Discrete-Time Signals. Time-Domain Representation Example 12 3<n<4 0.5<n<8 is a finite-length sequence of length 12 obtained by zero- padding xn]=n2,-3≤n≤4 with 4 zero-valued samples 16 Copyright C 2001, S K Mitra
16 Copyright © 2001, S. K. Mitra Discrete-Time Signals: Time-Domain Representation • Example - is a finite-length sequence of length 12 obtained by zero-padding with 4 zero-valued samples − = 0 5 8 3 4 2 n n n xe n , , [ ] 3 4 2 x[n] = n , − n
Discrete-Time Signals Time-Domain Representation A right-sided sequence xn] has zero-valued samples for n<N1 A right-Sided sequence If w120. a right-sided sequence is called a causal sequence 17 Copyright C 2001, S K Mitra
17 Copyright © 2001, S. K. Mitra Discrete-Time Signals: Time-Domain Representation • A right-sided sequence x[n] has zero-valued samples for • If a right-sided sequence is called a causal sequence 0, N1 n N1 A right-sided sequence
Discrete-Time Signals. Time-Domain Representation aleft-sided sequence x[n has zero-valued samples for n>N2 N A left-sided sequence If n, so, a left-sided sequence is called an anti-causal sequence 18 Copyright C 2001, S K Mitra
18 Copyright © 2001, S. K. Mitra Discrete-Time Signals: Time-Domain Representation • A left-sided sequence x[n] has zero-valued samples for • If a left-sided sequence is called an anti-causal sequence n N2 0, N2 A left-sided sequence
Operations on Sequences A single-input, single-outputSISO) discrete-time system operates on a sequence, called the input sequence, according some prescribed rules and develops another sequence called the output sequence, with more desirable properties Discrete-time system Input sequence Output sequence 19 Copyright C 2001, S K Mitra
19 Copyright © 2001, S. K. Mitra Operations on Sequences • A single-input, single-output (SISO) discrete-time system operates on a sequence, called the input sequence, according some prescribed rules and develops another sequence, called the output sequence, with more desirable properties x[n] y[n] Input sequence Output sequence Discrete-time system
Operations on Sequences For example the input may be a signal corrupted with additive noise Discrete-time system is designed to generate an output by removing the noise component from the input In most cases, the operation defining a particular discrete-time system is composed of some basic operations 20 Copyright C 2001, S K Mitra
20 Copyright © 2001, S. K. Mitra Operations on Sequences • For example, the input may be a signal corrupted with additive noise • Discrete-time system is designed to generate an output by removing the noise component from the input • In most cases, the operation defining a particular discrete-time system is composed of some basic operations