Signals and Systems

Question 1

What is the complex representation of a wave ?

Answer 1

Question 2

Complex Representation: Euler Identity

Answer 2

Question 3

What is the Complex Exponential Representation?

Answer 3

Question 4

Represent the following in complex exponenetial form

Answer 4

Question 5

What is the fourier series?

Square wave?

Answer 5

Is the sum of sinusoidal signals

A square wave may be synthesized as a sum of sinusoidal components comprising of the fundamental component and the odd harmonics; with amplitudes decreasing with harmonic order.

Question 6

Describe all the parts of the fourier series eq.

Answer 6

x(t) is periodic function that could be expressed as a sum of sinusoids

Sigma is the sum

the exponential is the sum of sinusoids (based off of Euler’s identity)

n = to the harmonic

C_n = Determines the amplitude and phase. We don’t know what C is for each value of n, another equation is used for that.

Question 7

Is some of your signal function is zero for a part of the period, what can you do when calculating C_n ?

Answer 7

You do not have to integrate for the part that is zero.

Question 8

What is the x with the dash represent?

Answer 8

It is the mean of x(t), it is equal to the zeroth value of the coefficient function, C₀ . It is also called the DC bias of the sinusoid because it has a frequency of zero a constant value.

Question 9

What identity are you likely to have to use when doing fourier?

Answer 9

Question 10

For fourier series if you if you have a DC bias, what do you have to remember to put under the sum signal?

Answer 10

That cannot be equal to zero.