Transformada Z

Laplace and Z transform for TI89, TI92+, V200

Jiri Bazant

bazant.jiri@gmail.com george.bazant@email.cz

1. Installation
Unpack a file lzt.zip Send a file lztR7.89g to your calculator though graph-link cable and software. In the calc a folder lzt is appearing. • Unpack a file kerno.zip under distributed_files and send KerNO.89z to the calc. If your calculator is HW2 or HW3 version sendalso hw3patch.89z. The HW should be determined by pressing F1 and A.
• •

Install KERNO – On calculator type kerno() and press EXE. If HW2 or HW3 version install hw3patch before – type hw3patch(). • Install LZT – Type lzt\install().
•

Choose whether an answer expressions shall be of common denominator form at all cost (Rational fce.) or of partial fractions form (Partial frac.). TheInstallation process creates a custom menu. It can be switched between custom and main menu by pressing 2nd and CUSTOM.

Laplace and Z transform for TI89, TI92+, V200

Jiri Bazant

bazant.jiri@gmail.com george.bazant@email.cz

Laplace and Z transform for TI89, TI92+, V200

Jiri Bazant

bazant.jiri@gmail.com george.bazant@email.cz

Some items of mode options are changing within theinstallation. ANGLE is set to RADIAN COMPLEX FORMAT is set to RECTANGULAR EXACT/APPROX is set to AUTO

Keep these options when you are using LZT.

Laplace and Z transform for TI89, TI92+, V200

Jiri Bazant

bazant.jiri@gmail.com george.bazant@email.cz

Laplace and Z transform for TI89, TI92+, V200

Jiri Bazant

bazant.jiri@gmail.com george.bazant@email.cz

2. Direct Laplace transformationlzt \ ltrn ( f ( t ) , t , s )
f(t) t s a time dependent function you want to transform an independent continuous time variable an independent complex variable of Laplace transform

Unit step, Dirac pulse
h ( t – t0 ) d ( t – t0 )
possibly

an unit step, h ( t – t0 ) = 0 when t < t0 , else = 1 a dirac pulse in time t0

h ( p(t) ), d ( p(t) ) where p(t) is a polynomial function of realroots

Laplace and Z transform for TI89, TI92+, V200

Jiri Bazant

bazant.jiri@gmail.com george.bazant@email.cz

Laplace and Z transform for TI89, TI92+, V200

Jiri Bazant

bazant.jiri@gmail.com george.bazant@email.cz

3. Inverse Laplace transformation
lzt \ invl ( F ( s ) , s , t )
F(s) s t Laplace transform of f ( t ) the independent complex variable of Laplace transform theindependent continuous time variable

Inverse transformation of expressions with several multiple roots or fractions
lzt \ finvl ( F ( s ) , s , t )

In such a case will finvl evaluate a result many times faster than invl. When the evaluation is taking a long time then break it (press ON) and try it the other way.

Laplace and Z transform for TI89, TI92+, V200

Jiri Bazantbazant.jiri@gmail.com george.bazant@email.cz

Laplace and Z transform for TI89, TI92+, V200

Jiri Bazant

bazant.jiri@gmail.com george.bazant@email.cz

4. Direct Z transformation
lzt \ ztrn ( f ( k ) , k , z )
f(k) k z a discrete function you want to transform an independent discrete variable an independent complex variable of Z transform

Unit step, Dirac pulse
h ( k – k0 ) the unit step, h ( k – k0) = 0 when k < k0 , else = 1 d ( k – k0 ) the dirac pulse, d ( k – k0 ) = 1 when k = k0 , else = 0
possibly

h ( p(k) ), d ( p(k) ) where p(k) is a polynomial function of real roots

Laplace and Z transform for TI89, TI92+, V200

Jiri Bazant

bazant.jiri@gmail.com george.bazant@email.cz

Laplace and Z transform for TI89, TI92+, V200

Jiri Bazant

bazant.jiri@gmail.comgeorge.bazant@email.cz

Conversion of Unit steps to discrete Dirac pulses
lzt \ heav2dir ( f ( k ) , k )
f(k) a discrete function containing one or more different unit steps

This function may simplify an answer of invz tool, when it contains more than one unit step or the unit step and dirac pulses at once.

Answer with separated numerators and denominators of partial fractions
lzt \ ztrn ( f ( k )...