SIGNALS AND SYSTEMS QUIZ 5 ECE, Quizzes of Signals and Systems

Download SIGNALS AND SYSTEMS QUIZ 5 ECE and more Quizzes Signals and Systems in PDF only on Docsity!

Ans: Ans:

>. Institute of Information Technology Kottayam Time: 20 minutes INDIAN INSTITUTE OF INFORMATION TECHNOLOGY KOTTAYAM Department of Electronics and Communication Engineering IEC 122 SIGNALS & SYSTEMS Quiz V - April 2025 (A) Semester II Max marks: 1C 1. The ROC (region of convergence) of the z-transform of a discrete-time signal is represented by the shaded region in the z-plane. z-transform is represented by A. im Unit cirele Cc. Im ni Ans: 2e(n) = aint If the signal x[m] = (2.0)!"!,c0 < n < +00, then the ROC of its =plone as —— Re aA Re 2, LE LEED Pre ee HEE GLO: im ‘Unit circle =plane (ROC does not exist) <4 No =-trensform/Roc for x>1 2. A discrete-time signal x[n] = 6[n — 3] + 26[”a — 5] has z-transform X(z). If Y(z) = X(—z) is the z-transform of another signal y[n], then (A) yln] = x(n] (B) y[n] =«[-n] Ans: Ler yin] = -x[n] (D) y[n] =—x[-n] X[nJ= §[n-3] +2§(n-5] —2 > Kez) = 274227 Y¥(2) = XX gf) -3 =. - - C2 +2¢2)% = -Z?-227 ~ §£n-3]- 2${n-5] = -x(v] 3. If the impulse response of a discrete-time system is h[n] = —5"u[—n — 1], then the system function H(z) is ‘equal to (A (Cc and the system is unstable or > = 5 and the system is stable (D) = Ans: h[n) = -Suf-n-i] <2 Ho) - 2 : |z[< 5° z-5 71 Roc includes unit civcle Iz[=1 Hence sy stem is stable 4. A sequence x[n] with the z-transform X(z) = 744 <2 — 2z¢ +2 - 3z-‘ is applied as an input to a linear, time-invariant system with the impulse response h[7] = 26[n — 3] where 1, n=0 6[n] = | . 0, otherwise The output at n = 4 is (A) -6 BY zer0 (C) 2 (D) -4 Ans: 42 aed XQ) aot 2242-32 } ez) = X(2) Hez) = (24 z*- 2242-32") 227 Hezy= 223 -2 . Yos= 22 saz tystey z3_¢77 ~ yCn] = 28 (n4i} + 2 5(n-1)—- 4§&-2)+ 4 § -9 -6 & (n-77 n=2 n=3 n=7 yl1=0 5. Letx[n] = (-3] u(n)— (-3) u(—n— 1). The Region of Convergence (ROC) of the z-transform of x(n) is 1 A> 5 SH er kl> 4 | (B) |z| < 3 (D) does not exist Ans: x[n] = (-5) won) ~(-3) u(-n- 1) —2 +5 XQ) = ar + a 7 3 —u“— = OC (z)>4 bzeL foc 4 ssjL«lzl< L 3 —277! 6. The discrete-time transfer function ———— is 1-057 (A) non-minimum phase and unstable (C) minimum phase and stable (B) minimum phase and unstable I non-minimum phase and stable Ans: ~— Hcez)= 1-22! -» Zero: ==2 L-osz'! Pole + zZ=z0-5 Zeve z=2 fs outside Jzj=1. .* System is non-mirimum Phose. Pole z=o0°S inside unit civele [2z/=L covvesponds to stable system 1 10. The z-transform of the sequence x[n] is given by X(z) = Coen with the region of convergence |e] > 2. Then x[2] is “ Ans: Qube aoa = Pala "uf n)<2> 2) = x(n) = (2)"4(9] x(2)U{n} Xe) aa Using matrix methed of convolution (2)” a @|1 4 * C01 = {44,12 32, ---] 2 & 2 =x(2zJ=12