digital signal processing fundamentals_complex number

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Khan, Ashfaq. Digital Signal Processing Fundamentals. Hingham, MA, USA: Da Vinci Engineering Press, 2005. p 57 http://site.ebrary.com/lib/ubdlib/Doc?id=10078516&ppg=57 Copyright © 2005. Da Vinci Engineering Press. All rights Reserved. May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law.

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Page 1: Digital Signal Processing Fundamentals_Complex Number

Khan, Ashfaq. Digital Signal Processing Fundamentals.Hingham, MA, USA: Da Vinci Engineering Press, 2005. p 57http://site.ebrary.com/lib/ubdlib/Doc?id=10078516&ppg=57Copyright © 2005. Da Vinci Engineering Press. All rights Reserved.May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law.

Page 2: Digital Signal Processing Fundamentals_Complex Number

Khan, Ashfaq. Digital Signal Processing Fundamentals.Hingham, MA, USA: Da Vinci Engineering Press, 2005. p 58http://site.ebrary.com/lib/ubdlib/Doc?id=10078516&ppg=58Copyright © 2005. Da Vinci Engineering Press. All rights Reserved.May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law.

Page 3: Digital Signal Processing Fundamentals_Complex Number

Khan, Ashfaq. Digital Signal Processing Fundamentals.Hingham, MA, USA: Da Vinci Engineering Press, 2005. p 59http://site.ebrary.com/lib/ubdlib/Doc?id=10078516&ppg=59Copyright © 2005. Da Vinci Engineering Press. All rights Reserved.May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law.

Page 4: Digital Signal Processing Fundamentals_Complex Number

Khan, Ashfaq. Digital Signal Processing Fundamentals.Hingham, MA, USA: Da Vinci Engineering Press, 2005. p 60http://site.ebrary.com/lib/ubdlib/Doc?id=10078516&ppg=60Copyright © 2005. Da Vinci Engineering Press. All rights Reserved.May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law.

Page 5: Digital Signal Processing Fundamentals_Complex Number

Khan, Ashfaq. Digital Signal Processing Fundamentals.Hingham, MA, USA: Da Vinci Engineering Press, 2005. p 61http://site.ebrary.com/lib/ubdlib/Doc?id=10078516&ppg=61Copyright © 2005. Da Vinci Engineering Press. All rights Reserved.May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law.

Page 6: Digital Signal Processing Fundamentals_Complex Number

Khan, Ashfaq. Digital Signal Processing Fundamentals.Hingham, MA, USA: Da Vinci Engineering Press, 2005. p 62http://site.ebrary.com/lib/ubdlib/Doc?id=10078516&ppg=62Copyright © 2005. Da Vinci Engineering Press. All rights Reserved.May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law.

Page 7: Digital Signal Processing Fundamentals_Complex Number

Khan, Ashfaq. Digital Signal Processing Fundamentals.Hingham, MA, USA: Da Vinci Engineering Press, 2005. p 63http://site.ebrary.com/lib/ubdlib/Doc?id=10078516&ppg=63Copyright © 2005. Da Vinci Engineering Press. All rights Reserved.May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law.

Page 8: Digital Signal Processing Fundamentals_Complex Number

Khan, Ashfaq. Digital Signal Processing Fundamentals.Hingham, MA, USA: Da Vinci Engineering Press, 2005. p 64http://site.ebrary.com/lib/ubdlib/Doc?id=10078516&ppg=64Copyright © 2005. Da Vinci Engineering Press. All rights Reserved.May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law.

Page 9: Digital Signal Processing Fundamentals_Complex Number

Khan, Ashfaq. Digital Signal Processing Fundamentals.Hingham, MA, USA: Da Vinci Engineering Press, 2005. p 65http://site.ebrary.com/lib/ubdlib/Doc?id=10078516&ppg=65Copyright © 2005. Da Vinci Engineering Press. All rights Reserved.May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law.

Page 10: Digital Signal Processing Fundamentals_Complex Number

Khan, Ashfaq. Digital Signal Processing Fundamentals.Hingham, MA, USA: Da Vinci Engineering Press, 2005. p 66http://site.ebrary.com/lib/ubdlib/Doc?id=10078516&ppg=66Copyright © 2005. Da Vinci Engineering Press. All rights Reserved.May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law.

Page 11: Digital Signal Processing Fundamentals_Complex Number

Khan, Ashfaq. Digital Signal Processing Fundamentals.Hingham, MA, USA: Da Vinci Engineering Press, 2005. p 67http://site.ebrary.com/lib/ubdlib/Doc?id=10078516&ppg=67Copyright © 2005. Da Vinci Engineering Press. All rights Reserved.May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law.

Page 12: Digital Signal Processing Fundamentals_Complex Number

Khan, Ashfaq. Digital Signal Processing Fundamentals.Hingham, MA, USA: Da Vinci Engineering Press, 2005. p 68http://site.ebrary.com/lib/ubdlib/Doc?id=10078516&ppg=68Copyright © 2005. Da Vinci Engineering Press. All rights Reserved.May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law.

Page 13: Digital Signal Processing Fundamentals_Complex Number

Khan, Ashfaq. Digital Signal Processing Fundamentals.Hingham, MA, USA: Da Vinci Engineering Press, 2005. p 69http://site.ebrary.com/lib/ubdlib/Doc?id=10078516&ppg=69Copyright © 2005. Da Vinci Engineering Press. All rights Reserved.May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law.

Page 14: Digital Signal Processing Fundamentals_Complex Number

Khan, Ashfaq. Digital Signal Processing Fundamentals.Hingham, MA, USA: Da Vinci Engineering Press, 2005. p 70http://site.ebrary.com/lib/ubdlib/Doc?id=10078516&ppg=70Copyright © 2005. Da Vinci Engineering Press. All rights Reserved.May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law.

Page 15: Digital Signal Processing Fundamentals_Complex Number

Khan, Ashfaq. Digital Signal Processing Fundamentals.Hingham, MA, USA: Da Vinci Engineering Press, 2005. p 71http://site.ebrary.com/lib/ubdlib/Doc?id=10078516&ppg=71Copyright © 2005. Da Vinci Engineering Press. All rights Reserved.May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law.

Page 16: Digital Signal Processing Fundamentals_Complex Number

Khan, Ashfaq. Digital Signal Processing Fundamentals.Hingham, MA, USA: Da Vinci Engineering Press, 2005. p 72http://site.ebrary.com/lib/ubdlib/Doc?id=10078516&ppg=72Copyright © 2005. Da Vinci Engineering Press. All rights Reserved.May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law.

Page 17: Digital Signal Processing Fundamentals_Complex Number

Khan, Ashfaq. Digital Signal Processing Fundamentals.Hingham, MA, USA: Da Vinci Engineering Press, 2005. p 73http://site.ebrary.com/lib/ubdlib/Doc?id=10078516&ppg=73Copyright © 2005. Da Vinci Engineering Press. All rights Reserved.May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law.

Page 18: Digital Signal Processing Fundamentals_Complex Number

Khan, Ashfaq. Digital Signal Processing Fundamentals.Hingham, MA, USA: Da Vinci Engineering Press, 2005. p 74http://site.ebrary.com/lib/ubdlib/Doc?id=10078516&ppg=74Copyright © 2005. Da Vinci Engineering Press. All rights Reserved.May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law.

Page 19: Digital Signal Processing Fundamentals_Complex Number

Khan, Ashfaq. Digital Signal Processing Fundamentals.Hingham, MA, USA: Da Vinci Engineering Press, 2005. p 75http://site.ebrary.com/lib/ubdlib/Doc?id=10078516&ppg=75Copyright © 2005. Da Vinci Engineering Press. All rights Reserved.May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law.

Page 20: Digital Signal Processing Fundamentals_Complex Number

Khan, Ashfaq. Digital Signal Processing Fundamentals.Hingham, MA, USA: Da Vinci Engineering Press, 2005. p 76http://site.ebrary.com/lib/ubdlib/Doc?id=10078516&ppg=76Copyright © 2005. Da Vinci Engineering Press. All rights Reserved.May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law.

Page 21: Digital Signal Processing Fundamentals_Complex Number

Khan, Ashfaq. Digital Signal Processing Fundamentals.Hingham, MA, USA: Da Vinci Engineering Press, 2005. p 77http://site.ebrary.com/lib/ubdlib/Doc?id=10078516&ppg=77Copyright © 2005. Da Vinci Engineering Press. All rights Reserved.May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law.

Page 22: Digital Signal Processing Fundamentals_Complex Number

Khan, Ashfaq. Digital Signal Processing Fundamentals.Hingham, MA, USA: Da Vinci Engineering Press, 2005. p 78http://site.ebrary.com/lib/ubdlib/Doc?id=10078516&ppg=78Copyright © 2005. Da Vinci Engineering Press. All rights Reserved.May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law.

Page 23: Digital Signal Processing Fundamentals_Complex Number

Khan, Ashfaq. Digital Signal Processing Fundamentals.Hingham, MA, USA: Da Vinci Engineering Press, 2005. p 79http://site.ebrary.com/lib/ubdlib/Doc?id=10078516&ppg=79Copyright © 2005. Da Vinci Engineering Press. All rights Reserved.May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law.

Page 24: Digital Signal Processing Fundamentals_Complex Number

Khan, Ashfaq. Digital Signal Processing Fundamentals.Hingham, MA, USA: Da Vinci Engineering Press, 2005. p 80http://site.ebrary.com/lib/ubdlib/Doc?id=10078516&ppg=80Copyright © 2005. Da Vinci Engineering Press. All rights Reserved.May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law.

Page 25: Digital Signal Processing Fundamentals_Complex Number

Khan, Ashfaq. Digital Signal Processing Fundamentals.Hingham, MA, USA: Da Vinci Engineering Press, 2005. p 81http://site.ebrary.com/lib/ubdlib/Doc?id=10078516&ppg=81Copyright © 2005. Da Vinci Engineering Press. All rights Reserved.May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law.

Page 26: Digital Signal Processing Fundamentals_Complex Number

Khan, Ashfaq. Digital Signal Processing Fundamentals.Hingham, MA, USA: Da Vinci Engineering Press, 2005. p 82http://site.ebrary.com/lib/ubdlib/Doc?id=10078516&ppg=82Copyright © 2005. Da Vinci Engineering Press. All rights Reserved.May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law.

Page 27: Digital Signal Processing Fundamentals_Complex Number

Khan, Ashfaq. Digital Signal Processing Fundamentals.Hingham, MA, USA: Da Vinci Engineering Press, 2005. p 83http://site.ebrary.com/lib/ubdlib/Doc?id=10078516&ppg=83Copyright © 2005. Da Vinci Engineering Press. All rights Reserved.May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law.

Page 28: Digital Signal Processing Fundamentals_Complex Number

Khan, Ashfaq. Digital Signal Processing Fundamentals.Hingham, MA, USA: Da Vinci Engineering Press, 2005. p 84http://site.ebrary.com/lib/ubdlib/Doc?id=10078516&ppg=84Copyright © 2005. Da Vinci Engineering Press. All rights Reserved.May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law.

Page 29: Digital Signal Processing Fundamentals_Complex Number

Khan, Ashfaq. Digital Signal Processing Fundamentals.Hingham, MA, USA: Da Vinci Engineering Press, 2005. p 85http://site.ebrary.com/lib/ubdlib/Doc?id=10078516&ppg=85Copyright © 2005. Da Vinci Engineering Press. All rights Reserved.May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law.

Page 30: Digital Signal Processing Fundamentals_Complex Number

Khan, Ashfaq. Digital Signal Processing Fundamentals.Hingham, MA, USA: Da Vinci Engineering Press, 2005. p 86http://site.ebrary.com/lib/ubdlib/Doc?id=10078516&ppg=86Copyright © 2005. Da Vinci Engineering Press. All rights Reserved.May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law.

Page 31: Digital Signal Processing Fundamentals_Complex Number

Khan, Ashfaq. Digital Signal Processing Fundamentals.Hingham, MA, USA: Da Vinci Engineering Press, 2005. p 87http://site.ebrary.com/lib/ubdlib/Doc?id=10078516&ppg=87Copyright © 2005. Da Vinci Engineering Press. All rights Reserved.May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law.

Page 32: Digital Signal Processing Fundamentals_Complex Number

Khan, Ashfaq. Digital Signal Processing Fundamentals.Hingham, MA, USA: Da Vinci Engineering Press, 2005. p 88http://site.ebrary.com/lib/ubdlib/Doc?id=10078516&ppg=88Copyright © 2005. Da Vinci Engineering Press. All rights Reserved.May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law.

Page 33: Digital Signal Processing Fundamentals_Complex Number

Khan, Ashfaq. Digital Signal Processing Fundamentals.Hingham, MA, USA: Da Vinci Engineering Press, 2005. p 89http://site.ebrary.com/lib/ubdlib/Doc?id=10078516&ppg=89Copyright © 2005. Da Vinci Engineering Press. All rights Reserved.May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law.

Page 34: Digital Signal Processing Fundamentals_Complex Number

Khan, Ashfaq. Digital Signal Processing Fundamentals.Hingham, MA, USA: Da Vinci Engineering Press, 2005. p 90http://site.ebrary.com/lib/ubdlib/Doc?id=10078516&ppg=90Copyright © 2005. Da Vinci Engineering Press. All rights Reserved.May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law.