1. Definition Type 2: Continuous-Time Fourier Series (CTFS Continuous Periodical xa (t) ()<X(kg2 Aperiodical 0/ Discrete 2 x(k90)= x。(t)eat xn(t)=∑x2(kQ isnot
1. Definition
1 Definition Type 3: Discrete-Time Fourier Transform (DTFT Aperiodical x(n)<> X(e) Continuous x(e)=∑ x(ne J0、Jan x(n)= 2丌 ∫x d
1. Definition
1. Definition Type 4: Discrete Fourier Transform ( DFT) Discrete Periodical Periodical x()< X(k) Discrete x(k)=∑x(m)形,0≤k≤N-1 r=0 N-1 x(n)=∑(k)Wx",0≤n≤N-1
1. Definition
1. Definition Examples Rectangular Pulse RMn), width N Its N-point DFT is given by N x(k)=∑x(m=∑W N k n=0 7 WE//2-W AN/2 N 6/2 W-k/2-WK k/2 Geometric Progression kr sin(k) sin(k /N)
1. Definition
1 Definition Its 2N-point DFT is given by N-少 x()=2x(n∑7 0 n=0 1-W 2N=e nKr sin(kT/2) 1-W 2N sin(k/2N) So the length of DFT plays a very important role in dft
1. Definition