16.362 Signal and System I The representation of discrete-time signals in terms of impulse Example.

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Presentation transcript:

Signal and System I The representation of discrete-time signals in terms of impulse Example

Signal and System I The representation of discrete-time signals in terms of impulse Convolution

Signal and System I The representation of continuous-time signals in terms of impulse Properties of LIT systems Commutative property Distributive property

Signal and System I Properties of LIT systems Associative property Causality for t<0. for n<0. Stability

Signal and System I The unit step response of an LTI system

Signal and System I The unit step response of an LTI system

Signal and System I The unit step response of an LTI system

Signal and System I Linear constant-coefficient difference equations depends on x[n].We don’t know y[n] unless x[n] is given. But h[n] doesn’t depend on x[n]. We should be able to obtain h[n] without x[n]. How? Discrete Fourier transform, --- Ch. 5. LTI system response properties, this chapter. + delay

Signal and System I Linear constant-coefficient difference equations When n  1, Causality + delay

Signal and System I Linear constant-coefficient difference equations + delay Determine A by initial condition: When n = 0, A = 1

Signal and System I Linear constant-coefficient difference equations Two ways: (1) Repeat the procedure (2) + delay

Signal and System I The unit step response of an LTI system, continuous time

Signal and System I Linear constant-coefficient difference equations depends on x(t).We don’t know y(t) unless x(t) is given. But h(t) doesn’t depend on x(t). We should be able to obtain h(t) without x(t). How? Continuous time Fourier transform. LTI system response properties, this chapter. +

Signal and System I Linear constant-coefficient difference equations When t>0, Determine A by initial condition: Causality +

Signal and System I Linear constant-coefficient difference equations Determine A by initial condition: A = 1 +

Signal and System I Linear constant-coefficient difference equations +

Signal and System I Singularity functions Define:

Signal and System I Singularity functions

Signal and System I Singularity functions k terms

Signal and System I Singularity functions

Signal and System I Singularity functions --- discrete time Define:

Signal and System I Singularity functions --- discrete time Define: