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What are the properties of discrete time LTI?
Dr. Deepa Kundur (University of Toronto)Discrete-Time LTI Systems and Analysis8 / 61 Discrete-Time LTI SystemsDiscrete-time Systems Common Properties ICausal system: output of system at any time n depends only on present and past inputs Ia system is causal i y(n) = F [x(n);x(n 1);x(n 2);:::] for all n.
How are signals and linear systems in discrete time?
Signals and Linear and Time-Invariant Systems in Discrete Time • Properties of signals and systems (di↵erence equations) • Time-domain analysis – ZIR, system characteristic values and modes – ZSR, unit-pulse response and convolution – stability, eigenresponse and transfer function • Frequency-domain analysis c2016 George Kesidis 1
Which is the best definition of a discrete time system?
Discrete–Time Linear, Time Invariant Systems and z–Transforms. Linear, time invariant systems “Continuous–time, linear, time invariant systems” refer to circuits or processors that take one input signal and produce one output signal with the following properties. ◦ Both the input and output are continuous–time signals. ◦ The system is linear.
Which is the convolution sum proof for discrete-time LTI systems?
Discrete-Time LTI SystemsThe Convolution Sum PROOF Therefore, X1 n=1 jh(n)j= 1 guarantees that there exists a bounded input that will result in an unbounded output, so it is also anecessarycondition and we can write: X1 n=1 jh(n)j<1(=LTI system is stable Puttingsu\ciencyandnecessitytogether we obtain: X1 n=1
Which is the equivalent of B in LTI?
IA is EQUIVALENT to B IA = B Dr. Deepa Kundur (University of Toronto)Discrete-Time LTI Systems and Analysis5 / 61 Discrete-Time LTI SystemsDiscrete-time Systems Common Properties ITime-invariant system: input-output characteristics do not change with time Ia system is time-invariant i x(n) ! Ty(n) =) x(n n 0) ! Ty(n n
What is the value of 2T in LTI?
2T[x 2(n)] for any arbitrary input sequences x 1(n) and x 2(n), and any arbitrary constants a 1and a 2. Dr. Deepa Kundur (University of Toronto)Discrete-Time LTI Systems and Analysis7 / 61 Discrete-Time LTI SystemsDiscrete-time Systems Additivity: Homogeneity: Dr. Deepa Kundur (University of Toronto)Discrete-Time LTI Systems and Analysis8 / 61
Which is the direct Z transform for LTI?
Dr. Deepa Kundur (University of Toronto)Discrete-Time LTI Systems and Analysis17 / 61 Discrete-Time LTI SystemsThe z-Transform and System Function The Direct z-Transform IDirect z-Transform: X(z) = X1 n=1