Signals and Systems Flashcards
What 2 types of signals are there
- continuous time varying (curved brackets ie y(t)= 3x(t) )
- discrete time varying [squared brackets ie. y[n] = 3x[n] ]
given x(t) = e ^-at what happens if a is potive
x(t) decays exponentially
given x(t) = e ^-at what happens if a is negative
x(t) grows exponentially
What is a damped sinusoid
sinusoidal signal multiplied by exponentail
what is the equivalent trig ident: sinAsinB
0.5[cos(A-B) - cos(A+B)
What is the trig ident: 2sin^2(A)
1-cos2A
what is the trig ident: cos(A-B)
cosAcosB + sinAsinB
reverse signs for plus
what is a step function
s(t) = Au(t) where A is not equal to 0. ie. switch closed at t=0 and current has a constant value >= 0
what is a unit step function
s(t) = Au(t) where A=1 at t=0
Name the 5 system properties
- memory
- causality
- stability
- linearity
- time invariance
What is a memoryless system
a system if its output y(to) depends on the input x(t), applied at t=to. y(to) is independent of the input applied before and after t=to
what is a system with memory
if the output value depends on past or future inputs eg. -unit time delay -voltage across a capacitor (integrated) -accumulate output (autosum)
what is a causal system
if the system’s output at the current time depends only on pass and current inputs; independent f future outs
-all memoryless systems are causal
what is a stable system
systems in which output does not diverge when the input x(t) is limited
what is a linear system
- if response to x1(t) + x2(t) is y1(t) + y2(t) (additivity property or superposition)
- response to ax1(t) is ay1(t) where a is constant (homogeneity property)
what is a time-invariant system
if the characteristics of a system are independent of time
- a time shift in the input signal will result in an identical shift in the output signal
- eg. RC low pass circuit since R and C are constant over time
