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barcode lib ssrs CHAP. 91 in Software
CHAP. 91 Decoding Code 128 Code Set B In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. Code128 Maker In None Using Barcode creator for Software Control to generate, create Code 128A image in Software applications. FILTER DESIGN
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Generate Code 128 Code Set A In Visual Basic .NET Using Barcode generation for .NET framework Control to generate, create Code 128 Code Set B image in VS .NET applications. Bar Code Generation In None Using Barcode generator for Software Control to generate, create barcode image in Software applications. The inverse of a linear shiftinvariant system with unit sample response g(n) and system function G ( z ) is the system that has a unit sample response, h(n),such that Encoding Bar Code In None Using Barcode generation for Software Control to generate, create barcode image in Software applications. Generate GTIN  12 In None Using Barcode creation for Software Control to generate, create UPCA image in Software applications. solution. One of the reasons is that, In most applications, the system function H ( z ) = I/G(z) is not a v~able unless G ( z )is minimum phase, I / G ( z )cannot be both causal and stable. Another consideration comes from the fact that, in some applications, it may be necessary to constrain H ( 2 ) to be an FIR filter. Because l / G ( z )will be infinite in length unless G ( z )is an allpole filter, constraining h ( n )to be FIR would only be an approximation to the inverse filter. In the FIR leastsquares inverse filter design problem. the goal is to find the FIR filter h ( n )of length N such that h ( n )* ~ ( n ) S(n) The filter that minimizes the squared error Print Data Matrix 2d Barcode In None Using Barcode encoder for Software Control to generate, create Data Matrix ECC200 image in Software applications. Code39 Generation In None Using Barcode creator for Software Control to generate, create Code39 image in Software applications. where may be found by solving the linear equations
Paint ANSI/AIM ITF 25 In None Using Barcode printer for Software Control to generate, create I2/5 image in Software applications. Draw Bar Code In C# Using Barcode drawer for .NET Control to generate, create barcode image in .NET framework applications. where In many cases, constraining the leastsquares inverse filter to minimize the difference between h ( n )* ~ ( n ) and S(n) is overly restrictive. For example. if a delay may be tolerated, we may consider finding the filter h ( n ) so that h ( n )* ~ ( n ) 6(n  no) for some delay no. In most cases, a nonzero delay will produce a better approximate inverse filter and, in many cases, the improvement will be substantial. The leastsquares inverse filter with delay is found by solving the linear equations Code 39 Extended Maker In None Using Barcode maker for Microsoft Word Control to generate, create Code 3/9 image in Microsoft Word applications. Barcode Recognizer In Java Using Barcode Control SDK for Java Control to generate, create, read, scan barcode image in Java applications. FILTER DESIGN
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Use the window design method to design a linear phase FIR filter of order N = 24 to approximate the following ideal frequency response magnitude: The ideal filter that we would like to approximate is a lowpass filter with a cutoff frequency w, = 0 . 2 ~ .With N = 24, the frequency response of the filter that is to be designed has the form Therefore, the delay of h ( n ) is a = N / 2 = 12. and the ideal unit sample response that is to be windowed is All that is left to do in the design is to select a window. With the length of the window fixed, there is a tradeoff between the width of the transition band and the amplitude of the passband and stopband ripple. With a rectangular window, which provides the smallest transition band, and the filter is
otherwise
However. the stopband attenuation is only 21 dB. which is equivalent to a ripple of 6, = 0.089. With a Hamming window, on the other hand, and the stopband attenuation is 53 dB, or 6 , = 0.0022. However, the width of the transition band increases to which, for most designs, would be too wide.
Use the window design method to design a minimumorder highpass filter with a stopband cutoff frequency w, = 0.22n, a passband cutoff frequency w,, = 0.28n, and a stopband ripple 6 , = 0.003. A stopband ripple of 6, = 0.003 corresponds to a stopband attenuation of a,= 20 log 6, = 50.46. For the minimumorder filter. we use a Kaiser window with Because the transition width is Aw = 0.06n, or A f = 0.03. the required window length is
CHAP. 91
FILTER DESIGN
38 1 Rounding this up to N = 99 results in a type I1 linear phase filter, which will have a zero in its system function at z = 1. Because this produces a null in the frequency response at w = n , this is not acceptable. Therefore, we increase the order by I to obtain a type 1 linear phase filter with N =: 100. to In order to have a transition band that extends from o,= 0 . 2 2 ~ w, = 0.28n, we set the cutoff frequency of the ideal highpass filter equal to the midpoint: The unit sample response of an ideal zerophase highpass filter with a cutoff frequency w,. = 0 . 2 5 ~ is where the second term is a lowpass filter with a cutoff frequency w,. = 0.25n. Delaying hh,(n) by N / 2 = 50, we have and the resulting FIR highpass filter is h(n) = hd(n). w(n) where w(n) is a Kaiser window with N = I00 and B = 4.6. Given a desired frequency response Hd(eJ"), show that the rectangular window design minimizes the leastsquares error For this problem, we use Parseval's theorem to express the leastsquares error ELs in the time domain: If we assume that h(n) is of order N , with h(n) = 0 for n < 0 and n z N , Because the last two terms are constants that are not affected by the filler h(n), the leastsquares errorELs is minimized by minimizing the first term, which is done by setting h(n) = hd(n) for n = 0, I . . . . N (i.e., using a rectangular window in the window design method). If hd(n) is the unit sample response of an ideal filter, and h ( n ) is an N thorder FIR filter, the leastsquares error fLS= I\ 277 =

