Types of Discrete Time Signal

Basic Signals

  1. Impulse Signals
  2. Unit Step Signal
  3. Ramp Signal
  4. Exponential
Classification of Discrete Time Signals
  1. Energy & Power Signals: E(n)=Summation from -inf to +inf (|x(n)^2|);  P(n)=(Summation from -inf to +inf (|x(n)^2|))/(2N+1)
    • If the signal is periodic with period N, then: P(n)=(Summation from 0 to n=N-1 (|x(n)^2|))/N
    • Aperiodic signals are generally Energy Signals whereas Periodic ones are Power Signal
  2. Periodic and Aperiodic Signals: x(n)=x(n+N), so if x(n)=Acos(2*pi*f*n)
    • So, x(n+N)=Acos(2*pi*f*(n+N))= Acos(2*pi*f*n+2*pi*f*N)
    • Now 2*pi*f*N=2*pi*K
    • so f=K/N (K & N are integers)
    • A signal is periodic only if the normalized frequency is a rational number that is K/N otherwise the signal is not periodic.
    • All continuous time sinusoidal are periodic whereas all discrete time sinusoidal are not periodic.
  3. Even and Odd Signal
    • Symmetric: x(n)=x(-n)
    • Antisymmetric: x(n)=-x(n)
    • Even part: xe= (x(n)+x(-n))/2
    • Odd part: xe= (x(n)-x(-n))/2

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