university of illinois at urbana-champaign, Lecture notes of Chemistry

Download university of illinois at urbana-champaign and more Lecture notes Chemistry in PDF only on Docsity! UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Department of Electrical and Computer Engineering ECE 417 Multimedia Signal Processing Fall 2019 PRACTICE EXAM 2 Tuesday, October 22, 2019 • This is a PRACTICE exam. On the real exam, you’ll be allowed to use one sheet (front and back) of handwritten notes. • No calculators are permitted. You need not simplify explicit numerical expressions. • The real exam will have a total of 50 points. Each problem specifies its point total. Plan your work accordingly. • You must SHOW YOUR WORK to get full credit. NAME: Practice Exam 2 Page 2 Possibly Useful Formulas YPbPr and Sobel Mask Y Pb Pr  =  0.299 0.587 0.114 −0.168736 −0.331264 0.5 0.5 −0.418688 −0.081312  R G B  Gx[n1, n2] =  1 0 −1 2 0 −2 1 0 −1  ∗ ∗I[n1, n2], Gy[n1, n2] =  1 2 1 0 0 0 −1 −2 −1  ∗ ∗I[n1, n2] Integral Image and Lowpass Filter ii[n1, n2] = n1∑ m1=0 n2∑ m2=0 i[m1,m2] H(ω1, ω2) = { 1 |ω1| < φ1, |ω2| < φ2 0 otherwise h[n1, n2] = ( φ1 π )( φ2 π ) sinc (φ1n1) sinc (φ2n2) Orthogonality Principle and LPC ε = E (x[n]− p∑ m=1 αmx[n−m] )2  , ∂ε ∂αk = −2E [ x[n− k] ( x[n]− 12∑ m=1 αmx[n−m] )] Rxx[k] = 12∑ m=1 αmRxx[k −m] Autocorrelation and Power Spectrum Rxx[n] = E {x[m]x[m− n]} ↔ Sxx(ω) = ∞∑ n=−∞ Rxx[n]e−jωn rxx[n] = ∞∑ m=−∞ x[m]x[m− n]↔ sxx(ω) = ∞∑ n=−∞ rxx[n]e−jωn Fourier Series x[n] = P−1∑ k=0 Xke j2πkn/P Xk = 1 P P−1∑ n=0 x[n]e−j2πkn/P Autocorrelation and Power Spectrum Rxx[n] = E {x[m]x[m− n]} ↔ Sxx(ω) = ∞∑ n=−∞ Rxx[n]e−jωn rxx[n] = ∞∑ m=−∞ x[m]x[m− n]↔ sxx(ω) = ∞∑ n=−∞ rxx[n]e−jωn