Ch3.2 Discrete Fourier Transform

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Ch3.2: Frequency Analysis for DT Signals • Discrete Fourier Transform • Circular Convolution Elec3100 Chapter 3 18
Circular Shift of a Sequence • Consider a length-N sequence defined for 01. Sample values are equal to zero for values of 0and . • For any arbitrary integer , the shifted sequence , is no longer defined for the range 0 1. • Thus, we need to define another type of “shift” that will always keep the shifted sequence in the range 0 1. • The desired shift, called the circular shift, is defined using a modulo operation: For 0(right circular shift), the above equation implies ,for 1 ,for 0 Elec3100 Chapter 3 19
Page 1 and 2: Ch3: Frequency Analysis for DT Sign
Page 3 and 4: WiFi and OFDM Elec3100 Chapter 3 3
Page 5 and 6: Discrete Fourier Transform (DFT)
Page 7 and 8: Inverse Discrete Fourier Transform
Page 9 and 10: Discrete Fourier Transform • Exam
Page 11 and 12: Matrix Relations • The IDFT relat
Page 13 and 14: General Properties of DFT Elec3100
Page 15 and 16: Physical Interpretation: Example
Page 17: Physical Interpretation: Example
Page 21 and 22: Circular Convolution • Circular c
Page 23 and 24: Circular Convolution • Example -
Page 25 and 26: Circular Convolution • Example -
Page 27 and 28: Circular Convolution Elec3100 Chapt
Page 29 and 30: Circular Convolution Elec3100 Chapt
Page 31: Linear Convolution Using the DFT El

Ch3.2 Discrete Fourier Transform

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