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H ~ ( P  H () j W ) ( ' d w ~ ~ e Code 128 Code Set B Reader In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. Encode Code 128C In None Using Barcode generator for Software Control to generate, create Code 128B image in Software applications. is minimized when h(n) is designed using the rectangular window design method. If ER is the squared error using a rectangular window, find the excess squared emor that results when a Hanning window is used instead of a rectangular window; that is, find an expression for Code 128 Code Set A Decoder In None Using Barcode scanner for Software Control to read, scan read, scan image in Software applications. Create ANSI/AIM Code 128 In Visual C# Using Barcode printer for .NET framework Control to generate, create Code 128 Code Set B image in Visual Studio .NET applications. where EH is the squared error using a Hanning window.
Encode Code 128 Code Set B In .NET Using Barcode printer for ASP.NET Control to generate, create Code 128 Code Set C image in ASP.NET applications. Print Code 128 In .NET Using Barcode creation for VS .NET Control to generate, create Code 128B image in Visual Studio .NET applications. Using Parseval's theorem. it is more convenient to express the leastsquares error in the time domain as follows: Print Code128 In VB.NET Using Barcode creator for VS .NET Control to generate, create Code 128A image in .NET applications. Creating Barcode In None Using Barcode creation for Software Control to generate, create barcode image in Software applications. FlLTER DESIGN Because e(n) = hd(n)  h(n) = hd(n) for n c 0 and n > N.
Encoding UCC.EAN  128 In None Using Barcode printer for Software Control to generate, create EAN 128 image in Software applications. Generate Barcode In None Using Barcode generator for Software Control to generate, create bar code image in Software applications. [CHAP. 9
Make Code 128C In None Using Barcode generation for Software Control to generate, create Code 128 image in Software applications. Creating EAN13 In None Using Barcode printer for Software Control to generate, create EAN / UCC  13 image in Software applications. where wH(n) and wx(n) are the Hanning and rectangular windows, respectively. However, the second sum is equal to zero. Therefore, the excess squared error is simply Print NW7 In None Using Barcode generation for Software Control to generate, create USS Codabar image in Software applications. Data Matrix 2d Barcode Generator In VB.NET Using Barcode drawer for .NET framework Control to generate, create Data Matrix 2d barcode image in .NET applications. which is the desired relationship.
GS1  13 Generation In Visual Studio .NET Using Barcode creator for Reporting Service Control to generate, create EAN13 image in Reporting Service applications. Generating Code 128 In Java Using Barcode creator for Eclipse BIRT Control to generate, create Code128 image in BIRT reports applications. Consider the following specifications for a lowpass filter: EAN13 Reader In Visual Studio .NET Using Barcode reader for Visual Studio .NET Control to read, scan read, scan image in .NET framework applications. Code 128B Reader In Java Using Barcode reader for Java Control to read, scan read, scan image in Java applications. Design a linear phase FIR filter to meet these specifications using the window design method. Designing a lowpass filter with the window design method generally produces a filter with ripples of the same amplitude in the passband and stopband. Therefore, because the passband and stopband ripples in the filter specifications are the same, we only need to be concerned about the slopband ripple requirement. A stopband ripple of 6 , = 0.01 corresponds to a stopband attenuation of 40 dB. Therefore. froin Table 92 it follows that we may use a Hanning window, which provides an attenuation of approximately 44 dB. The specification on the transition band is that Aw = 0.05rr, or A f = 0.025. Therefore, the required filter order is EAN13 Encoder In Java Using Barcode printer for Java Control to generate, create EAN13 image in Java applications. Reading EAN 13 In Java Using Barcode recognizer for Java Control to read, scan read, scan image in Java applications. and we have
With an ideal lowpass filter that has a cutoff frequency of w,. = 0.325 (the midpoint of the transition band), and a delay of N/2 = 62 so that hd(n) is placed symmetrically within the interval [O, 1241, we have Therefore, the filter is 0.5  0.5 cos  sin[0.325~(n 62)] ~ (  62) n
O S n s 124
Note that if we were to use a Hamming or a Blackman window instead of a Hanning window, the stopband and passband ripple requirements would have been exceeded, and the required filter order would have been larger. With a Blackman window, for example, the filter order required to meet the transition band requirement is W e would like t o filter an analog signal x,(t) with a n analog lowpass filter that has a cutoff frequency f,. = 2 kHz, a transition width Af = 500 Hz, a n d a stopband attenuation o f 50 dB. This filter is t o b e implemented digitally, a s illustrated in the following figure: CHAP. 91
FILTER DESIGN
4 1 ) y(n) H(ejw) yo ( t ) Design a digital filter to meet the analog filter specifications with a sampling frequency f, = 10 kHz. With a sampling frequency of 10 kHz, the digital filter should have a cutoff frequency w, = 2 n f,./f, = 0.41~ and a transition bandwidth Aw = 2nAf/f, = O.lrr. For a stopband attenuation of 50 dB, we may use a Kaiser window with B = 0.l l02(50  8.7) = 4.55 For the length of the window, we have or N = 59. Finally, the unit sample response of the ideal filter that is to be windowed is a lowpass filter with a ~ cutoff frequency w,. = 0 . 4 and a delay N / 2 = 29.5. Therefore, where w ( n ) is a Kaiser window with N = 59 and
B = 4.55. and
Find the Kaiser window parameters, B and N , to designa lowpass filter with acutofffrequency w, = n / 2 , a stopband ripple 6 = 0.002, and a transition bandwidth no 1a.rger than 0.117. , The parameter
B for the Kaiser window depends only on the stopband ripple requirements.
With 6, = 0.002, and we have = 0.1 102(0r,  8.7) = 4.99 The window length, N , on the other hand, is determined by the stopband ripple, 6,. and the transition width as follows: Therefore, the required filter order is N = 65
Consider the following specifications for a bandpass filter: (a) Design a linear phase FIR filter to meet these specifications using a Blackman window
(b) Repeat part (a) using a Kaiser window.
(a) For this filter, the width of each transition band is Aw = 0 . 1 ~ The ripples in the lower stopband, passband, . and upper stopband are 4 = 0.01. a2 = 0.05, and a3 = 0.02, respectively, and are all different. Because the ripples produced with the window design method will be approximately the same in all three bands, the filter must be designed so that it has a maximum ripple of 8, = 0.01 in all three bands. With

