Breeding of sweetpotato for improvement }( }} Çu v t -carotene ......Objectives 1. To determine the...

36
Breeding of sweetpotato for improvement of root dry ŵatter aŶd β-carotene contents in Ethiopia Fekadu G. Balcha South Agricultural Research Institute 15th SPHI Sweetpotato SpeedBreeders Annual Meeting 8-10 June 2016 BecA-ILRI Research Platform, Nairobi, Kenya

Transcript of Breeding of sweetpotato for improvement }( }} Çu v t -carotene ......Objectives 1. To determine the...

Page 1: Breeding of sweetpotato for improvement }( }} Çu v t -carotene ......Objectives 1. To determine the combining ability, type of gene ]}vv Z ] ]o] Ç}(Z D v t -carotene content, and

Breeding of sweetpotato for improvement

of root dry atter a d β-carotene

contents in Ethiopia

Fekadu G. Balcha

South Agricultural Research Institute

15th SPHI Sweetpotato SpeedBreeders Annual Meeting

8-10 June 2016

BecA-ILRI Research Platform, Nairobi, Kenya

Page 2: Breeding of sweetpotato for improvement }( }} Çu v t -carotene ......Objectives 1. To determine the combining ability, type of gene ]}vv Z ] ]o] Ç}(Z D v t -carotene content, and

Introduction

• Sweetpotato is among most important root

crops in Ethiopia

• The second in terms of area coverage and first

in terms of production among root and tuber

crops

South Agricultural Research Institute (SARI)

Page 3: Breeding of sweetpotato for improvement }( }} Çu v t -carotene ......Objectives 1. To determine the combining ability, type of gene ]}vv Z ] ]o] Ç}(Z D v t -carotene content, and

I trodu tio …

Table 1. Area and production for selected root crops in Ethiopia, 2013/14-2014/15

Source: CSA (2015)

Crop

Area in hectares Production (ton)

2013/14 2014/15 2013/14 2014/15

Sweetpotato 53,369.19 59,269.07 1,782,725 2,701,599

Potato 66,745.61 67,361.87 784,993 921,832

Taro 42,656.73 48,817.41 1,193,538 1,448,834

Cassava - - - -

South Agricultural Research Institute (SARI)

Page 4: Breeding of sweetpotato for improvement }( }} Çu v t -carotene ......Objectives 1. To determine the combining ability, type of gene ]}vv Z ] ]o] Ç}(Z D v t -carotene content, and

I trodu tio …

Key traits in sweetpotato/breeding goals

Root yield

β-carotene content

Dry matter content

Diseases (SP virus)

Insects (SP weevil)

South Agricultural Research Institute (SARI)

Page 5: Breeding of sweetpotato for improvement }( }} Çu v t -carotene ......Objectives 1. To determine the combining ability, type of gene ]}vv Z ] ]o] Ç}(Z D v t -carotene content, and

Why β-carotene?

• Vitamin A deficiency is a serious health problem

Results in blindness, stunted growth, weak

resistance and death

Serious problem for

pre-school children

Pregnant mothers and

Lactating mothers

South Agricultural Research Institute (SARI)

Page 6: Breeding of sweetpotato for improvement }( }} Çu v t -carotene ......Objectives 1. To determine the combining ability, type of gene ]}vv Z ] ]o] Ç}(Z D v t -carotene content, and

Why β-carotene? Trends of vitamin A deficiency in children in 138 low-income and middle-income

countries between 1991 and 2013: a pooled analysis of population-based surveys

South Agricultural Research Institute (SARI)

Page 7: Breeding of sweetpotato for improvement }( }} Çu v t -carotene ......Objectives 1. To determine the combining ability, type of gene ]}vv Z ] ]o] Ç}(Z D v t -carotene content, and

Why β-carotene?...

To combat the problem of VAD

Orange fleshed sweetpotato (OFSP):

Good source of vitamin A

Cheapest staple food

Easily accessible

Year-round source of vitamin A

White-fleshed are the most popular

There is a need for cultivars with high β-carotene – i.e

OFSP

South Agricultural Research Institute (SARI)

Page 8: Breeding of sweetpotato for improvement }( }} Çu v t -carotene ......Objectives 1. To determine the combining ability, type of gene ]}vv Z ] ]o] Ç}(Z D v t -carotene content, and

Why dry matter?

OFSP cultivars:

Low acceptance by farmers/consumers

B/se of low root dry matter content (RDMC)

• RDMC is one of the limiting factors

• Most consumers prefer cultivars with high RDMC

Good eating quality, long shelf-life and processing quality

• OFSPs in Ethiopia have low RDMC

Improving the RDMC – to increase acceptability of the OFSP

cultivars

South Agricultural Research Institute (SARI)

Page 9: Breeding of sweetpotato for improvement }( }} Çu v t -carotene ......Objectives 1. To determine the combining ability, type of gene ]}vv Z ] ]o] Ç}(Z D v t -carotene content, and

Objectives

1. To determine the combining ability, type of gene a tio a d herita ility of RDMC a d β-carotene content, and yield related traits of selected sweetpotato clones, for further evaluation and breeding.

2. To estimate the magnitude of G x E interactions and to select stable and high yielding candidate sweetpotato clones for RDMC, β-carotene content and fresh root yield, and to identify the most discriminating and representative test environments in Ethiopia.

South Agricultural Research Institute (SARI)

Page 10: Breeding of sweetpotato for improvement }( }} Çu v t -carotene ......Objectives 1. To determine the combining ability, type of gene ]}vv Z ] ]o] Ç}(Z D v t -carotene content, and

O je ti es…

3. To assess associations between yield and yield

related traits and to identify the most efficient yield-

predicting traits in sweetpotato for effective selection.

4. To determine the nutritional value of newly

developed OFSP clones and to establish the

associations between β-carotene content and other

micro-nutrients for targeted large scale production to

alleviate nutrient deficiencies.

South Agricultural Research Institute (SARI)

Page 11: Breeding of sweetpotato for improvement }( }} Çu v t -carotene ......Objectives 1. To determine the combining ability, type of gene ]}vv Z ] ]o] Ç}(Z D v t -carotene content, and

Ge eti a alysis of root dry atter a d β-

carotene contents, and yield related traits in

sweetpotato

South Agricultural Research Institute (SARI)

Page 12: Breeding of sweetpotato for improvement }( }} Çu v t -carotene ......Objectives 1. To determine the combining ability, type of gene ]}vv Z ] ]o] Ç}(Z D v t -carotene content, and

No. Genotypes Root flesh

colour

RDMC

(%)

Source Resistance to

SPVD

1 Ukrewe Pale orange 28.5 CIP Unknown

2 Resisto Deep orange 25.0 CIP Susceptible

3 Ejumula Deep orange 29.0 CIP Susceptible

4 PIPI Pale yellow 31.5 CIP Resistant

5 NASPOT-1 Pale yellow 26.5 CIP Resistant

6 Temesgen White 33.0 Ethiopia

(Released variety)

Susceptible

7 Ogansagan White 34.5 Ethiopia (Released

variety)

Unknown

Table 1. List of the seven sweetpotato parents used in a diallel crosses

Materials and Methods

South Agricultural Research Institute (SARI)

Page 13: Breeding of sweetpotato for improvement }( }} Çu v t -carotene ......Objectives 1. To determine the combining ability, type of gene ]}vv Z ] ]o] Ç}(Z D v t -carotene content, and

Crossing

the first controlled crossing in Ethiopia

20 parents (10 WFSP and 10 OFSP)

flowering problem

only 7 parents produced sufficient

flowers

changed design from NC-II to half

diallel

self- and cross-incompatibility

low seed set

germination problem

Materials a d Methods…

South Agricultural Research Institute (SARI)

Page 14: Breeding of sweetpotato for improvement }( }} Çu v t -carotene ......Objectives 1. To determine the combining ability, type of gene ]}vv Z ] ]o] Ç}(Z D v t -carotene content, and

F1 seeds were harvested

scarified with sulphuric acid

germination test done

planted on polystyrene trays

Materials a d ethods…

South Agricultural Research Institute (SARI)

Page 15: Breeding of sweetpotato for improvement }( }} Çu v t -carotene ......Objectives 1. To determine the combining ability, type of gene ]}vv Z ] ]o] Ç}(Z D v t -carotene content, and

Materials a d ethods…

Transplanted to pots

South Agricultural Research Institute (SARI)

Page 16: Breeding of sweetpotato for improvement }( }} Çu v t -carotene ......Objectives 1. To determine the combining ability, type of gene ]}vv Z ] ]o] Ç}(Z D v t -carotene content, and

Materials a d ethods… Field evaluation

South Agricultural Research Institute (SARI)

Page 17: Breeding of sweetpotato for improvement }( }} Çu v t -carotene ......Objectives 1. To determine the combining ability, type of gene ]}vv Z ] ]o] Ç}(Z D v t -carotene content, and

Results

• The GCA to SCA variance ratios were 0.96, 0.94, 0.74,

0.9 a d 0.9 for RDMC, β-carotene content, SPVD, fresh

root yield and HI, respectively, indicating that the

inheritance of these traits was controlled mainly by

additive genes.

• Progenies of some of the crosses showed positive

heterosis for RDMC and fresh root yield, indicating the

possibility of selecting progenies that outperform both of

their parents.

South Agricultural Research Institute (SARI)

Page 18: Breeding of sweetpotato for improvement }( }} Çu v t -carotene ......Objectives 1. To determine the combining ability, type of gene ]}vv Z ] ]o] Ç}(Z D v t -carotene content, and

Results…

• Crosses such as Ukrewe x Resisto, Resisto x

Ogansagan, Ejumula x PIPI and NASPOT-1 x

Temesgen had:

– High β-carotene content and

– High RDMC that exceeded the mean of the best parent

– Medium to high mean fresh root yield

• Continuous progeny selection among these families

is important to develop OFSP varieties with high

RDMC

South Agricultural Research Institute (SARI)

Page 19: Breeding of sweetpotato for improvement }( }} Çu v t -carotene ......Objectives 1. To determine the combining ability, type of gene ]}vv Z ] ]o] Ç}(Z D v t -carotene content, and

Results…

20

22

24

26

28

30

32

34

36

38

40

42

44

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Ro

ot d

ry m

att

er

co

nte

nt (%

)

β-carotene content (mg 100 g-1)

South Agricultural Research Institute (SARI)

Page 20: Breeding of sweetpotato for improvement }( }} Çu v t -carotene ......Objectives 1. To determine the combining ability, type of gene ]}vv Z ] ]o] Ç}(Z D v t -carotene content, and

Genotype-by-environment interaction and stability

of s eetpotato lo es for root dry atter a d β-

carotene contents, and fresh root yield

South Agricultural Research Institute (SARI)

Page 21: Breeding of sweetpotato for improvement }( }} Çu v t -carotene ......Objectives 1. To determine the combining ability, type of gene ]}vv Z ] ]o] Ç}(Z D v t -carotene content, and

Introduction

• Genotype by environment (G x E) interaction

is a differential response of crop varieties

when grown across target environments

• Presence of G x E interaction implies the need

for systematic selection and ranking of

varieties across representative environments

to determine their level of adaptation and

yield expression prior to recommendation

South Agricultural Research Institute (SARI)

Page 22: Breeding of sweetpotato for improvement }( }} Çu v t -carotene ......Objectives 1. To determine the combining ability, type of gene ]}vv Z ] ]o] Ç}(Z D v t -carotene content, and

Materials and methods

• The experiment was conducted at six

environments

• 24 F1 progenies and one check variety were

used for the G x E study

• G x E and stability analysis was conducted

using GGE Bi-plot and AMMI analysis.

South Agricultural Research Institute (SARI)

Page 23: Breeding of sweetpotato for improvement }( }} Çu v t -carotene ......Objectives 1. To determine the combining ability, type of gene ]}vv Z ] ]o] Ç}(Z D v t -carotene content, and

Results

• Environment, genotype and G x E interaction

variances were found to be significant (p < 0.01)

for RDMC, β-carotene contents, and fresh root

yield

• Four clones: Ukrewe x Ejumula-10 (G1), Resisto x

Ejumula-7 (G6), Resisto x Ogansagen-23 (G19)

and Ejumula x PIPI-10 (G20) were selected based

on their performance and stability

South Agricultural Research Institute (SARI)

Page 24: Breeding of sweetpotato for improvement }( }} Çu v t -carotene ......Objectives 1. To determine the combining ability, type of gene ]}vv Z ] ]o] Ç}(Z D v t -carotene content, and

Results…

– These clones had:

• RDMCs of 31.82, 32.60, 33.09 and 30.06%

• High β-carotene contents of 12.48, 14.27, 16.30 and

13.99 mg 100 g-1 and

• Stable and high fresh root yields of 25.09, 26.92, 21.30

and 25.46 t ha-1

• The study demonstrated the possibility of breeding

sweetpotato varieties with a balance of high RDMC,

ediu β-carotene content and a high fresh root yield,

with wide or specific adaptation

South Agricultural Research Institute (SARI)

Page 25: Breeding of sweetpotato for improvement }( }} Çu v t -carotene ......Objectives 1. To determine the combining ability, type of gene ]}vv Z ] ]o] Ç}(Z D v t -carotene content, and

Results…

G8

G10

G12

G2

G11G19

G6

G18

G4

G17

G25 G16

G23

G15

G21

G14

G7

G9

G22G20

G5

G24

G1

G13

G3

KOK

AM

ARE

DIL

HAL

HAW

4.00-2.00

-3.00

0.00

-2.00

2.00

-1.00

0.00

-1.00 3.00

3.00

1.00

1.00

2.00

PC1 ( 61.63%)South Agricultural Research Institute (SARI)

Page 26: Breeding of sweetpotato for improvement }( }} Çu v t -carotene ......Objectives 1. To determine the combining ability, type of gene ]}vv Z ] ]o] Ç}(Z D v t -carotene content, and

Results…

G8

G10G12

G2

G11

G19

G6

G18G4

G17

G25

G16G23 G15

G21G14

G7

G9

G22G20

G5

G24

G1

G13

G3

KOK

AM

ARE

DIL

HAL

HAW

4.00-2.00

-3.00

0.00

-2.00

2.00

-1.00

0.00

-1.00 3.00

3.00

1.00

1.00

2.00

PC1 ( 93.76%)South Agricultural Research Institute (SARI)

Page 27: Breeding of sweetpotato for improvement }( }} Çu v t -carotene ......Objectives 1. To determine the combining ability, type of gene ]}vv Z ] ]o] Ç}(Z D v t -carotene content, and

Correlation and path-coefficient analyses of root

yield and related traits among selected

sweetpotato clones

South Agricultural Research Institute (SARI)

Page 28: Breeding of sweetpotato for improvement }( }} Çu v t -carotene ......Objectives 1. To determine the combining ability, type of gene ]}vv Z ] ]o] Ç}(Z D v t -carotene content, and

Results • Root yield was positively and significantly correlated with

most traits studied, indicating that component characters

should be simultaneously selected for improvement of

sweetpotato.

• Path-coefficient analysis showed that individual root weight,

number of roots per plant, RDMC and above ground fresh

weigh had high positive direct effects of 0.821, 0.776, 0.276

and 0.410, respectively, on fresh root yield

• Therefore, the above traits were identified as the most

important characters determining fresh root yield in

sweetpotato and can be recommended as indirect selection

criteria.

South Agricultural Research Institute (SARI)

Page 29: Breeding of sweetpotato for improvement }( }} Çu v t -carotene ......Objectives 1. To determine the combining ability, type of gene ]}vv Z ] ]o] Ç}(Z D v t -carotene content, and

Evaluation of newly developed orange fleshed

sweetpotato clones for nutritional quality traits

South Agricultural Research Institute (SARI)

Page 30: Breeding of sweetpotato for improvement }( }} Çu v t -carotene ......Objectives 1. To determine the combining ability, type of gene ]}vv Z ] ]o] Ç}(Z D v t -carotene content, and

Materials and methods

• Fresh root samples were freeze dried at the

Ethiopia Institute of Agricultural Research

(EIAR), Agricultural Research Quality

Laboratory

• The dried samples were sent to International

Potato Ce ter CIP , Uga da, for a alysis of β-

carotene and other micro-nutrients

South Agricultural Research Institute (SARI)

Page 31: Breeding of sweetpotato for improvement }( }} Çu v t -carotene ......Objectives 1. To determine the combining ability, type of gene ]}vv Z ] ]o] Ç}(Z D v t -carotene content, and

Materials a d ethods…

South Agricultural Research Institute (SARI)

Page 32: Breeding of sweetpotato for improvement }( }} Çu v t -carotene ......Objectives 1. To determine the combining ability, type of gene ]}vv Z ] ]o] Ç}(Z D v t -carotene content, and

Results

• β-carotene content had significant positive correlations with

iron (r = 0.27), zinc (r = 0.14), fructose (r = 0.1), glucose (r =

0.12) and sucrose (r = 0.36)

• This reflects the potential to breed for OFSP varieties enriched

with the important micro-nutrients.

• Overall, the candidate OFSP clones, G8 (Resisto x PIPI-2), G15

(Resisto x Temesgen-23) and G19 (Resisto x Ogansagen-23)

were good sources of nutritional traits such as vitamin A, iron

zinc, protein, sucrose, glucose and fructose

• The selected genotypes can be recommended for large-scale

production, food processing or further sweetpotato

improvement to alleviate nutrient deficiencies in Ethiopia

South Agricultural Research Institute (SARI)

Page 33: Breeding of sweetpotato for improvement }( }} Çu v t -carotene ......Objectives 1. To determine the combining ability, type of gene ]}vv Z ] ]o] Ç}(Z D v t -carotene content, and

Results…

South Agricultural Research Institute (SARI)

45

50

55

60

65

70

75

0

5

10

15

20

25

Sta

rch

co

nte

nt

β-ca

rote

ne

, P

rote

in, Ir

on, Z

inc, F

ructo

se,

Glu

cose

and

Su

cro

se

co

nte

nts

Genotypes

β-carotene

Protein

Iron

Zinc

Fructose

Glucose

Sucrose

Starch

Page 34: Breeding of sweetpotato for improvement }( }} Çu v t -carotene ......Objectives 1. To determine the combining ability, type of gene ]}vv Z ] ]o] Ç}(Z D v t -carotene content, and

General conclusions • Major achievements:

– Major sweetpotato production constraints were identified

– Sweetpotato families with high combining ability and heterosis for RDMC, β-carotene content and fresh root yield were developed

– Sta le ge otypes with high RDMC, oderate β-carotene content and high fresh root yield were identified

– Four traits, including individual root weight, number of roots per plant, RDMC and above ground fresh weight, were identified as indirect selection criteria to improve root yield

– It was demonstrated that the newly developed candidate OFSP clones are good sources of vitamin A, iron and zinc with high levels of protein and soluble sugars including sucrose, glucose and fructose

– Therefore, there is a possibility of improving OFSP for high RDMC, fresh root yields and nutritional traits in Ethiopia

South Agricultural Research Institute (SARI)

Page 35: Breeding of sweetpotato for improvement }( }} Çu v t -carotene ......Objectives 1. To determine the combining ability, type of gene ]}vv Z ] ]o] Ç}(Z D v t -carotene content, and

Acknowledgements

• Supervisors

• UKZN

• AGRA

• ACCI

• IFS

• SARI

• CIP

South Agricultural Research Institute (SARI)

Page 36: Breeding of sweetpotato for improvement }( }} Çu v t -carotene ......Objectives 1. To determine the combining ability, type of gene ]}vv Z ] ]o] Ç}(Z D v t -carotene content, and

South Agricultural Research Institute (SARI)


Distribución Normal Z

Distribución Normal Z

Chapter 2 Response to Harmonic Excitation · 2018. 1. 30. · 2 2 2 2 22 2 ( ) cos( tan ) ( ) (2 ) n p nn n X f x t t T]Z Z Z Z Z ]Z Z ZZ §· ¨¸ ©¹ Add homogeneous and particular

Chapter 2 Response to Harmonic Excitation · 2018. 1. 30. · 2 2 2 2 22 2 ( ) cos( tan ) ( ) (2 ) n p nn n X f x t t T]Z Z Z Z Z ]Z Z ZZ §· ¨¸ ©¹ Add homogeneous and particular

ENSC380 Lecture 28 Objectives: z-TransformUnilateral z-Transform • Analogous to unilateral Laplace transform, the unilateral z-transform is defined as: X(z) = X∞ n=0 x[n]z−n

ENSC380 Lecture 28 Objectives: z-TransformUnilateral z-Transform • Analogous to unilateral Laplace transform, the unilateral z-transform is defined as: X(z) = X∞ n=0 x[n]z−n

Z V I J E Z D E (2 . dio)

Z V I J E Z D E (2 . dio)

β-carotene from orange peel and carrot waste for cotton dyeingbada.hb.se/bitstream/2320/14082/1/2014.14.04.pdf · peel and carrot waste for cotton dyeing ... Extraction of β-carotene

β-carotene from orange peel and carrot waste for cotton dyeingbada.hb.se/bitstream/2320/14082/1/2014.14.04.pdf · peel and carrot waste for cotton dyeing ... Extraction of β-carotene

α-Tocopherol and β-Carotene in Forages and their ...3.2.5 Body weight, body condition score, fertility and health 29 3.3 Analyses 29 3.3.1 Analyses of α-tocopherol and β-carotene

α-Tocopherol and β-Carotene in Forages and their ...3.2.5 Body weight, body condition score, fertility and health 29 3.3 Analyses 29 3.3.1 Analyses of α-tocopherol and β-carotene

Generalized Social Marginal Welfare Weights for Optimal Tax ......R i w iu ci dT(z i) = R i g idT(z i). ChangeintaxpaidperpersonisdT(z i)+T0(z i)dz i. Definition AreformdT(z) isbudgetneutralifandonlyif

Generalized Social Marginal Welfare Weights for Optimal Tax ......R i w iu ci dT(z i) = R i g idT(z i). ChangeintaxpaidperpersonisdT(z i)+T0(z i)dz i. Definition AreformdT(z) isbudgetneutralifandonlyif

Hypoosmotic expression of Dunaliella bardawil ζ-carotene ...

Hypoosmotic expression of Dunaliella bardawil ζ-carotene ...

Medial z flaschards

Medial z flaschards

élyi[1])toBracewell)[2,3] - University of Rochester · 2013. 9. 13. · Qz z z F v vz µπ µµ πµ ... 3322 4 22 2 1 2 m vm v m v v vv z z mvm z Fvz v

élyi[1])toBracewell)[2,3] - University of Rochester · 2013. 9. 13. · Qz z z F v vz µπ µµ πµ ... 3322 4 22 2 1 2 m vm v m v v vv z z mvm z Fvz v

Published: Acid, Phenols, b-Carotene, and ISSN: … · b-Carotene, and Soluble Sugars ... mature fruits were collected for extraction and quantification of ascorbic acid ... and 2.2%

Published: Acid, Phenols, b-Carotene, and ISSN: … · b-Carotene, and Soluble Sugars ... mature fruits were collected for extraction and quantification of ascorbic acid ... and 2.2%

ΜΕΤΑΣΧΗΜΑΤΙΣΜΟΣ -Z

ΜΕΤΑΣΧΗΜΑΤΙΣΜΟΣ -Z

Literature Seminar on Expansion of Pd chains through Beta-Carotene & Tetraphosphine ligands

Literature Seminar on Expansion of Pd chains through Beta-Carotene & Tetraphosphine ligands

Inhibition of ζ carotene desaturase gene in chili

Inhibition of ζ carotene desaturase gene in chili

5054415D003 Ixengo L - Somfy · 2015. 6. 17. · P1: Z = 78 mm P9: Z = 203 mm P2: Z = 90 mm P10: Z = 215 mm P3: Z = 102 mm P11: Z = 227 mm P4: Z = 114 mm P12: Z = 239 mm P5: Z = 155

5054415D003 Ixengo L - Somfy · 2015. 6. 17. · P1: Z = 78 mm P9: Z = 203 mm P2: Z = 90 mm P10: Z = 215 mm P3: Z = 102 mm P11: Z = 227 mm P4: Z = 114 mm P12: Z = 239 mm P5: Z = 155

Encapsulation of -Carotene by Emulsion Electrospraying ... (1...molecules Article Encapsulation of -Carotene by Emulsion Electrospraying Using Deep Eutectic Solvents Ahmet Ozan Basar

Encapsulation of -Carotene by Emulsion Electrospraying ... (1...molecules Article Encapsulation of -Carotene by Emulsion Electrospraying Using Deep Eutectic Solvents Ahmet Ozan Basar

Beta Carotene (synthetic) - galean.com.uagalean.com.ua/upload/files/Beta Carotene.pdf · FOR INTERNAL USE ONLY 1 Beta Carotene Basics Todd Katz May 2013

Beta Carotene (synthetic) - galean.com.uagalean.com.ua/upload/files/Beta Carotene.pdf · FOR INTERNAL USE ONLY 1 Beta Carotene Basics Todd Katz May 2013

03 MatCc 2bach Soluc - IES Pravia · 2018. 1. 22. · 06 2 54 xy z 503 111 2x + 5 2y z + 3 x + 1 y + 1 z + 1 xy z 503 111 1 5 5x y z 1 0 3/5 111 xy z 503 111 3x y z 503 111 ... 7

03 MatCc 2bach Soluc - IES Pravia · 2018. 1. 22. · 06 2 54 xy z 503 111 2x + 5 2y z + 3 x + 1 y + 1 z + 1 xy z 503 111 1 5 5x y z 1 0 3/5 111 xy z 503 111 3x y z 503 111 ... 7

The z Transform - UTKweb.eecs.utk.edu/~hli31/ECE316_2015_files/Chapter9.pdf · Existence of the z Transform! The z transform of x[n]=αnun−n [0], α∈ is X(z)=αnun−n [0]z−n

The z Transform - UTKweb.eecs.utk.edu/~hli31/ECE316_2015_files/Chapter9.pdf · Existence of the z Transform! The z transform of x[n]=αnun−n [0], α∈ is X(z)=αnun−n [0]z−n

Aniiz Z P Riin Cz Z

Aniiz Z P Riin Cz Z