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# homework4 - EE4150 DIGITAL SIGNAL PROCESSING HOMEWORK 4...

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EE4150 DIGITAL SIGNAL PROCESSING HOMEWORK # 4 CHAPTER 5 (Discrete Fourier Transform) OBJECTIVES : 1. Let the students understand and use the DFT (Discrete Fourier Transform) as a tool to analyze and process experimental data in frequency domain. 2. Let the students familiarize with MATLAB. 1 Introduction The DFT of a discrete sequence { x [ n ] } is defined as sampled version of the FT at equally spaced frequency points X [ k ] = X 2 πk N = N - 1 X n =0 x [ n ] e - j 2 πkn/N k = 0 , 1 , . . . , N - 1 (1) where N is the number of samples used in the transformation. Thus, the DFT provides fre- quency information of the sequence { x [ n ] } in the interval 0 ω 2 π with spacing Δ ω = 2 π/N . However, for sequences with infinite length the DFT provides just an approximation of the frequency content of the time sequence. Now, if the discrete sequence { x [ n ] } is obtained from sampling a continuous time signal x a ( t ), i.e. x [ n ] = x a ( nT ) - ∞ < n < (2) where T is the sampling period. Then, there exists a relation between frequency in discrete time f

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