Digital Signal Processing
18TE5DCDSP
DAYANANDA SAGAR COLLEGE OF ENGINEERING
DEPARTMENT OF TELECOMMUNICATION ENGINEERING
Digital Signal Processing
Module - 1
Module - 1
Dept. of TCE, DSCE
Digital Signal Processing
18TE5DCDSP
1.0. Discrete Fourier Transform (DFT): Definition
1.1 Inverse Discrete Fourier Transform (IDFT): Definition
Module - 1
Dept. of TCE, DSCE
Digital Signal Processing
18TE5DCDSP
1.2 Twiddle Factor
Module - 1
Dept. of TCE, DSCE
Digital Signal Processing
Module - 1
18TE5DCDSP
Dept. of TCE, DSCE
Digital Signal Processing
18TE5DCDSP
1.4 Example Problems
Module - 1
Dept. of TCE, DSCE
Digital Signal Processing
Module - 1
18TE5DCDSP
Dept. of TCE, DSCE
Digital Signal Processing
18TE5DCDSP
Magnitude and Phase Response
Module - 1
Dept. of TCE, DSCE
Digital Signal Processing
18TE5DCDSP
3.
Module - 1
Dept. of TCE, DSCE
Digital Signal Processing
Module - 1
18TE5DCDSP
Dept. of TCE, DSCE
Digital Signal Processing
Module - 1
18TE5DCDSP
Dept. of TCE, DSCE
Digital Signal Processing
18TE5DCDSP
4.
Module - 1
Dept. of TCE, DSCE
Digital Signal Processing
18TE5DCDSP
N
Module - 1
Dept. of TCE, DSCE
Digital Signal Processing
Module - 1
18TE5DCDSP
Dept. of TCE, DSCE
Digital Signal Processing
Module - 1
18TE5DCDSP
Dept. of TCE, DSCE
Digital Signal Processing
Module - 1
18TE5DCDSP
Dept. of TCE, DSCE
Digital Signal Processing
Module - 1
18TE5DCDSP
Dept. of TCE, DSCE
Digital Signal Processing
Module - 1
18TE5DCDSP
Dept. of TCE, DSCE
Digital Signal Processing
Module - 1
18TE5DCDSP
Dept. of TCE, DSCE
Digital Signal Processing
Module - 1
18TE5DCDSP
Dept. of TCE, DSCE
Digital Signal Processing
18TE5DCDSP
1.5 DFT as a Linear Transformation
Module - 1
Dept. of TCE, DSCE
Digital Signal Processing
Module - 1
18TE5DCDSP
Dept. of TCE, DSCE
Digital Signal Processing
Module - 1
18TE5DCDSP
Dept. of TCE, DSCE
Digital Signal Processing
18TE5DCDSP
Example Problems
Module - 1
Dept. of TCE, DSCE
Digital Signal Processing
Module - 1
18TE5DCDSP
Dept. of TCE, DSCE
Digital Signal Processing
Module - 1
18TE5DCDSP
Dept. of TCE, DSCE
Digital Signal Processing
Module - 1
18TE5DCDSP
Dept. of TCE, DSCE
Digital Signal Processing
18TE5DCDSP
1.6 Properties of DFT
a. Periodicity Property
Module - 1
Dept. of TCE, DSCE
Digital Signal Processing
Module - 1
18TE5DCDSP
Dept. of TCE, DSCE
Digital Signal Processing
18TE5DCDSP
b. Linearity Property
Module - 1
Dept. of TCE, DSCE
Digital Signal Processing
18TE5DCDSP
C . Circular Time shift Property
Module - 1
Dept. of TCE, DSCE
Digital Signal Processing
18TE5DCDSP
d . Circular Frequency shift Property
Module - 1
Dept. of TCE, DSCE
Digital Signal Processing
18TE5DCDSP
e . Circular Folding Property
Module - 1
Dept. of TCE, DSCE
Digital Signal Processing
18TE5DCDSP
Example Problem 1 :
Module - 1
Dept. of TCE, DSCE
Digital Signal Processing
Module - 1
18TE5DCDSP
Dept. of TCE, DSCE
Digital Signal Processing
18TE5DCDSP
Example Problem 2 :
Module - 1
Dept. of TCE, DSCE
Digital Signal Processing
Module - 1
18TE5DCDSP
Dept. of TCE, DSCE
Digital Signal Processing
18TE5DCDSP
Example Problem 3 :
Module - 1
Dept. of TCE, DSCE
Digital Signal Processing
18TE5DCDSP
Example Problem 4 :
Module - 1
Dept. of TCE, DSCE
Digital Signal Processing
Module - 1
18TE5DCDSP
Dept. of TCE, DSCE
Digital Signal Processing
18TE5DCDSP
Example Problem 5 :
Module - 1
Dept. of TCE, DSCE
Digital Signal Processing
18TE5DCDSP
Example Problem 6 :
Module - 1
Dept. of TCE, DSCE
Digital Signal Processing
Module - 1
18TE5DCDSP
Dept. of TCE, DSCE
Digital Signal Processing
18TE5DCDSP
f . Symmetry Property:
I.
if x(n) is purely real sequence
Module - 1
Dept. of TCE, DSCE
Digital Signal Processing
18TE5DCDSP
II. . If x(n) = xe(n) + xo(n) , then its DFT { xe(n)} is purely real and DFT{
xo(n) } is purely imaginary
\
Module - 1
Dept. of TCE, DSCE
Digital Signal Processing
18TE5DCDSP
Example Problem 7 :
Module - 1
Dept. of TCE, DSCE
Digital Signal Processing
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18TE5DCDSP
Dept. of TCE, DSCE
Digital Signal Processing
18TE5DCDSP
Example Problem 8 :
Module - 1
Dept. of TCE, DSCE
Digital Signal Processing
18TE5DCDSP
Example Problem 9 :
Module - 1
Dept. of TCE, DSCE
Digital Signal Processing
18TE5DCDSP
Example Problem 10 :
Module - 1
Dept. of TCE, DSCE
Digital Signal Processing
Module - 1
18TE5DCDSP
Dept. of TCE, DSCE