Orthogonal Transform o The basis sequences satisfy the condition 「1,1=k ∑vk,n]v[,n n=0 0.l≠k
Orthogonal Transform ⚫ The basis sequences satisfy the condition 1 * 0 1 1, , , 0, N n l k k n l n N l k − = = =
Orthogonal Transform o An important consequence of the orthogonality of the basis sequence is energy preservation property of the transform ∑ 可=∑xi N k=0
Orthogonal Transform ⚫ An important consequence of the orthogonality of the basis sequence is energy preservation property of the transform 1 1 2 2 0 0 1 N N n k x n X k N − − = = =
Discrete Fourier Transform ● Definition ● Matrix relations o DFT Computation Using MATLAB o Relation between dTFT and dFt and their Inverses
Discrete Fourier Transform ⚫ Definition ⚫ Matrix Relations ⚫ DFT Computation Using MATLAB ⚫ Relation between DTFT and DFT and their inverses
Discrete Fourier transform o In this section we define the discrete fourier transform, usually known as the DFT, and develop the inverse transformation, often abbreviated as DT
Discrete Fourier transform ⚫ In this section, we define the discrete Fourier transform, usually known as the DFT, and develop the inverse transformation, often abbreviated as IDFT
1 Definition The discrete Fourier transform(DFt) of length-N time domain sequence xn] is defined by X[]=∑x[e2xb,0≤k≤N-1 The basis sequence is plk.nl=e 2Tkn/n Which are complex exponential sequences commonly used notation 2丌/N
1. Definition ⚫ The discrete Fourier transform (DFT) of length-N time domain sequence x[n] is defined by 1 2 / 0 , 0 1 N j kn N n X k x n e k N − − = = − ⚫ The basis sequence is ,which are complex exponential sequences commonly used notation 2 / , j kn N k n e = j N 2 / W e N − =