Subject: Signals and Systemslcwu.edu.pk/ocd/cfiles/Electrical Engineering/EE207...Subject: Signals and Systems Topic: Fourier Series Representation of Discrete Time Periodic Signals

Page 1 <img data-url='document/subject-signals-and-engineeringee207-subject-signals-and-systems-topic-fourier.html?page=1' data-page='1' class='cut-thumb lazyload' alt='Page 1: Subject: Signals and Systemslcwu.edu.pk/ocd/cfiles/Electrical Engineering/EE207...Subject: Signals and Systems Topic: Fourier Series Representation of Discrete Time Periodic Signals' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022070219/6128d06684afbe35103ba340/html5/thumbnails/1.jpg' width='140' height='200' /> Subject: Signals and Systems

Topic: Fourier Series Representation

of Discrete Time Periodic Signals

Text Book: Signals & Systems By: Alan V. Oppenheim,

Alan S. Willsky with S. Hamid Nawab, 2nd Edition

Page 2 <img data-url='document/subject-signals-and-engineeringee207-subject-signals-and-systems-topic-fourier.html?page=2' data-page='2' class='cut-thumb lazyload' alt='Page 2: Subject: Signals and Systemslcwu.edu.pk/ocd/cfiles/Electrical Engineering/EE207...Subject: Signals and Systems Topic: Fourier Series Representation of Discrete Time Periodic Signals' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022070219/6128d06684afbe35103ba340/html5/thumbnails/2.jpg' width='140' height='200' /> Linear Combinations of Harmonically

Related Complex Exponentials

Page 3 <img data-url='document/subject-signals-and-engineeringee207-subject-signals-and-systems-topic-fourier.html?page=3' data-page='3' class='cut-thumb lazyload' alt='Page 3: Subject: Signals and Systemslcwu.edu.pk/ocd/cfiles/Electrical Engineering/EE207...Subject: Signals and Systems Topic: Fourier Series Representation of Discrete Time Periodic Signals' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022070219/6128d06684afbe35103ba340/html5/thumbnails/3.jpg' width='140' height='200' /> Cont.

Page 4 <img data-url='document/subject-signals-and-engineeringee207-subject-signals-and-systems-topic-fourier.html?page=4' data-page='4' class='cut-thumb lazyload' alt='Page 4: Subject: Signals and Systemslcwu.edu.pk/ocd/cfiles/Electrical Engineering/EE207...Subject: Signals and Systems Topic: Fourier Series Representation of Discrete Time Periodic Signals' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022070219/6128d06684afbe35103ba340/html5/thumbnails/4.jpg' width='140' height='200' /> Cont.

Page 5 <img data-url='document/subject-signals-and-engineeringee207-subject-signals-and-systems-topic-fourier.html?page=5' data-page='5' class='cut-thumb lazyload' alt='Page 5: Subject: Signals and Systemslcwu.edu.pk/ocd/cfiles/Electrical Engineering/EE207...Subject: Signals and Systems Topic: Fourier Series Representation of Discrete Time Periodic Signals' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022070219/6128d06684afbe35103ba340/html5/thumbnails/5.jpg' width='140' height='200' /> Determination of Fourier Series

Representation of a Periodic Signal

Page 6 <img data-url='document/subject-signals-and-engineeringee207-subject-signals-and-systems-topic-fourier.html?page=6' data-page='6' class='cut-thumb lazyload' alt='Page 6: Subject: Signals and Systemslcwu.edu.pk/ocd/cfiles/Electrical Engineering/EE207...Subject: Signals and Systems Topic: Fourier Series Representation of Discrete Time Periodic Signals' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022070219/6128d06684afbe35103ba340/html5/thumbnails/6.jpg' width='140' height='200' /> Cont.

Page 7 <img data-url='document/subject-signals-and-engineeringee207-subject-signals-and-systems-topic-fourier.html?page=7' data-page='7' class='cut-thumb lazyload' alt='Page 7: Subject: Signals and Systemslcwu.edu.pk/ocd/cfiles/Electrical Engineering/EE207...Subject: Signals and Systems Topic: Fourier Series Representation of Discrete Time Periodic Signals' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022070219/6128d06684afbe35103ba340/html5/thumbnails/7.jpg' width='140' height='200' /> Cont.

Page 8 <img data-url='document/subject-signals-and-engineeringee207-subject-signals-and-systems-topic-fourier.html?page=8' data-page='8' class='cut-thumb lazyload' alt='Page 8: Subject: Signals and Systemslcwu.edu.pk/ocd/cfiles/Electrical Engineering/EE207...Subject: Signals and Systems Topic: Fourier Series Representation of Discrete Time Periodic Signals' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022070219/6128d06684afbe35103ba340/html5/thumbnails/8.jpg' width='140' height='200' /> Cont.

Page 9 <img data-url='document/subject-signals-and-engineeringee207-subject-signals-and-systems-topic-fourier.html?page=9' data-page='9' class='cut-thumb lazyload' alt='Page 9: Subject: Signals and Systemslcwu.edu.pk/ocd/cfiles/Electrical Engineering/EE207...Subject: Signals and Systems Topic: Fourier Series Representation of Discrete Time Periodic Signals' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022070219/6128d06684afbe35103ba340/html5/thumbnails/9.jpg' width='140' height='200' /> Cont.

Page 10 <img data-url='document/subject-signals-and-engineeringee207-subject-signals-and-systems-topic-fourier.html?page=10' data-page='10' class='cut-thumb lazyload' alt='Page 10: Subject: Signals and Systemslcwu.edu.pk/ocd/cfiles/Electrical Engineering/EE207...Subject: Signals and Systems Topic: Fourier Series Representation of Discrete Time Periodic Signals' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022070219/6128d06684afbe35103ba340/html5/thumbnails/10.jpg' width='140' height='200' /> Example: 01

Page 11 <img data-url='document/subject-signals-and-engineeringee207-subject-signals-and-systems-topic-fourier.html?page=11' data-page='11' class='cut-thumb lazyload' alt='Page 11: Subject: Signals and Systemslcwu.edu.pk/ocd/cfiles/Electrical Engineering/EE207...Subject: Signals and Systems Topic: Fourier Series Representation of Discrete Time Periodic Signals' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022070219/6128d06684afbe35103ba340/html5/thumbnails/11.jpg' width='140' height='200' /> Cont.

Page 12 <img data-url='document/subject-signals-and-engineeringee207-subject-signals-and-systems-topic-fourier.html?page=12' data-page='12' class='cut-thumb lazyload' alt='Page 12: Subject: Signals and Systemslcwu.edu.pk/ocd/cfiles/Electrical Engineering/EE207...Subject: Signals and Systems Topic: Fourier Series Representation of Discrete Time Periodic Signals' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022070219/6128d06684afbe35103ba340/html5/thumbnails/12.jpg' width='140' height='200' /> Cont.

Page 13 <img data-url='document/subject-signals-and-engineeringee207-subject-signals-and-systems-topic-fourier.html?page=13' data-page='13' class='cut-thumb lazyload' alt='Page 13: Subject: Signals and Systemslcwu.edu.pk/ocd/cfiles/Electrical Engineering/EE207...Subject: Signals and Systems Topic: Fourier Series Representation of Discrete Time Periodic Signals' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022070219/6128d06684afbe35103ba340/html5/thumbnails/13.jpg' width='140' height='200' /> Cont.

Page 14 <img data-url='document/subject-signals-and-engineeringee207-subject-signals-and-systems-topic-fourier.html?page=14' data-page='14' class='cut-thumb lazyload' alt='Page 14: Subject: Signals and Systemslcwu.edu.pk/ocd/cfiles/Electrical Engineering/EE207...Subject: Signals and Systems Topic: Fourier Series Representation of Discrete Time Periodic Signals' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022070219/6128d06684afbe35103ba340/html5/thumbnails/14.jpg' width='140' height='200' /> Example: 02

Page 15 <img data-url='document/subject-signals-and-engineeringee207-subject-signals-and-systems-topic-fourier.html?page=15' data-page='15' class='cut-thumb lazyload' alt='Page 15: Subject: Signals and Systemslcwu.edu.pk/ocd/cfiles/Electrical Engineering/EE207...Subject: Signals and Systems Topic: Fourier Series Representation of Discrete Time Periodic Signals' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022070219/6128d06684afbe35103ba340/html5/thumbnails/15.jpg' width='140' height='200' /> Cont.

Page 16 <img data-url='document/subject-signals-and-engineeringee207-subject-signals-and-systems-topic-fourier.html?page=16' data-page='16' class='cut-thumb lazyload' alt='Page 16: Subject: Signals and Systemslcwu.edu.pk/ocd/cfiles/Electrical Engineering/EE207...Subject: Signals and Systems Topic: Fourier Series Representation of Discrete Time Periodic Signals' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022070219/6128d06684afbe35103ba340/html5/thumbnails/16.jpg' width='140' height='200' /> Page 17 <img data-url='document/subject-signals-and-engineeringee207-subject-signals-and-systems-topic-fourier.html?page=17' data-page='17' class='cut-thumb lazyload' alt='Page 17: Subject: Signals and Systemslcwu.edu.pk/ocd/cfiles/Electrical Engineering/EE207...Subject: Signals and Systems Topic: Fourier Series Representation of Discrete Time Periodic Signals' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022070219/6128d06684afbe35103ba340/html5/thumbnails/17.jpg' width='140' height='200' /> Cont.

Page 18 <img data-url='document/subject-signals-and-engineeringee207-subject-signals-and-systems-topic-fourier.html?page=18' data-page='18' class='cut-thumb lazyload' alt='Page 18: Subject: Signals and Systemslcwu.edu.pk/ocd/cfiles/Electrical Engineering/EE207...Subject: Signals and Systems Topic: Fourier Series Representation of Discrete Time Periodic Signals' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022070219/6128d06684afbe35103ba340/html5/thumbnails/18.jpg' width='140' height='200' /> Text Book: Signals & Systems By: Alan V.