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2d barcode generator vb.net SIMULATION in Visual Studio .NET
SIMULATION QR Code ISO/IEC18004 Scanner In Visual Studio .NET Using Barcode Control SDK for .NET framework Control to generate, create, read, scan barcode image in .NET applications. QR Code JIS X 0510 Generator In .NET Using Barcode encoder for .NET framework Control to generate, create Denso QR Bar Code image in Visual Studio .NET applications. Consider a continuoustime LTI system with input x ( t ) and output y(t). We wish to find a discretetime LTI system with input x[n] and output y[n] such that if x [ n ] =x(nT,) then y [ n ] where T, is the sampling interval. Read QR Code 2d Barcode In .NET Using Barcode reader for Visual Studio .NET Control to read, scan read, scan image in .NET applications. Making Barcode In .NET Framework Using Barcode drawer for VS .NET Control to generate, create barcode image in VS .NET applications. = y(nT,) Decode Bar Code In .NET Using Barcode decoder for Visual Studio .NET Control to read, scan read, scan image in Visual Studio .NET applications. Quick Response Code Generator In C# Using Barcode creation for .NET framework Control to generate, create QR Code image in Visual Studio .NET applications. (6.86) QR Code ISO/IEC18004 Drawer In .NET Using Barcode creator for ASP.NET Control to generate, create QR Code image in ASP.NET applications. QR Code 2d Barcode Generation In VB.NET Using Barcode maker for Visual Studio .NET Control to generate, create Quick Response Code image in VS .NET applications. FOURIER ANALYSIS OF DISCRETETIME SIGNALS AND SYSTEMS
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Generating 1D In VS .NET Using Barcode creator for ASP.NET Control to generate, create 1D Barcode image in ASP.NET applications. Encode Bar Code In .NET Using Barcode creator for Reporting Service Control to generate, create bar code image in Reporting Service applications. (6.88) Code 128 Code Set B Creation In ObjectiveC Using Barcode printer for iPhone Control to generate, create Code 128C image in iPhone applications. Encode Barcode In .NET Framework Using Barcode maker for ASP.NET Control to generate, create barcode image in ASP.NET applications. Thus, the requirement y[n] = y(nTs) leads to the condition H,(jo) eJnwT,= Hd(ejwK) e~nwrs from which it follows that H,(jw) = Hd(ejwT1) In terms of the Fourier transform, Eq. (6.89) can be expressed as H A 4 = HdW) R = wTs (6.90) Note that the frequency response Hd(R) of the discretetime system is a periodic function of w (with period 27r/Ts), but that the frequency response H,(o) of the continuoustime system is not. Therefore, Eq. (6.90) or Eq. (6.89) cannot, in general, be true for every w . If the input x(t) is bandlimited [Eq. (5.9411, then it is possible, in principle, to satisfy Eq. (6.89) for every w in the frequency range (rr/Ts,r/Ts) (Fig. 66). However, from Eqs. (5.85) and (6.771, we see that Hc(w) is a rational function of w, whereas Hd(R) is a rational function of eJn (R = wT,). Therefore, Eq. (6.89) is impossible to satisfy. However, there are methods for determining a discretetime system so as to satisfy Eq. (6.89) with reasonable accuracy for every w in the band of the input (Probs. 6.43 to 6.47). Fig. 65 Digital simulation of analog systems.
2n
" T, 2n  Fig. 66 CHAP. 61 FOURIER ANALYSIS OF DISCRETETIME SIGNALS AND SYSTEMS
6.8 THE DISCRETE FOURIER TRANSFORM
In this section we introduce the technique known as the discrete Fourier transform (DFT) for finitelength sequences. It should be noted that the DFT should not be confused with the Fourier transform. Definition: Let x [ n ] be a finitelength sequence of length N, that is, x [ n ]= O
N l
outside the range 0 I n I N  1 The DFT of x [ n ] ,denoted as X [ k ] ,is defined by X [ k ]= x[n]W,kn
k = 0 , 1 , ..., N  1 where WN is the Nth root of unity given by The inverse DFT (IDFT) is given by
The DFT pair is denoted by x b l X[kI Important features of the DFT are the following: 1. There is a onetoone correspondence between x [ n ] and X [ k ] . 2. There is an extremely fast algorithm, called the fast Fourier transform (FFT) for its calculation. 3. The DFT is closely related to the discrete Fourier series and the Fourier transform. 4. The DFT is the appropriate Fourier representation for digital computer realization because it is discrete and of finite length in both the time and frequency domains. Note that the choice of N in Eq. (6.92) is not fixed. If x [ n ] has length N , < N, we want to assume that x [ n ] has length N by simply adding ( N  Nl) samples with a value of 0. This addition of dummy samples is known as zero padding. Then the resultant x [ n ] is often referred to as an Npoint sequence, and X [ k ] defined in Eq. (6.92) is referred to as an Npoint DFT. By a judicious choice of N, such as choosing it to be a power of 2, computational efficiencies can be gained. B. Relationship between the DET and the Discrete Fourier Series: Comparing Eqs. (6.94) and (6.92) with Eqs. (6.7) and (6.81, we see that X [ k ] of finite sequence x [ n ] can be interpreted as the coefficients c, in the discrete Fourier series representation of its periodic extension multiplied by the period N,, and NO= N. That is, X [ k ] = Nc, (6.96) Actually, the two can be made identical by including the factor 1/N with the D R rather than with the IDFT.

