1 Definition e We can rewrite as X[]=∑x[]W,0≤k≤N-1 The inverse discrete Fourier transform(IDFT)is given by x{n]=∑X[]W,0≤n≤N-1 k=0
1. Definition ⚫ We can rewrite as 1 0 , 0 1 N kn N n X k x n W k N − = = − 1 0 1 , 0 1 N kn N k x n X k W n N N − − = = − ⚫ The inverse discrete Fourier transform (IDFT) is given by
1. Definition To verify the above expression, we multiply both sides of the above equation by b w and N sum the result from n=0 to n=N-1 resulting 11N-1 ∑x(m)m=∑∑x(如 n 月=U k=0 N-1N-1 =N∑∑x(k)x4m -k-1)n N ∑x(k)∑形
1. Definition
1 Definition Making use of the identity ∑x4={M,ftrk=1=N ran integer 7=0 0 otherwise Hence r(n)mon X()
1. Definition
1 Definition Mapping Relations between time-domain and frequency-domain (T ime-domain)(Frequency-domain) Continuous < Aperiodical Discrete < Periodical Periodical Discrete Aperiodical < Continuous
1. Definition
1. Definition Type 1: Continuous-Time Fourier Transform (CTFT) Continuous Aperiodical Aperiodical xa(t)← x(92) Continuous x2(j2)=[x()ea X, (S)e dQ2 2丌
1. Definition