written 8.0 years ago by | modified 2.8 years ago by |
Mumbai University > Computer Engineering > Sem 7 > Digital Signal Processing
Marks: 10 Marks
Year: May 2016
written 8.0 years ago by | modified 2.8 years ago by |
Mumbai University > Computer Engineering > Sem 7 > Digital Signal Processing
Marks: 10 Marks
Year: May 2016
written 8.0 years ago by |
1. Shifting Property
If $x(n) \leftarrow FT\rightarrow x(k) OR x(n) \leftarrow FT\rightarrow X(\omega)$
Then, $x(n-m)\leftarrow FT\rightarrow W_N^{mk}.x(k)$
i.e, $x(n-m)\leftarrow FT\rightarrow e^{-j\omega k } X(\omega)$
& $x(n+m) \leftarrow FT\rightarrow W_N^{-mk}.x(k)$
Shifting property states that when a signal is shifted by m samples then the magnitude spectrum is unchanged but the phase spectrum is changed by amount $(-\omega k)$.
2. Frequency Shifting
$W_N^{mn}.x(k) \leftarrow FT\rightarrow x(k+m) \\ W_N^{-mn}.x(k) \leftarrow FT\rightarrow x(k-m)$
3. Conjugate Property
$x(n) \leftarrow FT\rightarrow x(k) \\ x*(n) \leftarrow FT\rightarrow x*(-k)$
4. Symmetric Property
$x(n) \leftarrow FT\rightarrow x(k)$
If x(n) = x(-n)
Then x(k) = x*(N-k)
5. Convolution Property
If, $x_1(n) \leftarrow FT\rightarrow x_1(k) \& x_2(n) \leftarrow FT\rightarrow x_2(k)$
Then, $x_1(n) * x_2(n) \leftarrow FT\rightarrow x_1(k).x_2(k)$
Convolution of two signals in time domain is equivalent to multiplication in frequency domain.