Signals.and.Systems.with.MATLAB.Computing.and.Simulink.Modeling.4th_Part56

Signals.and.Systems.with.MATLAB.Computing.and.Simulink.Modeling.4th_Part56

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Signals and Systems with MATLAB Computing and Simulink Modeling, Fourth Edition 10 37 Copyright © Orchard Publications Solutions to End of Chapter Exercises We are asked to compute only. However, we will derive all equations as we did in Exam- ple 10.5. Column 1 (C=1): (1) Column 2 (C=2): (2) Column 3 (C=3): (3) (4) F3 () Y01 , Y00 , Y40 , + = Y11 , Y10 , Y50 , + = Y21 , Y20 , Y60 , + = Y31 , Y30 , Y70 , + = Y41 , [] W N 0 , Y 40 , = Y51 , W N 1 , Y 50 , = Y61 , W N 2 , Y 60 , = Y71 , W N 3 , Y 70 , = Y02 , , , + = Y12 , , , + = Y22 , W N 0 , Y 21 , = Y32 , W N 2 , Y 31 , = Y42 , , , + = Y52 , , , + = Y62 , W N 0 , Y 61 , = Y72 , W N 2 , Y 71 , = Y03 , , , + = Y13 , W N 0 , Y 12 , [ ] = Y23 , , , + = Y33 , W N 0 , Y 32 , [ ] = Y43 , , , + = Y53 , W N 0 , Y 52 , [ ] = Y63 , , , + = Y73 , W N 0 , Y 72 , [ ] = X3 , , , + == =
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Chapter 10 The DFT and the FFT Algorithm 10 38 Signals and Systems with MATLAB Computing and Simulink Modeling, Fourth Edition Copyright © Orchard Publications where and From (1) and by substitution into (4) (5) From Exercise 4, (6) Since , and (see proof below), we see that , , , , , and . Therefore, (5) and (6) are the same. Proof that : 6 . The rectangular pulse is produced with the MATLAB script below. x=[linspace( 2, 1,100) linspace( 1,1,100) linspace(1,2,100)];. .. y=[linspace(0,0,100) linspace(1,1,100) linspace(0,0,100)]; plot(x,y) and the FFT is produced with plot(x, fft(y)) The Inverse FFT is produced with plot(x,ifft(fft(y))) Y62 , () W N 0 Y41 , Y 61 , [] = Y72 , W N 2 Y51 , Y 71 , = , W N 0 Y00 , Y 40 , = , W N 1 Y10 , Y 50 , = Y61 , W N 2 Y20 , Y 60 , = Y71 , W N 3 Y30 , Y 70 , = F3 X3 W N 0 , W N 3 , W N 2 , W N 5 , + == W N 0 Y40 , W N 3 Y50 , W N 2 Y60 , W N 5 Y70 , + + x0 W N 3 x1 W N 6 x2 W N 9 x3 +++ +W N 12 x4 W N 15 x5 W N 18 x6 W N 21 x7 Yk0 , xk = W 8 8i n + W 8 n = W 8 n4 ± W 8 n = W 8 6 W 8 2 = W 8 9 W 8 5 = W 8 12 W 8 0 = W 8 15 W 8 3 = W 8 18 W 8 2 = W 8 21 W N 5 = W 8 ± W 8 n = W 8 ± W 8 n W 8 4 ± W 8 n e j2 π 8 4 ± W 8 n ππ sin + cos W 8 n = =
Background image of page 2
Signals and Systems with MATLAB Computing and Simulink Modeling, Fourth Edition 10 39 Copyright © Orchard Publications Solutions to End of Chapter Exercises The original rectangular pulse, its FFT, and the Inverse FFT are shown below.
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 8

Signals.and.Systems.with.MATLAB.Computing.and.Simulink.Modeling.4th_Part56

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online