DSP 6 The Fast Fourier Transform FFT CESd
- Slides: 38
DSP 6 The Fast Fourier Transform (FFT) ��������� ผศ. ดร. พระพล ยวภษตานนท ภาควชา วศวกรรมอเลกทรอนกส CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 6 -1
���� • นศ รจกความหมายของ การแปลงฟรเยรแบบเรว (Fast Fourier Transform : FFT) และผลการแปลงจากสญญาณในโดเมนเวลา • นศ รจก FFT แบบ Decimation in time (DIT) หรอ DIT-FFT CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 6 -2
�������������������� ������ ������ ������ CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 6 -4
���������� �� 2 -point DFT ���� N=2 �������� 4 ���� CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 6 -5
���������� �� 4 -point DFT ���� N=4 CESd. SP ��������� 16 ����� EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 6 -6
���������� � ������� N=2 ������� CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 6 -7
���������� �(��� ) ���������������� ������ WN ���������� CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 6 -8
������ Butterfly �������� (signal flo ������������ �� 1 1 Note: �������� =1 ����= -1, ������������ � DSP 6 -10 CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon
���� N =4 ���� N=4 DIT-FFT ��������� ”�������� ”��� ” (re CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 6 -11
��������� (Recomposite) ����������� DFT ��� 2 ������� �� CESd. SP DFT ��� 4 ��� = DFT ��� 2 ��� + Wk 4 x DFT ��� 2 �� EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 6 -12
หา ������ Recomposite ���� : �������� CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 6 -14
หา ������ Recomposite CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 6 -15
หา ������ Recomposite CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 6 -16
หา ������ Recomposite CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 6 -17
ผลลพททายสดคอ 4 -point DIT-FFT 1 1 CESd. SP 2 -point DFT x 2 ������ Recomposite EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 6 -18
8 -point DIT-FFT ������� CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 6 -19
8 -point DIT-FFT (��� ) ��������� 4 -po CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 6 -20
�������� ? ��������� ����� CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 6 -21
8 -point ������ Recomposite 4 -point DFT CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 6 -22
�������� 8 -point DFT ������ 4 -point DFTx 2 -point DFT ������� 4 -point DFT ������� 2 -point D CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 6 -23
��� 4 -point DFT ������� 2 -point DFT ������ x(0), x(2), x(4) ��� x(6) 1 1 4 -point DFT CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 6 -24
สำหรบ x(1), x(3), x(5) และ x(7) 2 -point DFT ������� 4 -point DFT ������� 2 -point D CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 6 -25
��� 4 -point DFT ������� 2 -point DFT ������ x(1), x(3), x(5) ��� x(7) 1 1 4 -point DFT CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 6 -26
DIT-FFT ������ N=8 CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 6 -27
���� 8 -point DFT �������� 2 point DFT 8 -point DFT 4 -point DFT + Wk 8 x 4 -point DFT 2 -point DFT + W 4 k x 2 -point DFT CESd. SP 2 -point DFT + W 4 k x 2 -point DFT EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 6 -28
���� 8 -point DIT-FFT ������ 4 -point DFT ������ 8 -point DFT (Recomposition to 8 -point DFT) ������ 4 -point DFT CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 6 -29
���� N-point DIT-FFT 2 -point DFT 2 -point DFT CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 6 -30
���� FFT ������� N log 2 N ? ������ R ��������� (stage) ������ CESd. SP ������ 4–point DFT, R=1 ������ 8–point DFT, R=2 EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 6 -31
�������� (R) 4 -point DFT 2 4 2 ������ (R)= 1 CESd. SP 8 -point DFT 2 4 2 8 2 4 2 ������ (R)= 1 EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 6 -32
���������� (B) 4 -point DFT 8 -point DFT 2 2 2 4 4 8 ������� 4 ���� (B)= 2 2 ������������ 4 4 (B)= 4 ������ 3 ������ CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 6 -33
��������� = �. �. ����������� X �. �. ������� X ���� 2 ��������� CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 6 -34
����������� DFT ��� FFT ������� N 2 4 8 : 256 512 1, 024 CESd. SP DFT FFT N 2 )N log 2 N( 4 2 16 8 64 24 : : 65, 536 2, 048 262, 144 4, 608 1, 048, 576 10, 240 EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 6 -35
�������� ��� r= ���������� 1 CESd. SP 1����� �. �. ������� (N/2 EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 6 -36
������ 4 -point DFT ������ 1 1 -1 1 1 1 1 - 1 -1 ������. �. ��������� (N/2)log 2 N= 4 CESd. SP EEET 0485 Digital Signal Processing http: //embedsigproc. wordpress. com Asst. Prof. Dr. P. Yuvapoositanon DSP 6 -37
- Fast fourier transform (fft)
- Fast fourier transform in r
- Introduction to fast fourier transform
- Java fft
- Fast fourier transform
- Fourier transformation definition
- Fourier transform of gaussian
- Fourier transform of reciprocal function
- Fourier transform formula
- Fourier basis
- Discrete fourier transform formula
- Dft of delta function
- Filter
- Duality of fourier transform
- Discrete fourier transform
- Fourier transform
- Fourier transform in computer vision
- Properties of fourier transform
- Mri fourier transform
- Fourier transform of shifted rectangular pulse
- Relation between fourier and laplace transform
- Sinc function fourier transform
- Windowed fourier transform
- Fourier cosine transform of f(x)=1
- Fourier transform definition
- Fourier series orthogonality
- Stft
- Short time fourier transform applications
- Comb function matlab
- Application of discrete fourier transform
- Fourier transform definition
- Quantum fourier transform applications
- Heat equation
- Discrete time fourier series
- Fouries
- Cosine integral
- Even fourier
- Line spectrum in signals and systems
- Overlap save method