Fourier transform - signal processing by Mohammed Salih Salih

By Mohammed Salih Salih

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12 and a DFT SIMULINK block. The results for the proposed WASA model and the steady flow DFT are shown in Fig. 18. The display block is adopted to display the calculated and the estimated DFT coefficients from the sliding DFT and the proposed WASA models respectively. After performing the running of the model, it is clearly seen that the results are absolutely coincident as they appear in their respective display blocks. A Proposed Model-Based Adaptive System for DFT Coefficients Estimation Using SIMULINK 49 Another interesting result to be shown here is the instantaneous error signal, ε j .

5 R2 − 1 (93) Interpolation Algorithms of DFT for Parameters Estimation of Sinusoidal and Damped Sinusoidal Signals 23 |V (ω0 )|=|Vk ||W H (0)|/|W H (ωk )| , A =|V (ω0 )|/e − d( N − 1)/2 , (94) arg{V (ω0 )} = arg{V (ωk )} ± arg{ W H (δ 2π / N − jd )} . 3 Higher order RVCI windows In general, the spectrum of the damped wn = wn e − dn RVCI window order M is a sum of rescaled and moved in frequency spectra of damped rectangular window WM ( e jω ) = M ∑ (−1)m m=0 Amw R j(ω −ωm ) Aw W (e ) + ( −1)m m W R ( e j (ω +ωm ) ) .

The main features of such a spectrum analysis are simplicity, adaptability, and suitability with parallel computations and VLSI implementation. This is owing to the nature of the LMS algorithm, which lends itself to this type of implementation. Later on, Mccgee showed that Widrow’s spectrum analyzer could be used as a recursive estimator for the sake of solving the exponentially-weighted least squares estimation and a filter bank model was deduced. The fundamental outcome of that work was that the LMS algorithm could act as a bank of filters with two modes of operation, which means when the LMS learning rate is chosen to be ½, the filter poles are located at the origin.

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