MAE 2381 CHAPTER 2 EXAM QUESTIONS AND ANSWERS

MAE 2381 CHAPTER 2 EXAM
QUESTIONS AND ANSWERS

Fourier Series Equation - ANSWERy(t) = A0 + sum[An*cos(2*n*pi*t/T) +
Bn*sin(2**n**pi*t/T)]

DC Part - ANSWERA0

Even Part - ANSWERAn*cos(2*n*pi*t/T)

Odd Part - ANSWERBn*sin(2*n*pi*t/T)

w - ANSWER2*pi/T

Fourier Series Equation with w - ANSWERy(t) = A0 + sum[An*cos(n*w*t) +
Bn*sin(n*w*t)]

Fourier Analysis - ANSWER- Given a function or signal: Assuming it can be written
as a sum of sinusoids allows us to determine the amplitudes, frequencies, and
phases of its unique set of sinusoids

Fourier Synthesis - ANSWERTo reconstruct the original function or signal from the
amplitudes, frequencies, and phases of a unique set of sinusoids

Conversion of signal from frequency domain to time domain - ANSWERFourier
Synthesis

Breaking a complex signal into many pieces and analyzing each of them -
ANSWERFourier Analysis

Fourier Analysis Equations - ANSWERA0 = (1/T)*int(-T/2 → T/2)[y(t)dt]
An = (2/T)*int(-T/2 → T/2)[y(t)cos(nwt)dt]
Bn = (2/T)*int(-T/2 → T/2)[y(t)sin(nwt)dt]

Fourier Synthesis Equation - ANSWERy(t) = A0 + sum[An*cos(n*w*t) +
Bn*sin(n*w*t)]

Fourier Series Cycle - ANSWERFourier Analysis → Frequency Domain → Fourier
Synthesis → Time Domain → Fourier Analysis

f(-x) = f(x)
I = int(-a → a)[f(x)]
= int(-a → 0)[f(x)] + int(0 → a)[f(x)]
= int(0 → a)[f(-x)] + int(0 → a)[f(x)]
= 2*int(0 → a)[f(x)] - ANSWEREven Function