# hwB34 - ENEE 241 02∗ HOMEWORK ASSIGNMENT 34 4 −1 0 1...

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Unformatted text preview: ENEE 241 02∗ HOMEWORK ASSIGNMENT 34 4 −1 0 1 −4 T Due Mon 05/05 . Consider the FIR ﬁlter with coeﬃcient vector b = The following MATLAB script computes a segment of the ﬁlter output sequence y (1) [ · ] for an input sequence x(1) [ · ] which has period L = 5. Speciﬁcally, the vector y1 equals y (1) [1 : 5]. b H x1 X1 Y1 y1 = = = = = = [4 -1 0 1 -4].’ ; fft(b) ; [2 3 1 -1 -2 ].’ ; fft(x1) ; H.*X1 ; ifft(Y1) (i) (3 pts.) Display the vector x(1) [0 : 4]. (ii) (5 pts.) Compute y (1) [1 : 5] using a circular convolution, based on the ﬁlter’s input-output relationship. The following MATLAB script computes a segment of the ﬁlter output sequence y (2) [ · ] for an input sequence x(2) [ · ] which has period L = 4. Speciﬁcally, the vector y2 equals y (2) [0 : 7]. b H x2 X2 Y2 y2 = = = = = = [4 -1 0 1 -4].’ ; fft(b,8) ; [3 1 0 -5 3 1 0 -5].’ ; fft(x2) ; H.*X2 ; ifft(Y2) (iii) (2 pts.) Display the vector x(2) [0 : 3]. (iv) (5 pts.) Compute y (2) [0 : 7] using a circular convolution, based on the ﬁlter’s input-output relationship. (v) (5 pts.) Fully explain the relationship between y3 computed below and y2 computed earlier. b H H x3 X3 Y3 y3 = = = = = = = [4 -1 0 1 -4].’ ; fft(b,8) ; H(1:2:8) ; [3 1 0 -5].’ ; fft(x3) ; H.*X3 ; ifft(Y3) Solved Examples S 34.1 (P 4.3 in textbook). Consider the signal sequence x deﬁned by x[n] = cos 3πn − 1.8 + 2 cos 14 18πn − 0.7 + 6 cos 35 17πn + 2.0 24 (i) Is the sequence periodic, and if so, what is its period? (ii) Sketch the amplitude and phase spectra of x (both of which are line spectra). S 34.2 (P 4.7 in textbook). Consider a FIR ﬁlter whose input x and output y are related by 8 y [n] = k=0 bk x[n − k ] , where the coeﬃcient vector b is given by b = [ 1 2 −2 −1 4 −1 −2 2 1 ]T Let the input x be an inﬁnite periodic sequence with period L = 7, and such that x[0 : 6] = [ 1 −1 0 3 1 −2 0 ]T Using DFT’s (and MATLAB), determine the ﬁrst period y [0 : 6] of the output sequence y. ...
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## This note was uploaded on 03/21/2010 for the course ENEE 241 taught by Professor Staff during the Spring '08 term at Maryland.

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hwB34 - ENEE 241 02∗ HOMEWORK ASSIGNMENT 34 4 −1 0 1...

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