Hi Will,

I'm struggling to understand why H(w) = sqrt (a + jb)(a - jb) on page 108.

From what I understand you can work out the magnitude of a complex number, R, from sqrt of A squared + B squared. The complex number that we have is 1.0 - j0.

Why in this instance does H(w) != sqrt (1 squared + 0 squared)?

Could you please explain how you reach H(w) = sqrt (a + jb)(a - jb)?

Many ThanksÂ

Jake

I'm struggling to understand why H(w) = sqrt (a + jb)(a - jb) on page 108.Â Could you please explain how you reach H(w) = sqrt (a + jb)(a - jb)?

It's actually the magnitude of H(w) which is written |H(w)| and it is defined as the square root of the product of the complex number and its complex conjugate - there is nothing to "reach" here - it's the definition of the magnitude of the complex number. By multiplying the polynomial out, and knowing that j^2 = -1, you will arrive at the shortcut version, |H| = sqrt(a^2 + b^2).Â

For the number 1.0 - j0.0, the complex conjugate is 1.0 + j0.0

|H| = sqrt((1.0*1.0) - j0.0*1.0 +j0.0*1.0 -j^2(0.0) = sqrt(1.0 + 0.0) = sqrt(a^2 + b^2)

- Will

Most Users Ever Online: 152

Currently Online:

10 Guest(s)

Currently Browsing this Page:

1 Guest(s)

Top Posters:

Chaes: 56

Skyler: 48

StevieD: 46

Derek: 46

Frodson: 45

Peter: 43

TheSmile: 43

Nickolai: 43

clau_ste: 39

jeanlecode: 37

Member Stats:

Guest Posters: 2

Members: 786

Moderators: 1

Admins: 6

Forum Stats:

Groups: 13

Forums: 42

Topics: 853

Posts: 3385

Newest Members:

F_Marchal, plenge, Kevin_1, jkarstedt, JohnW, Sean, loss1234, Murray J, Dave, jcloungeModerators: W Pirkle: 698