Module 1

Module 1

1. DFT

   • EQN
   • TWIDDLE FACTORS

2. IDFT

3. PROPERTIES - DFT

   • LINEARITY
   • PERIODICITY
   • SYMMETRY
     • Real valued
     • real & even
     • real & odd
     • purely imaginary
   • Time reversal
   • circular time shift
   • circular frequency shift
   • circular correlation
   • multiplication
   • Parseval's
   • complex conjugate

4. CONVOLUTION

   • LINEAR
     • Equation
     • Using circular conv.
   • CIRCULAR
     • Concentric circle
     • Matrix

5. BLOCK CONV.

   • Overlap save
   • Overlap add

6. FFT

   • DIT
     • DFT
     • IDFT
   • DIF
     • DFT
     • IDFT

7. RELATION TO DFT

   • Fourier series coeff. (periodic)
   • Fourier transform (aperiodic)
   • z transform
   • Fourier series coeff. (CT s/g)

8. Frequency analysis

   • Efficient computation -DFT
     • 2 Real seq.
     • 2N point real seq.
   • windowing