3 Assessing Complex Sinusoids

Question 1

Why complex sinusoid?

Answer 1

(1) separation of time dependent part of sinusoid from time independent part of sinusoid​
(2) efficient addition of complex sinusoids
(3) efficient multiplication of complex sinusoids
(4) efficient coding of complex sinusoids

Question 2

Euler’s form is required as:

Answer 2

A complex number in Cartesian coordinates is related to a
complex number in polar coordinates by Euler’s formula

Question 3

Euler’s formula in terms of complex signals?

Answer 3

Question 4

Rotating phasor?

Answer 4

The rotating phasor describes the time dependent part of
a sinusoid (counterclockwise rotation)

Question 5

Equation and diagrams to describe a rotating phasor?

Answer 5

Question 6

The multiplication of two complex numbers?

Answer 6

Question 7

How is the complex amplitude and rotating phasor used together to describe a complex sinusoid?

Answer 7

Question 8

Proving that the real description of a sinusoid is entirely equivalent to the complex description of a sinusoid?

Answer 8

Question 9

How can the percentage data saving be found for transmitting four words instead of the entire signal?

Answer 9

Question 10

The equation for complex amplitude?

Answer 10

Question 11

The equation for the rotating phasor?

Answer 11

Question 12

How are the equations for the complex amplitude and rotating phasor used together to describe a sinusoid?

Answer 12