Functions Flashcards
1
Q
Complex Functions
A
Functions of the form
Z = x + iy
Have a ‘Domain’ & ‘Image’
2
Q
Joukowski Transform
A
f(z) = Z + 1/Z
3
Q
Sinc Function
A
sin(ω)/ω
Very useful in signal analysis
4
Q
Heaviside Step Function
A
Allows you to ‘Switch On’ a function at time t = T
H(t) = {0 t < 0
{1 t >= 0
5
Q
Unit Impulse Function (Rect)
A
‘Switch On’ & ‘Switch Off’ function.
Results in area under graph =1
RectT(t) = (1/T){H(t+T/2) - H(t-T/2)}
where T = signal level
6
Q
Delta Function
A
Models an impulse e.g
t = {∞ t = 0
{0 Otherwise
δ(t) = δ(-t)
7
Q
Integral of Delta Function
A
∫[∞,-∞] f(t)*δ(t) dt = f(0)
8
Q
Even Functions
A
f(t) = f(-t) e.g cos(t), t²
Reflected in x-axis
9
Q
Odd Functions
A
f(t) = -f(-t) e.g sin(t), t
Flipped Quadrants
