S 2.2.2 Sampling Rate Alteration Employed to generate a new sequence y[n]with a sampling rate F'r higher or lower than that of the sampling rate Fr of a given sequence x[n] Sampling rate alteration ratio is R=FT/FT If R 1,the process called interpolation If R<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
2.2.3 Classification of Sequences based on periodicity Example- 2 1.5 01 90.5 00 000 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
S 2.2.4 Classification of Sequences Energy and Power Signals Total energy of a sequence x[n]is defined by =2m2 n=-o0 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
§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
S 2.2.4 Classification of Sequences Energy and Power Signals The average power of an aperiodic sequence is defined by n n=-K Define the energy of a sequence xn over a finite interval-K≤n≤Kas Ex =xn
§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
S 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
§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