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Appendix E Window Functionsh[n]A(f)(a)Figure E.2. Resultant amplitude response when the impulse response is abruptly truncatedTherefore, we are seeking a suitable window function that will result in an amplitude responsewith a lower ripple in the stop band such as the one shown in Figure E.3.A(f)t(b)fFigure E.3. Acceptable amplitude responseAlthough an impulse response may converge uniformly, when it is multiplied * by a rectangularwindow function it results in an undesirable amplitude response. However, the rectangular windowfunction is the basis in studying window functions, so we begin with the description of therectangular window function.E.2.1 Rectangular Window FunctionThe rectangular window function is defined asfft () rect =τ1 for |t| < --2= 0 otherwise(E.1)and its time−domain waveform is as shown in Figure E.4.f(t)– τ ⁄ 2τ ⁄ 2Figure E.4. Rectangular window function in time−domaint* We recall that multiplication in the time domain corresponds to convolution in the frequency domain.E−2Signals and Systems with MATLAB ® Computing and Simulink ® Modeling, Fourth EditionCopyright © Orchard Publications