82.2.2 Sampling Rate Alteration Employed to generate a new sequence yIn] with a sampling rate FT highe er or lower than that of the sampling rate FT of a given sequence xn Sampling rate alteration ratio is R=FT/FT IfR>1, the process called interpolation Ifr< 1, the process called decimation
§2.2.2 Sampling Rate Alteration • Employed to generate a new sequence y[n] with a sampling rate F’T higher or lower than that of the sampling rate FT of a given sequence x[n] • Sampling rate alteration ratio is R= F’T / FT • If R > 1, the process called interpolation • If R < 1, the process called decimation
E 82.2. 3 Classification of Sequences based on periodicity example 05 n 6-54-3-2-10123456789101112131415 a sequence satisfying the periodicity condition is called an periodic sequence
§2.2.3 Classification of Sequences based on periodicity •Example - •A sequence satisfying the periodicity condition is called an periodic sequence
82. 2.4 Classification of Sequences Energy and power signals Total energy of a sequence xn] is defined by Ex=∑ n=-0 An infinite length sequence with finite sample values may or may not have finite eners a finite length sequence with finite sample values has finite energy
§2.2.4 Classification of Sequences Energy and Power Signals • Total energy of a sequence x[n] is defined by = ∑ ∞ n=−∞ x n 2 x ε [ ] •An infinite length sequence with finite sample values may or may not have finite energy •A finite length sequence with finite sample values has finite energy
82. 2.4 Classification of Sequences Energy and power signals The average power of an aperiodic sequence is defined by K K-02K+1 n=-K Define the energy of a sequence x over a finite interval -Ksnskas K Ek=∑x n=-K
§2.2.4 Classification of Sequences Energy and Power Signals • The average power of an aperiodic sequence is defined by = ∑ =− + →∞ K n K K K P x n 2 2 1 1 x lim [ ] = ∑ =− K n K x K x n 2 , ε [ ] • Define the energy of a sequence x[n] over a finite interval -K≤ n ≤ K as
82. 2.4 Classification of Sequences Energy and power signals An infinite energy signal with finite average power is called a power signal Example- a periodic sequence which has a finite average power but infinite energy A finite energy signal with zero average power is called an energy signal Example A finite-length sequence which has finite energy but zero average power
§2.2.4 Classification of Sequences Energy and Power Signals • An infinite energy signal with finite average power is called a power signal Example - A periodic sequence which has a finite average power but infinite energy • A finite energy signal with zero average power is called an energy signal Example - A finite-length sequence which has finite energy but zero average power