PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB
490 Practical MATLAB® Applications for Engineers Let wN = e−j(2/N) then Fk f n WNnk k N n N ()() 0 1 ∑ for 0,1,2,3, ,... ...
DTFT, DFT, ZT, and FFT 491 then by increasing the length N no distortion is introduced. The new augmented sequence f_ aug(n) is ...
492 Practical MATLAB® Applications for Engineers For the signal f(t) = cos(2πt) just considered (R.5.98), the power spectrum for ...
DTFT, DFT, ZT, and FFT 493 R.5.104 The properties of DFT are similar to DTFT and ZT. For completeness, the most important proper ...
494 Practical MATLAB® Applications for Engineers R.5.107 Let the notation f(n − 1) 7 denote that the fi nite sequence f(n) consi ...
DTFT, DFT, ZT, and FFT 495 fC(3) = 1(3) + 0(2) + 2(1) + 4(2) + 2(5) fC(3) = 4 + 0 + 2 + 8 + 10 = 24 fC(4) = f 1 (0)f 2 (4) + f 1 ...
496 Practical MATLAB® Applications for Engineers >> % evaluation of DFT using equations >> F0 =1+2*exp(-j*4*pi*0/5)+ ...
DTFT, DFT, ZT, and FFT 497 Observe that if each segment fi (m), for i = 1, 2, 3, ..., is of length M, then each convo- lution [h ...
498 Practical MATLAB® Applications for Engineers The analysis of the circular convolution for f 1 (n) with h(n), denoted by gC(n ...
DTFT, DFT, ZT, and FFT 499 In addition, since WN^0 = 1 and Wn(N/2)+k = −Wnk, the total number of computations is further reduced ...
500 Practical MATLAB® Applications for Engineers R.5.130 The MATLAB command fft2(f) where f is an n by m matrix returns the 2-D ...
DTFT, DFT, ZT, and FFT 501 MATLAB Solution >> fn _ 8 = [1 2 3 4 5 6 7 8]; >> DFT _ fn _ 8 = (fft(fn _ 8))’ % part(a) ...
502 Practical MATLAB® Applications for Engineers >> f _ 3by3 = magic(3) % part(f) f_3by3 = 8 1 6 3 5 7 4 9 2 >> DFT ...
DTFT, DFT, ZT, and FFT 503 R.5.139 The cross-correlation of two sequences f 1 (n) with f 2 (n) is given by xcorr f s f s((), ()) ...
504 Practical MATLAB® Applications for Engineers ANALYTICAL Solution R 11 (0) = [0 1 2 1 2 0 1 0]. * [0 1 2 1 2 0 1 0] = [0 1 4 ...
DTFT, DFT, ZT, and FFT 505 5.4 Examples Example 5.1 Let f(n) = 0.6nu(n). a. Evaluate the DTFT of f(n) by hand. b. Create the scr ...
506 Practical MATLAB® Applications for Engineers − 4 − 3 − 2 − 1 0 1 2 3 4 0.5 1 1.5 2 2.5 DTFT [0.6n^ u(n)] = 1./(1-0.6*exp(-j. ...
DTFT, DFT, ZT, and FFT 507 0.5 1 1.5 2 2.5 DTFT [0.6n u(n)] using freqz Magnitude − 4 − 3 − 2 − 1 0 1 2 3 4 − 1 −0.5 0 0.5 1 fre ...
508 Practical MATLAB® Applications for Engineers Example 5.2 Given the sequences f 1 (n) = [0.3nu(n)] and f 2 (n) = [0.9nu(n)] a ...
DTFT, DFT, ZT, and FFT 509 stem (nn,f1nn) ylabel (‘Amplitude of f1(n)’);xlabel (‘time index n’); title(‘f1(n) vs. n’) axis ([-4 ...
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