 ## Text File Encryption Using Fft Technique In Lab View 8-Free PDF

• Date:19 Nov 2020
• Views:1
• Pages:17
• Size:783.88 KB

Share Pdf : Text File Encryption Using Fft Technique In Lab View 8

Download and Preview : Text File Encryption Using Fft Technique In Lab View 8

Report CopyRight/DMCA Form For : Text File Encryption Using Fft Technique In Lab View 8

Transcription:

IJRET International Journal of Research in Engineering and Technology ISSN 2319 1163. Since DFT and IDFT involve basically the same type of But WN2 WN 2 With this substitution the equation can be. computations our discussion of efficient computational expressed as. algorithms for the DFT applies as well to the efficient. computation of the IDFT, We observe that for each value of k direct computation. of X k involves N complex multiplications 4N real, multiplications and N 1 complex additions 4N 2 real. additions Consequently to compute all N values of the DFT. requires N 2 complex multiplications and N 2 N complex Where F1 k and F2 k are the N 2 point DFTs of the. additions sequences f1 m and f2 m respectively, Direct computation of the DFT is basically inefficient Since F1 k and F2 k are periodic with period N 2 we. primarily because it does not exploit the symmetry and have F1 k N 2 F1 k and F2 k N 2 F2 k In addition the. periodicity properties of the phase factor W N In particular factor WNk N 2 WNk Hence the equation may be expressed. these two properties are as, The computationally efficient algorithms described in this. section known collectively as fast Fourier transform FFT. algorithms exploit these two basic properties of the phase We observe that the direct computation of F1 k requires. factor N 2 2 complex multiplications The same applies to the. computation of F2 k Furthermore there are N 2 additional. 2 1Radix 2 FFT Algorithms complex multiplications required to compute WNkF2 k Hence. the computation of X k requires 2 N 2 2 N 2 N 2 2 N 2. Let us consider the computation of the N 2v point DFT by complex multiplications This first step results in a reduction. the divide and conquer approach We split the N point data of the number of multiplications from N 2 to N 2 2 N 2. sequence into two N 2 point data sequences f1 n and f2 n which is about a factor of 2 for N large. corresponding to the even numbered and odd numbered. samples of x n respectively that is, Thus f1 n and f2 n are obtained by decimating x n by a.
factor of 2 and hence the resulting FFT algorithm is called. a decimation in time algorithm, Now the N point DFT can be expressed in terms of the DFT s. of the decimated sequences as follows, Figure 1 1 First step in the decimation in time algorithm. By computing N 4 point DFTs we would obtain the N 2 point. DFTs F1 k and F2 k from the relations, Volume 01 Issue 01 Sep 2012 Available http www ijret org 30. IJRET International Journal of Research in Engineering and Technology ISSN 2319 1163. The decimation of the data sequence can be repeated again. and again until the resulting sequences are reduced to one. point sequences For N 2v this decimation can be performed. v log2N times Thus the total number of complex, multiplications is reduced to N 2 log2N The number of. complex additions is Nlog2N, For illustrative purposes Figure 1 2 depicts the computation.
of N 8 point DFT We observe that the computation is. performed in three stages beginning with the computations of. four two point DFTs then two four point DFTs and finally. one eight point DFT The combination for the smaller DFTs to. form the larger DFT is illustrated in Figure 2 3 for N 8. Figure 1 3 Eight point decimation in time FFT algorithms. Figure 1 4 basic butterfly computations in the decimation in. time FFT algorithm, An important observation is concerned with the order of the. input data sequence after it is decimated v 1 times For. example if we consider the case where N 8 we know that. Figure 1 2 Three stages in the computation of an N 8. the first decimation yields the sequence x 0 x 2 x 4 x 6. x 1 x 3 x 5 x 7 and the second decimation results in the. sequence x 0 x 4 x 2 x 6 x 1 x 5 x 3, x 7 This shuffling of the input data sequence has a well. defined order as can be ascertained from observing Figure1 5. which illustrates the decimation of the eight point sequence. Volume 01 Issue 01 Sep 2012 Available http www ijret org 31. IJRET International Journal of Research in Engineering and Technology ISSN 2319 1163. where we have used the fact that WN2 WN 2, The computational procedure above can be repeated through. decimation of the N 2 point DFTs X 2k and X 2k 1 The. entire process involves v log2N stages of decimation where. each stage involves N 2 butterflies of the type shown in. Figure2 7 Consequently the computation of the N point DFT. via the decimation in frequency FFT requires N 2 log2N. complex multiplications and Nlog2N complex additions just. as in the decimation in time algorithm For illustrative. purposes the eight point decimation in frequency algorithm is. given in Figure 1 8,Figure 1 5 Shuffling of the data and bit reversal. Another important radix 2 FFT algorithm called the. decimation in frequency algorithm is obtained by using the. divide and conquer approach To derive the algorithm we. begin by splitting the DFT formula into two summations one. of which involves the sum over the first N 2 data points and. the second sum involves the last N 2 data points Thus we. Figure 1 6 First stage of the decimation in frequency FFT. Now let us split decimate X k into the even and odd algorithm. numbered samples Thus we obtain, Volume 01 Issue 01 Sep 2012 Available http www ijret org 32.