Please consider registering

sp_LogInOut Log In sp_Registration Register

Register | Lost password?
Advanced Search

— Forum Scope —

— Match —

— Forum Options —

Minimum search word length is 3 characters - maximum search word length is 84 characters

sp_Feed sp_TopicIcon
Ch 5.17 - Equation 5.56 (p.133-134)
No permission to create posts
November 21, 2016
12:12 am
New Member
Forum Posts: 2
Member Since:
November 20, 2016
sp_UserOfflineSmall Offline

It mention that the equation : 1 + α1z-1 + α2z-2
can be factored to: (1-Z1z-1)(1-Z2z-1)
with some algebra.

Would anyone have the algebra steps to arrive at that conclusion?
Im a bit confuse about how this was deduced.


November 21, 2016
5:55 pm
New Member
Forum Posts: 2
Member Since:
November 20, 2016
sp_UserOfflineSmall Offline

Never mind. I was looking too deep into it :P.
Just realized the conjugate pair was added in to replace the "pre-FOIL" coefficients, with the knowledge the imaginary part would cancel out, leaving real numbers.

July 25, 2017
3:50 pm
New Member
Forum Posts: 2
Member Since:
July 25, 2017
sp_UserOfflineSmall Offline

I did have exactly the same question. I wanted to know the algebra steps involved. Digging a little bit, I found this link with the explanation behind the algebra. Very useful and interesting.


Here is a little summary

"we can write the general transfer function for the recursive LTI digital filter as

$displaystyle H(z) = gfrac{1 + eta_1 z^{-1}+ cdots + eta_M z^{-M}}{1 + a_1 z^{-1}+ cdots + a_N z^{-N}} protect$Image Enlarger


In the same way that

$ z^2 + 3z + 2$

can be factored into

$ (z + 1)(z + 2)$

we can factor the numerator and denominator to obtain.

$displaystyle H(z) = gfrac{(1-q_1z^{-1})(1-q_2z^{-1})cdots(1-q_Mz^{-1})}{(1-p_1z^{-1})(1-p_2z^{-1})cdots(1-p_Nz^{-1})}. protect$Image Enlarger

Hope this helps!


Forum Timezone: America/New_York

Most Users Ever Online: 36

Currently Online:
5 Guest(s)

Currently Browsing this Page:
1 Guest(s)

Top Posters:

Skyler: 48

Derek: 41

Peter: 41

Frodson: 40

clau_ste: 39

Gwen: 32

EZB: 24

lppier: 23

Msaldaña: 18

Jorge: 17

Member Stats:

Guest Posters: 1

Members: 495

Moderators: 1

Admins: 4

Forum Stats:

Groups: 11

Forums: 31

Topics: 511

Posts: 1966

Newest Members:

CoraDias, Edoardo, knooierd, daniel, Merril Bradshaw, BillPlunkett, Pajczur, michaelwayneharwood, RickM, rainbow wind

Moderators: W Pirkle: 187

Administrators: Tom: 66, JD Young: 80, Will Pirkle: 0, W Pirkle: 187