MODULE 6 Flashcards
1
Q
- TIME SHIFT
A
x(n-k)↔e^(-jΩk) X(Ω)
2
Q
- FREQUENCY SHIFT
A
e^jΩn x(n)↔ X(Ω-Ω_0 )
e^(-jΩn_ ) x(n)↔ X(Ω+Ω_0 )
3
Q
- HALF PERIOD SHIFT
A
〖(-1)〗^n x(n)↔ X(Ω-π)
4
Q
- TIME FOLDING
A
x(-n)↔ X(-Ω)
5
Q
- AREA PROPERTY
A
∫(-π)^π▒〖X(Ω) e^(-jΩn( ) ) dΩ〗=2πx(n)
∫_(-π)^π▒X(Ω)dΩ=2πx(0)=AREA
5
Q
- SUMMATION PROPERTY
A
∑(n=-∞)^∞▒〖x(n)=〗 X(0)
∑(n=-∞)^∞▒〖〖(-1)〗^n x(n)=〗 X(π)
5
Q
- FREQUENCY DIFFERENTIATION
A
nx(n)↔j d/dΩ [X(Ω)]
5
Q
- PARSEVALS’S THEOREM
A
∑(-∞)^∞▒|x(n)|^2 =1/2π ∫(-∞)^∞▒|X(Ω)|^2 dΩ
5
Q
- MULTIPLICATION PROPERTY
A
〖x_1 (n)∙x〗_2 (n)↔1/2π (X_1 (Ω)⊛X(Ω))
5
Q
- CONVOLUTION PROPERTY
A
〖x_1 (n)*x〗_2 (n)↔X_1 (Ω)∙X_2 (Ω)
6
Q
Discrete-Time Fourier Transform
A
- The Discrete-time Fourier Transform (DTFT) refers to a signal processing operation that converts discrete-time signal into continuous frequency signal
7
Q
EXISTENCE OF DTFT
A
- If ROC includes the unit circle
- Unit circle r=1
