Fourier Analysis

Question 1

fundamental frequency

Answer 1

ω = 2π / T

Question 1

Waveform analysis equation

Answer 1

f(t) = A cos(ωt + Φ)

amplitude (A)
fundamental frequency (ω)
displacement in x axis (Φ)

Question 2

periodic function

Answer 2

f(t) = f(t + nT)

period (T)

Question 3

work out if f(x) is odd, even or neither

Answer 3

even: f(-x) = f(x), symmetrical about y axis
odd: f(-x) = - f(x), rotational symmetry about origin
neither: the above doesn’t apply

Question 4

how to tell if an or bn = 0

Answer 4

an: cos() = even
If f(x) is even/neither an ≠ 0
bn: sin() = odd
If f(x) is odd/neither an ≠ 0

Question 5

blueprint to working terms of fourier series

Answer 5

• use given period function to find period
• figure out if f(t) is odd/even/neither
• is average value of f(t) > 0, < 0, = 0

Question 6

How do you workout a0 by inspection

Answer 6

a0 = 2 x average of f(t)