Gate 2016 preparation-Signals and Systems

·         Continuous and Discrete Time Signals

• We  need to study here the impact of shifting and scaling operations on the waveform of the signals, Refer in  in Oppenheim book.
•  classifications of signals based on different criteria like:

a)      Periodic and Aperiodic Signal

b)      Even and Odd Signal

c)      Power and Energy Signals

• Linear Time Invariant Systems

This is the most important part in Signals and Systems .

• impulse response -The impulse response is useful when there is a connection of more than one systems like  in cascade configuration or parallel one but you need to remember the equivalent impulse response of thesystem.

• convolution methodology

by the help of convolution we can compute output at some points only and verify with the options given and save time.

• properties of Systems like

a)      Causality,

b)      Time-Invariance,

c)       Stability,

d)     Linearity

e)      and we need to study the criterion to determine each of these properties for a system

• Fourier Series

• two types of Fourier Series and Transforms  for Continuous Time Signals and other for Discrete Time Signals. for EEE GATE course discrete time Fourier Series is not included and hence they only need to prepare only continuous time fourier series.

Need to remember two things or rather three things which are:

• Analysis and Synthesis Equations

• Properties of Transforms
• Common Transform Pairs

Fourier Transform

• need to remember that Fourier Transform exists for Aperiodic Signals
• Fourier Series for Periodic Signals
• Fourier Transform approaches Fourier Series for periodic Signals.

Also, one more important thing is the fourier transform of rectangular and triangular functions and the converse also which can easily be computed using duality property.

Laplace Transform

• Laplace Transforms only exist for Continuous Time
• The concept of Region of Convergence (ROC) as the same transform may have different inverses based on different ROCs.
• no Laplace Transform is complete without
• the concept of Initial Value and Final Value Theorem
• Before applying final value theorem, please verify the stability.

Z-Transform

• Z-Transform is for the discrete time signals
• some striking differences also like in case of Final Value Theorem
• the concept of Stability and Causality
• pole-zero plot is given and system properties need to be identified.

Sampling

• important concept in Sampling is for the Nyquist Rate and Nyquist Frequency
• practice drawing one or two waveforms where sampling frequency is less than Nyquist Frequency
• Band-Pass Sampling Theorem as that may also be asked.