第2次作业讲è¯

第2次作业讲è¯

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Unformatted text preview: s ª 2h µÒ é 1.4 ”6 0 s (a ) ( e) shi9876@hzcnc.com 1 s ª 2˜ µÒ à 1.5 ˜ µ Òà 0.5t+1) f (t) ˜àÒª µ* (2) f (1-2t) s (3) f (- 1 shi9876@hzcnc.com 2 s ª 2è µÒ ã 1.6 s x(3-2t) ` x ( t) s s 3→ x(t + 3) → x(2t + 3) → x(−2t + 3) x(t ) 3 shi9876@hzcnc.com 3 s ª 2x µÒ â 3 shi9876@hzcnc.com 4 s ª 2H µÒ á 1.7 s * xª [µnÒ]á H x[2n+1] s (4) x[n-3]δ[n-3] s (2 (2)x[4-n] s (3) (4 ) shi9876@hzcnc.com ) 5 s ª 2å µÒ 1.9 0Áª*ЉLE ”† shi9876@hzcnc.com 6 s ª 2x µÒ é (1 1 xe (t ) = [ x(t ) + x(−t )] 2 1 xo (t ) = [ x(t ) − x(−t )] 2 shi9876@hzcnc.com 7 s ª 28 µÒ í (2) 1 xe [n] = { x[n] + x[−n]} 2 1 xo [n] = { x[n] − x[−n]} 2 shi9876@hzcnc.com 8 s ª 2h µÒ î 1.12 + 6 H J % á ` s (1) y (t ) = e x (t ) * ª µ tη Òî x(t ) = 0 * ª µ tη Òî *ª µ Òîh y (t ) = 1 ≠ 0 x1 (t ) → y1 (t ) = e x1 ( t ) y1 (t − t0 ) = e x1 ( t −t0 ) x2 (t ) = x1 (t − t0 ) → y2 (t ) = e x2 ( t ) = e x1 ( t −t0 ) = y1 (t − t0 ) s x(t ) < Ms y (t ) < e M shi9876@hzcnc.com s 9 s ª 2ˆ µÒ ì (2) y[n] = x[n]x[n − 1] * ª µ nˆì Ò n * nª −Ò 1ˆì µ x1[n] → y1[n] = x1[n]x1[n − 1] ª µ Ò ˆì y1[n − n0 ] = x1[n − n0 ]x1[n − n0 − 1] x2 [n] = ax1[n] → y2 [n] = x2 [n]x2 [n − 1] = ax1[n] ⋅ ax1[n − 1] = a 2 x1[n]x1[n − 1] ≠ ay1[n] x2 [n] = x1[n − n0 ] → y2 [n] = x2 [n]x2 [n − 1] = x1[n − n0 ]x1[n − n0 − 1] = y1[n − n0 ] x[n] < M y[n] < M 2 shi9876@hzcnc.com 10 s ª 2è µÊ ¥ (3) y (t ) = sin( 4t ) x(t ) * ª µ tÊ ¥ * ª µ tÊ ¥ x1 (t ) → y1 (t ) = sin( 4t ) x1 (t ) * ª µ Ê è¥ y1 (t − t0 ) = sin 4(t − t0 ) x1 (t − t0 ) x2 (t ) → y2 (t ) = sin( 4t ) x2 (t ) x3 (t ) = ax1 (t ) + bx2 (t ) → y3 (t ) = sin( 4t ) x3 (t ) = sin(4t )[ ax1 (t ) + bx2 (t )] = ay1 (t ) + by2 (t ) x2 (t ) = x1 (t − t0 ) → y2 (t ) = sin( 4t ) x1 (t − t0 ) s x(t ) < Ms y (t ) < M s shi9876@hzcnc.com 11 s ª 2ê µÒ (4) y[n] = x[4n] * ª µ nê Ò * ª 4µ n ê Ò x1[n] → y1[n] = x1[4n] * ª µÒ ê y1[n − n0 ] = x1[4n − 4n0 ] x 2 [ n ] → y 2 [ n ] = x2 [ 4 n ] x3 [n] = ax1[n] + bx2 [n] → y3 [n] = x3 [4n] = ax1[4n] + bx2 [4n] = ay1[n] + by2 [n] x2 [n] = x1[n − n0 ] → y2 [n] = x2 [4n] = x1[4n − n0 ] s x(t ) < Ms y (t ) < M s shi9876@hzcnc.com 12 s ª 2È µÊ © 1.14 p S Á”3È x(t ) = e − j 2t S → y (t ) = e − j 3t x(t ) = e j 2t S → y (t ) = e j 3t (1) x1 (t ) = cos(2t ) y1 (t ) (2) x2 (t ) = cos(2t − 1) y2 (t ) ( ) ( ) 1 j 2t 1 j 3t S − j 2t (1) x1 (t ) = cos(2t ) = e + e → = e + e − j 3t = cos(3t ) 2 2 1 1 (2) x2 (t ) = cos(2t − 1) = e j ( 2t −1) + e − j ( 2t −1) = e − j1e j 2t + e j1e − j 2t 2 2 1 S → y2 (t ) = e − j1e j 3t + e j1e − j 3t = cos(3t − 1) 2 ( ( ) ( ) ) shi9876@hzcnc.com 13 s ª 2È µÊ ¤ 1.18 LTI x(t ) = u (t ) y (t ) = e −t u (t ) + u (−1 − t ) à x(t ) * ª µÊ È ¤ x(t ) = u (t − 1) − u (t − 2) u (t − 1) → e − (t −1)u (t − 1) + u (−1 − (t − 1)) = e1−t u (t − 1) + u (−t ) u (t − 2) → e − (t − 2 )u (t − 2) + u (−1 − (t − 2)) = e 2−t u (t − 2) + u (−t + 1) y (t ) = u (−t ) − u (1 − t ) + e1−t u (t − 1) − e 2−t u (t − 2) shi9876@hzcnc.com 14 s ª 2H µÊ ¯ 1.18 * LTIH ª µÊ ¯ x1 (µ tÊ )H ª¯ y1 (t ) x2 (t ) x3ª (µ tÊ )H * ¯ shi9876@hzcnc.com 15 s ª 2x µÒ ê x2 (t ) = x1 (t ) − x1 (t − 2) x3 (t ) = x1 (t ) + x1 (t − 1) y2 (t ) shi9876@hzcnc.com 16 ...
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