DSP 5 The Discrete Fourier Transform DFT CESd

DSP 5 The Discrete Fourier Transform (DFT) ��������� ผศ. ดร. พระพล ยวภษตานนท ภาควชา วศวกรรมอเลกทรอนกส CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 5 -1

���� DFT ? �������������������� DTFT ����� n ����� ���������� DTFT �������������� n ������������� Discrete Fourier Transform (DFT) ������� CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 5 -3

���������� �� The Discrete Fourier Series (DFS( ����������� ��������� �������� ���� CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 5 -4

��������� เราแทน Analysis (DFS) equation: Synthesis (IDFS) equation: CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 5 -5

�� DFS �������������� = 4 (N=4 ������ k=0 k=1 k=2 k=3 CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 5 -6

ตวอยาง วธทำ ������� (pulse) �������� DFS L N CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon dsp_5_1. eps DSP 5 -7

���� DFT ���������� … ��������� ����������� CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 5 -8

������ L=5 ���� N=20 CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 5 -9

������ L=5 ���� N=40 CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 5 -10

ชวงพลสบวก CESd. SP L=5 และคาบเปน N=60 EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 5 -11

ชวงพลสบวก CESd. SP L=7 และคาบเปน N=60 EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 5 -12

����� • ชวงระยะพลสบวก สมพนธกบ คาบเวลาและขนาดของผลการแปลง DFS ดงน CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 5 -13

DFS ��� z-transform ��� DTFT ����������� N=6 0 5 ���������������� … ����� CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 5 -14

DFS ��� z-transform ��� DTFT (��� ( • ������ DFS ��� z-transform ������ DFS ��� DT CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 5 -15

CTFT DTFT 1 ��� 0 CESd. SP 0 N-1 DFS DFT EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon 0 0 k N-1 k DSP 5 -17

��������� (zero padding( �������������� 4 ��� CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 5 -18

����� DTFT ��� x(n( CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon dsp_5_6. eps DSP 5 -19

�� DFT ��� x(n( k=0 k=1 k=2 k=3 CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 5 -20

N=4 CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon dsp_5_7. eps DSP 5 -21

N=8 CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon dsp_5_8. eps DSP 5 -22

N=16 CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon dsp_5_9. eps DSP 5 -23

N=32 CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon dsp_5_10. eps DSP 5 -24

������ x(n) n=0 ��� 9 CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 5 -26

������� 40 ��� CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 5 -27

�������� 90 ���������� CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 5 -28

����� x(n) ����� 100 ������������ CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 5 -29

������ x(n)=[ … 0 1 0[ … CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 5 -30