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Fourier Series Method for Approximating an FIR Amplitude Response20Magnitude (dB)0-20-400 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Normalized Frequency (×π rad/sample)0Phase (degrees)-500-1000-1500-20000 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Normalized Frequency (×π rad/sample)Figure E.31. Normalized frequency plots for the triang window created with the MATLAB function fir10Magnitude Response (dB)-5-10Magnitude (dB)-15-20-25-30-35-400 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9Normalized Frequency (×π rad/sample)Figure E.32. Magnitude response for the triang window created with the MATLAB function fvtoolb. HanningWe recall from (E.6) that the Hanning window function is defined as2 1ft () Hann cos ( πt ⁄ τ)2-- ⎛ 1 + cos-------2πt⎞ τ= =for |t| < --⎝ τ ⎠2= 0 otherwise(E.27)Signals and Systems with MATLAB ® Computing and Simulink ® Modeling, Fourth EditionCopyright © Orchard PublicationsE−27