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Chapter 2 solutions © 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458. Full file at http://testbank360.eu/solution-manual-signals-systems-and-transforms-4th-edition-phillips
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© 2008 Pearson Education, Inc., Upper Saddle …testbank360.eu/...manual-signals-systems-and-transforms-4th-edition... · (c) xo(0)=-xo(-0)= -xo(0). The only number with a=-a is

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Page 1: © 2008 Pearson Education, Inc., Upper Saddle …testbank360.eu/...manual-signals-systems-and-transforms-4th-edition... · (c) xo(0)=-xo(-0)= -xo(0). The only number with a=-a is

Chapter 2 solutions

© 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise.

For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.

Full file at http://testbank360.eu/solution-manual-signals-systems-and-transforms-4th-edition-phillips

Page 2: © 2008 Pearson Education, Inc., Upper Saddle …testbank360.eu/...manual-signals-systems-and-transforms-4th-edition... · (c) xo(0)=-xo(-0)= -xo(0). The only number with a=-a is

© 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.This material is is protected by Copyright and written permission should be obtained from the publisher prior to any

prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to:

Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.Full file at http://testbank360.eu/solution-manual-signals-systems-and-transforms-4th-edition-phillips

Page 3: © 2008 Pearson Education, Inc., Upper Saddle …testbank360.eu/...manual-signals-systems-and-transforms-4th-edition... · (c) xo(0)=-xo(-0)= -xo(0). The only number with a=-a is

© 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.This material is is protected by Copyright and written permission should be obtained from the publisher prior to any

prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to:

Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.Full file at http://testbank360.eu/solution-manual-signals-systems-and-transforms-4th-edition-phillips

Page 4: © 2008 Pearson Education, Inc., Upper Saddle …testbank360.eu/...manual-signals-systems-and-transforms-4th-edition... · (c) xo(0)=-xo(-0)= -xo(0). The only number with a=-a is

© 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.This material is is protected by Copyright and written permission should be obtained from the publisher prior to any

prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to:

Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.Full file at http://testbank360.eu/solution-manual-signals-systems-and-transforms-4th-edition-phillips

Page 5: © 2008 Pearson Education, Inc., Upper Saddle …testbank360.eu/...manual-signals-systems-and-transforms-4th-edition... · (c) xo(0)=-xo(-0)= -xo(0). The only number with a=-a is

© 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.This material is is protected by Copyright and written permission should be obtained from the publisher prior to any

prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to:

Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.Full file at http://testbank360.eu/solution-manual-signals-systems-and-transforms-4th-edition-phillips

Page 6: © 2008 Pearson Education, Inc., Upper Saddle …testbank360.eu/...manual-signals-systems-and-transforms-4th-edition... · (c) xo(0)=-xo(-0)= -xo(0). The only number with a=-a is

© 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise.

For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.

Full file at http://testbank360.eu/solution-manual-signals-systems-and-transforms-4th-edition-phillips

Page 7: © 2008 Pearson Education, Inc., Upper Saddle …testbank360.eu/...manual-signals-systems-and-transforms-4th-edition... · (c) xo(0)=-xo(-0)= -xo(0). The only number with a=-a is

2.2

© 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.This material is is protected by Copyright and written permission should be obtained from the publisher prior to any

prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to:

Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.Full file at http://testbank360.eu/solution-manual-signals-systems-and-transforms-4th-edition-phillips

Page 8: © 2008 Pearson Education, Inc., Upper Saddle …testbank360.eu/...manual-signals-systems-and-transforms-4th-edition... · (c) xo(0)=-xo(-0)= -xo(0). The only number with a=-a is

© 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise.

For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.

Full file at http://testbank360.eu/solution-manual-signals-systems-and-transforms-4th-edition-phillips

Page 9: © 2008 Pearson Education, Inc., Upper Saddle …testbank360.eu/...manual-signals-systems-and-transforms-4th-edition... · (c) xo(0)=-xo(-0)= -xo(0). The only number with a=-a is

2.5

© 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.This material is is protected by Copyright and written permission should be obtained from the publisher prior to any

prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to:

Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.Full file at http://testbank360.eu/solution-manual-signals-systems-and-transforms-4th-edition-phillips

Page 10: © 2008 Pearson Education, Inc., Upper Saddle …testbank360.eu/...manual-signals-systems-and-transforms-4th-edition... · (c) xo(0)=-xo(-0)= -xo(0). The only number with a=-a is

2.6

© 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.This material is is protected by Copyright and written permission should be obtained from the publisher prior to any

prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to:

Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.Full file at http://testbank360.eu/solution-manual-signals-systems-and-transforms-4th-edition-phillips

Page 11: © 2008 Pearson Education, Inc., Upper Saddle …testbank360.eu/...manual-signals-systems-and-transforms-4th-edition... · (c) xo(0)=-xo(-0)= -xo(0). The only number with a=-a is

2.7

© 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.This material is is protected by Copyright and written permission should be obtained from the publisher prior to any

prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to:

Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.Full file at http://testbank360.eu/solution-manual-signals-systems-and-transforms-4th-edition-phillips

Page 12: © 2008 Pearson Education, Inc., Upper Saddle …testbank360.eu/...manual-signals-systems-and-transforms-4th-edition... · (c) xo(0)=-xo(-0)= -xo(0). The only number with a=-a is

© 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise.

For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.

Full file at http://testbank360.eu/solution-manual-signals-systems-and-transforms-4th-edition-phillips

Page 13: © 2008 Pearson Education, Inc., Upper Saddle …testbank360.eu/...manual-signals-systems-and-transforms-4th-edition... · (c) xo(0)=-xo(-0)= -xo(0). The only number with a=-a is

2.8

© 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise.

For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.

Full file at http://testbank360.eu/solution-manual-signals-systems-and-transforms-4th-edition-phillips

Page 14: © 2008 Pearson Education, Inc., Upper Saddle …testbank360.eu/...manual-signals-systems-and-transforms-4th-edition... · (c) xo(0)=-xo(-0)= -xo(0). The only number with a=-a is

(c) xo(0)=-xo(-0)= -xo(0). The only number with a=-a is a=0 so this implies xo(0)=0. x(0)=xe(0)+xo(0)=xe(0).

© 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.This material is is protected by Copyright and written permission should be obtained from the publisher prior to any

prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to:

Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.Full file at http://testbank360.eu/solution-manual-signals-systems-and-transforms-4th-edition-phillips

Page 15: © 2008 Pearson Education, Inc., Upper Saddle …testbank360.eu/...manual-signals-systems-and-transforms-4th-edition... · (c) xo(0)=-xo(-0)= -xo(0). The only number with a=-a is

2.11

© 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.This material is is protected by Copyright and written permission should be obtained from the publisher prior to any

prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to:

Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.Full file at http://testbank360.eu/solution-manual-signals-systems-and-transforms-4th-edition-phillips

Page 16: © 2008 Pearson Education, Inc., Upper Saddle …testbank360.eu/...manual-signals-systems-and-transforms-4th-edition... · (c) xo(0)=-xo(-0)= -xo(0). The only number with a=-a is

© 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise.

For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.

Full file at http://testbank360.eu/solution-manual-signals-systems-and-transforms-4th-edition-phillips

Page 17: © 2008 Pearson Education, Inc., Upper Saddle …testbank360.eu/...manual-signals-systems-and-transforms-4th-edition... · (c) xo(0)=-xo(-0)= -xo(0). The only number with a=-a is

2.17

© 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise.

For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.

Full file at http://testbank360.eu/solution-manual-signals-systems-and-transforms-4th-edition-phillips

Page 18: © 2008 Pearson Education, Inc., Upper Saddle …testbank360.eu/...manual-signals-systems-and-transforms-4th-edition... · (c) xo(0)=-xo(-0)= -xo(0). The only number with a=-a is

2.18

2.19

© 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.This material is is protected by Copyright and written permission should be obtained from the publisher prior to any

prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to:

Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.Full file at http://testbank360.eu/solution-manual-signals-systems-and-transforms-4th-edition-phillips

Page 19: © 2008 Pearson Education, Inc., Upper Saddle …testbank360.eu/...manual-signals-systems-and-transforms-4th-edition... · (c) xo(0)=-xo(-0)= -xo(0). The only number with a=-a is

(continued)…

© 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.This material is is protected by Copyright and written permission should be obtained from the publisher prior to any

prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to:

Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.Full file at http://testbank360.eu/solution-manual-signals-systems-and-transforms-4th-edition-phillips

Page 20: © 2008 Pearson Education, Inc., Upper Saddle …testbank360.eu/...manual-signals-systems-and-transforms-4th-edition... · (c) xo(0)=-xo(-0)= -xo(0). The only number with a=-a is

© 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise.

For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.

Full file at http://testbank360.eu/solution-manual-signals-systems-and-transforms-4th-edition-phillips

Page 21: © 2008 Pearson Education, Inc., Upper Saddle …testbank360.eu/...manual-signals-systems-and-transforms-4th-edition... · (c) xo(0)=-xo(-0)= -xo(0). The only number with a=-a is

© 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.This material is is protected by Copyright and written permission should be obtained from the publisher prior to any

prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to:

Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.Full file at http://testbank360.eu/solution-manual-signals-systems-and-transforms-4th-edition-phillips

Page 22: © 2008 Pearson Education, Inc., Upper Saddle …testbank360.eu/...manual-signals-systems-and-transforms-4th-edition... · (c) xo(0)=-xo(-0)= -xo(0). The only number with a=-a is

© 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise.

For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.

Full file at http://testbank360.eu/solution-manual-signals-systems-and-transforms-4th-edition-phillips

Page 23: © 2008 Pearson Education, Inc., Upper Saddle …testbank360.eu/...manual-signals-systems-and-transforms-4th-edition... · (c) xo(0)=-xo(-0)= -xo(0). The only number with a=-a is

© 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.This material is is protected by Copyright and written permission should be obtained from the publisher prior to any

prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to:

Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.Full file at http://testbank360.eu/solution-manual-signals-systems-and-transforms-4th-edition-phillips

Page 24: © 2008 Pearson Education, Inc., Upper Saddle …testbank360.eu/...manual-signals-systems-and-transforms-4th-edition... · (c) xo(0)=-xo(-0)= -xo(0). The only number with a=-a is

© 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.This material is is protected by Copyright and written permission should be obtained from the publisher prior to any

prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to:

Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.Full file at http://testbank360.eu/solution-manual-signals-systems-and-transforms-4th-edition-phillips

Page 25: © 2008 Pearson Education, Inc., Upper Saddle …testbank360.eu/...manual-signals-systems-and-transforms-4th-edition... · (c) xo(0)=-xo(-0)= -xo(0). The only number with a=-a is

2.29 i) not memoryless unless t0=0 ii) invertible: x(t)=y(t+t0)

2.30

© 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise.

For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.

Full file at http://testbank360.eu/solution-manual-signals-systems-and-transforms-4th-edition-phillips

Page 26: © 2008 Pearson Education, Inc., Upper Saddle …testbank360.eu/...manual-signals-systems-and-transforms-4th-edition... · (c) xo(0)=-xo(-0)= -xo(0). The only number with a=-a is

2.31

(parts c,d on next page) © 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise.

For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.

Full file at http://testbank360.eu/solution-manual-signals-systems-and-transforms-4th-edition-phillips

Page 27: © 2008 Pearson Education, Inc., Upper Saddle …testbank360.eu/...manual-signals-systems-and-transforms-4th-edition... · (c) xo(0)=-xo(-0)= -xo(0). The only number with a=-a is

© 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.This material is is protected by Copyright and written permission should be obtained from the publisher prior to any

prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to:

Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.Full file at http://testbank360.eu/solution-manual-signals-systems-and-transforms-4th-edition-phillips