem etc. are more important.
- Fourier Transform is one of the most important chapter of signal and system.Definition, every property should be learnt with utmost importance especially the coordinate formula. Also Fourier and inverse Fourier transform of rectangular pulse, triangular pulse should be in your finger tips. Parseval’s theorem Energy spectral density etc. find great attention in every exam. Also if you are strong in signal and system it will immensely help you in communication system subject. Some topics like Phase delay, group delay, Hilbart Transform, pre-envelope, complex envelope etc. has weight-age in recent gate examinations.
- Sampling Theorem is yet another important chapter for gate. Basic questions like frequency components present after passing a sampled signal through an Ideal LPF is asked. If you can draw the frequency components of a signal that is the F.T then it will be very easy to understand the topic. Also you need to learn the ideal sampling process, sampling formula of a periodic signal etc.
- Laplace transform is easy as you are more familiar to this subject though Engineering Mathematics. But here Region of Convergence is need to be find out as the signal may exists for any time value. If you are strong in laplace transform you can find fourier transform of stable signals by putiing s=jw in laplace transform. Final value theorem and intial value theorem is very important from this topic. You should know where these theorems will be applicable.
- Z-transform is yet another important topic for gate. It has some unique properties like scaling, time reversal, differentiation, accumulation etc. that have to be learnt. Also ROC concept is also important. FVT and IVT also are here. Stability condition, causality conditiy etc are also important. For finding ROC always draw the circles and keep in mind the properties of ROC like it never contains any pole etc. Minimum phase system, non minimum phase system, maximum phase system, all pass system definitions in both s ans z domain should be read. Also if you are good in one z domain you can easily find out Discrete Time Fourier Transform of a stable signal by putting Z=ejw. Different realization structures are also important which is given in oppenheim in lucid manner.
- DFT, IDFT, FFT topics are in general a little bit tough to the gate aspirants. Most of the gate aspirants do not cover this topic but it is equally important to cover this topic. Every year there is one question from this topic in GATE. Also interview point of view FFT is really vey important as it found practical importance in large number of domains. Try to cover this topic from Digital Signal Processing by John G. Proakis.
- The new topic introduced in GATE 2016 Digital Filters can be coverd from Digital Signal Processing by John G. Proakis. Importants topics are IIR filter designs ( Approximate derivatives, Impulse Invariant Technique(one ques in gate 2016) , Bilinear Transformation, Wrapping) , order and cutoff for Butterworth Protoype Filter, Chebyshev filter, Window technique for FIR filter etc.
Signal and system subject requires immense practice with sound knowledge of various propeties. This subject is not that much hard if it is prepared and revised timely. Also it carries a significant number of marks in GATE examination it is advisable to prepare this subject with exta care.
Some topics are very easy, some topics are hard but overall this is a scoring subject. To hold a good grip on this subject I suggest you to solve the all previous year papers of GATE (ECE, EE, IN) and IES(EE,ECE) and note down the topics, problems that you are not able to solve.Practice those questions and topics one more time so that you do not miss a question/topic. Signal and Systems by Schaum’s Series also contains very good solved examples which you can solve. All the best!
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