1 (a)
Determine whether the following signals are energy or power signals. Calculate their energy or power.
(i) x[n] = u[n]
(ii) x(t) = Asin(t) ; -∞ < t < ∞
(i) x[n] = u[n]
(ii) x(t) = Asin(t) ; -∞ < t < ∞
4 M
1 (b)
State and prove the following properties of Fourier Transform(i) Time Shifting.
(ii) Differentiation in time domain.
(ii) Differentiation in time domain.
4 M
1 (c)
Check whether the following systems are linear or non-linear, time-invariant or time-variant, causal or non-causal, static or dynamic -
(i) y(t) = x(t) cos(100πt)
(ii) y(t) = x(t + 10) + x2(t)
(i) y(t) = x(t) cos(100πt)
(ii) y(t) = x(t + 10) + x2(t)
4 M
1 (d)
Compare Discrete time Fourier Transform and Continuous Time Fourier Transform.
4 M
1 (e)
State and discuss the properties of Region of Convergence for Z-Transform.
4 M
2 (a)
Determine the exponential form of Fourier Series representation of the signal shown
10 M
2 (b)
Determine whether the following signals are periodic or non-periodic. If periodic, find the fundamental period.
(i) x(t) = cos(t)+ sin(√2 t)
(ii) x(t) = sin2t
(iii) x[n] = cos[n/2]
(iv) x[n] = cos2[πn/8]
(i) x(t) = cos(t)+ sin(√2 t)
(ii) x(t) = sin2t
(iii) x[n] = cos[n/2]
(iv) x[n] = cos2[πn/8]
10 M
3 (a)
The analog signal given below is sampled at 600 samples per second
x(t) = 2sin(480πt) + 3sin(720πt)
Calculate:
(i) Minimum Sampling rate to avoid aliasing.
(ii) If the signal is sampled at Fs=200Hz, what is the discrete time signal after sampling?
(iii) If the signal is sampled at Fs=75Hz, what is the discrete time signal after sampling?
x(t) = 2sin(480πt) + 3sin(720πt)
Calculate:
(i) Minimum Sampling rate to avoid aliasing.
(ii) If the signal is sampled at Fs=200Hz, what is the discrete time signal after sampling?
(iii) If the signal is sampled at Fs=75Hz, what is the discrete time signal after sampling?
10 M
3 (b)
Determine the DT sequence associated with Z-Transform given below -
![](data:image/png;base64,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)
10 M
4 (a)
Draw Cascade and Parallel Realization. The transfer function of discrete time causal system is given by
![](data:image/png;base64,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)
10 M
4 (b)
Obtain the convolution of
x(t) = u(t) and h(t) = 1 for -1 ≤ t ≤ 1
x(t) = u(t) and h(t) = 1 for -1 ≤ t ≤ 1
10 M
5 (a)
Obtain the inverse Laplace Transform of
![](data:image/png;base64,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)
10 M
5 (b)
Find the Fourier Transform of:
(i) e-2(t-1)u(t-1)
(ii) x(t)=|t|
(i) e-2(t-1)u(t-1)
(ii) x(t)=|t|
10 M
6 (a)
Determine the impulse response of DT-LTI system described by the difference equation (for n≥0)
y[n] - 0.5y[n-1] = x[n] + (1/3)x[n-1]
where all the initial conditions are zero.
y[n] - 0.5y[n-1] = x[n] + (1/3)x[n-1]
where all the initial conditions are zero.
10 M
6 (b)
A causal LTI system has a Transfer Function H(z) = H1(z) H2(z) where
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAuIAAACPCAMAAAH/z342AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAL0UExURQAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAHsVFDsAAAD8dFJOUwDWQYLDLm+wG/FcnQjeSYrLNne4I/lkpRDmUZLTPn8rbK0Y7lmaBdtGh8gzdLUg9mGiDeNOj9A7fL0o/mmqFetWlwLYQ4TFMHGyHfOfCuBLjM04ebol+2anEuhTlNVAgcItbq8a8FucB91Iico1drci+GOkD+VQkdI9fr8qa6wX7ViZBNpFhscyc7Qf9WAM4k2Ozzp7vCf9aKkU6lWWAddCg8QvcLEc8l2eCd9Ki8w3eCT6ZaYR51KT1D+AwSxtrhnvWpsG3EeIyTR1tiH3YqMO5E+Q0Tx9vin/aqsW7FeYA9lEhcYxcrMe9F+gC+FMjc45ersm/GeoE+lUlae5hmgAAAAJcEhZcwAAFxEAABcRAcom8z8AABfkSURBVHhe7Z17eFNVtsAXXkB6raJQfCC3wJQWfFxw0PqYWAaC4Q4CKiCIApeHIi8vFxlA7DgKDSMoCJcxQxW0go6WAVGsojBQwRmkIw9Fg+AS0ErxgaJVtMrjn7v2I8k5yTlpEpI0Cev3fTln753TZq+19tlnn73XWQeYU2Cb3seF3Md1gijT+zjyODyJCN0o1VEVxJPOqPZeAKyuLVCZyOldqBOK+wAGysQuuY2YIpynU+EoFZu3ZVLiCUV9QUbw3IkulZlCn1fpsxoeknl9pBFZfntLOAKvAOyXuTB0KxwIe2ZqvdFuJ32O71RZC87Qe0GV3qs2I0yqIQOHxadP32Gk5dcBHkO4RhcEEWgzUC0LIoL+OyIpj3T8PKzVhaGINiP+NbUZL0TeZnTdS2HaSKioR16GOS35rd7HkSKElzfJVCO5jZD903TCmmzRV9wNndqITPRnc/h/jrPk7tfzkIiq1pKg6sxeciV8TPuuKlsP56pdOX3OuYk29cj2vRTFoQ/L1lcUA1/IL2CN44hKSP5Cn7FQADkqqw81QqXiylUH/Woq4Z/yqFAa631hf8e1Zb1m6FwdYAtRnatVNoTNeq+4RO8FbtlauogkHgyj94AmxYWpJcBCN/xdZO2uY4bW8mxUrYXsL49/AW5TBRaI1kI1F63ltchbi/ekrDn996F5TrqUMQzD1EvlBzohWZPfibbe/AqVlUR/xYqcaDrPYLINN6qwfyuoCwb9xxH61rIJ3iL3CSH8JT88pprDLzCYtnQPv4UqX6nKEkmYmj9cBcWTAFpQctSLosC5XGzjxGSTtZd4nGfQuKBWjA3UF8/IbWzQ3bT4JyTbatphPmX6UOJmMfj4jTggeprWIDz4Yck+KBj7+l26TFL9CQy6kfZTVsIqGq3kz/kOrhDlR/VIJzomwgJhdKr5pbQbLooc9NkuBovvilzUbN0Cx0kNx7rSHbpJ5ZCntHQBfbbT5zP6/LCFNuK3xK1yzOifEQNBA1Z9C/2Qykpi6Vu66emDWrXzsVTvFeXiVwYg3q6yEpvZBSv0GdqNBmL+vuWwsK2vbwF5pxAftELE8E1m3hd7sk0RDJFFAOfpfQSYaq77FoAVielbTDXPgrLuMoHwVfd6550YhmEYhmEyknWmG73UIa5j5WhxxX6jsUsPOBULwT0QxEytcbYicRX3DNOJWDBV3DfG3/FTYIzv3e1UiQQwVu9jQVZc3h+qjFyxHk2f2+yXVOPGKVfch743aQxvJOfe5BQq7sWTOiUpReiw+GpSv7PCaxIpIeRint0KuJ6vkT4hqiKnMl8Twnpj76Mnoq6opR879YmocnErnSdWwsQKmCCeivxF7xX3AcwG9xHxC2KRjtgV2UKdBXqeSbQl0zyTmGaKfp5J4ShsNAmrWgHMdJmVoCfQaGOaQHOL35okvoiCKb4lQfUpoP+Yo9xVFFKAetEHK8ZAQSXV8RBsLYNvdZmCKv497e7QXZOYOzNKZrGGaYFe1tTzY6LSofNjtI8BB7wnrrcOeAtWmq9NauKvL6VME38rY/kxOr6OdgcOyuRx2Gm/XmrHZqNrD4HLf1xUfQOU7x7p6bzH6AE15XYx4eMUlXylH9RAJfWndku6dviWeo1EPq9HKjqkspJYLvlawRFMWHrzqWn5sZ6wlKe4UUeEb6xC5xqhxirZalZONagYxyrS68q4zE3kgh5oipl70duJ337c1wTkj0Ux02qqOGVorJL9FJ2OMc1H1oNvKURW3LeIs5maQCwTrbLiQlqRoI/yruuSkLGKrLjvXO3WSVdT/3C06D9RGk/wPKpJ4/4J4qbj6OeiniD2jVVUxdVY5cNGeZCIsUpn1H40quK/9s6jGqP3NcDaRlF7ejIMwzAMwzAMwzAM01Bsbhw0B8kkmkYJXOjNONofRtsF/T+1AjiIF8r05Ydpc3i9TCvkPCHiQUqmpcaHIi7UyeSSbavxAukdvbCXygk6Co2/U+z1Puwx9SNt4jddnUzGnsojBrET0Lh0npcoD/ob5TdtrpQZQYWcp95GVb1X5tOdBtd4MNkoFnw/0w9xwnW+pbHpOFmn0pwG0ngBDtCpEI7OB/gJs6EDLob9WEyNf6YbpuKbAIfm6kPSmt4HdCIebFiiE1C8QCcygwYX7Ak8Rts/U2MEGI3ab+UYmsJfjIzWLyNZrDhs78sWEMyNZwP0pFMtNQQbX0SbAvxEZnS/lIPGx9yJf32qEw3HmtZisf/I+fRpp0oqPVBOWTtMggHchS+mhmCb8Ruv19t+sHIH1Ro/JPxuqM7Z0Azl6KLSIRxwiNYuH0l4RjLA/SJOz85aeArmnzUATopR8PsDAX7n8LlyhGIWjFT/Mm3tBXMv13K5cvVfJIqWoh9xZulRhNb4eJ+v4rT31H4HGn21DKzU1YwH1+r/GUozvAtgsoO63QccR8BZTvdMl4pB/qqJ6nsrzIL13CB3KSDYAjmyW4ZTVbaH9PqFWur3iLF3ALQ7IVJfi/vFhmMCteXLbhJ+jC/dCTArizrvMS4abQ7W1bbAJNiHwreoWUkqCNat1rXOCZ2qaopFruqky1X7qXAOufI2ah+uqvx87whxaVqAQc5asSM9MoPZtu63dkN6xSeuWZDjOgcWuNYCVLseoSIXqbzY1svVJNiSGtnUPqJk4gSzpF7BAsyVsx2Kst3NdcqSoHmVh9DQtxrnVbIrHiaxv5bpEJI2rxK7YDBnhE4QRsG2CZfWchsXvYQIZr7n7NYqoHHTvEp2F98XFvMqKTmTFXQz3VJ5iwlCJ4zKhfGSJZh5XqWmbo/1vIrb1dx1Ad5MqZB5lSZe3H1L4p4SiZWAYG4RAWF2S9qoAbx5wqgAEWV5sgQzNwWn4SeD5lWI7/BXtE2TeZWgNt5b3wcQoYJ5cRxtkySYeV7F2KuY5lVy+1PBZy9B+syrBE0YGXoVv2CA02Dfo1Qwm0b6DSTYETkIyEQe+w+dYBiGYRiGYRiGYRiGYRiGYRiGYRiGYRiGiTctsnSCSQpT258MPIDIJIVXGuYpvXTFZf8qpV1vndVxo0o6W+Cm9qgeVQghTTVeudQUQDVJhH04/fD1ADOflEl33QqAn3GxzEgeU4/li1iV6anxcBEJEsd+DwyzVVdb7AowUT0e5dxDm7U6bmcwaanx3F3QEBon7B+Vbl7hBDgPX9BZ4Y76G9G/1HoLPblGh9DO6XnlDHJ3Thr2Gt+eRz38DvxQZwGuFp36gnKAcWjsAZvvxYuX6XQ60eAal08SSPSjwIdE080JVOtnGRY852XlaZ3+NLjGVShriRq9PDqTNjn4nMwATPAHdO5yKu9BSR1Sr1f5phV11m1xnsp95X8KbpoeMaY7qafxG8RY5esuqsE7xTMy2VdR6sfj1MEk+FnspNBQGrcPMpI9+FWAjtfKp2XgzuHUzZ91OUBtBQ0Tza/1SFPCRJZJILm9EfMKbaLgX4ZjN4on4Enjm1UH3w664zDvxVioDkhnOntJnpPWNxgxMGqNTsCOv+pEZtDggk3y7FkGzome5TKyztC2shBg0/M6QYwWvXFK0hyDXhRjwCRYsbdYv7M7BQRr9Sxt1uITtD0yx9cvfWl6Vc88c+Cd1KGslS9ejQUBwYqxKWlXPo2ZAoIdcYjIAB8Ja9ds76CvvZVBsfH2qcmolGMBinfaW2MQbINo1/eMoU0qCDZKnlnN+8hZDt9op02J3Pl5CPvpVINR6QGYCvBHapTtdF+wZtnLDvsxpkkwYmQWHZsKgk2SVTr3HpnRGi9AGZKpADfln8Q8+r6sbqsosLiPTxIFM8e6jmPbrt/+Yf7anr+XbzZt6qi5D0XHYYNJMEIEh7AXLCQ4ZuIY2cfr9S4qVdcVrfEbUb4Y6rlNAEPU68ne1oFIkhdNyowIinUOFjSBq45/CdU4V0XOctcd1d9bYBIMYJh44Ze9YMkLAOYs/XfabhGTqITWeBMZqE7gkhEVANa3lLtQvtANIx6s1P8zlK1inmbiKkqt2+mGZjgVysbQIM9d+l/qewvMgsF0McOTEoIdQ1HpE6giogVrfAXq17e1sauYRzeMeGCvcRmGrL8IlDf+aaptHx2rrK3D/vVjZsHmqn0qCHYGikoPUQG7gnoVqqeIWCd4/xa1D5kdTA5vVYmfvkb0wLS5dR+1ehE1773j+nsLTIKt1e+0thcMtmuxUEYHSiBFr4vtGJJBsEWNxwtQ3gh1xVdJWKHZsroJoqDB8Ad+G0QdijOruzE6nA0mwb59gDYzVqaEYH3E+y/dKNYgiWJUb68cTucu9HN8DJC/V+RDQmHGm3o8hEbO9PTqjHtmdJ1Ex7mxx483H8PC5YU/9l9EV1RrjII9IdtunTsVBCuuqdoKznWuWnG2Tc6/xFVTIoK1PbeTNje4euSX1PwgDrvgQbGNB038YXoN1O8h5Au195hYOprl2hWIx2eDSbAvZG+aS6nECWZJFK5P/yteK+znBQwbxDgyfxV4UrY065vEpK3lJ0AwZwt8rb2aQwglcsG+NNz+3qbj+lkT7K9ijApo9FeBs/aKlmZ9FifPeyJ2wUyBHI2OOIPvF/9KxK8MJQrB5jbVCcix7SsFIf4qxvhdRn8V6OufJtU0jIdQzIIZQ66ZHXHoTJiHpHY/WrCDiRLMvOpm1LjJX8WvcQt/lSRqPArMghk1HuKI8y7SoDtpgtlr3OSv0nfgQI8c64b6q6Soh5C9xoMdcY4e+Iq2SRPMX7HgyJdmf5XWi2pc2FMUhPirpKiHUEDjwcFKzY44lyD2HSUKkiWYv2L1+asALEEVFzM9/FUCGlfjLMHdMh8iWBFulvvkCGY++QyxRoP8VQTzbxXbNPFXMQtmDA8bIlh2qQwtnyTBzBUz9uMmfxVBWStRsXTxVzELZuzHQwSrHiycE5IlmNlfxahxo7+KW0zXDUK6wqSNv4pZMKPG/YJ1wMXZIo7/IGyWNMGC/VWMGjf6qzjvxItPIt2Wp4u/SrBgRo37BSONu3uht0EFy9h4upkbAplhGIZhGIZhGIZhGIZhGIZhGIZhGIZhGIZhGIZhGIZhGIZhGIZhGIZhGIZhGCYtaXK9CATEMBnJlqYbERfqIEwMk3FceP4OWNtm2jU6yzBxZmiLtrGElpq+vND7cAsR9M7MFcW13tpiz7vR/c9XGnETTyYxGj0NOTJ6DuJN0b+Nrl8NrvoA4LKN2PM8XSRwFyOeLcLSju6J2ML3yggzi7d5DLyp46ByE08esRo9DVlSk7d9YIdz8cqoR8Frf8E/7xCJC1viTIOu3BvweRVse949OMY6GHzbXBn9XbNN32RyE08SsRs9bckei9OildZ5IsuxWr5rxnniLWw/VRaauWskZr0YxaWQm3gyicXo6Uss0k7dh62GqvbbpCOebfXSqynl2Fy99KigEHFTfn7+Sbo65n1nFyCy8qKsm3WSSTjcxOtjyZe4UA9PctpYXfIKhmFH3wutnhu/SQzKmw3BO7qrkhA+X5e/rqbGW/L0Vg6RmhRO+ya+MhDLPsDdhlHHjXOMTfx9/3scfEy/Y+arOqkpcDlwtXpPIdPwnPZN3N3a/8JVP7mVhiY+9Rf/QGXHDByeI1N+5vbEDerlkH5WTMP39HshmRTgtG/i9eL2lJZOVK34YB6WiDdX+1nbFy9QL+H0M3c4fuYbtjCpwOnVxLf0wPejniJd3Ahf6iwS4y7Gnj+JgkmeV2U3/eG3jcRLT4lmM0rk/WbXsXiHHLa0e+tEFFMsTAKJyejpypHiA1g35KDORcz+7fjMJwCbi/AC+WLVN+Zjm1cAnE/s1EN3oq6FW6wROY5/LI6ozN+5V71amWloYjR6OjK5Kv/kJTTQrqkt+fRr+7evW7Lri9Wf5q97ZJfKtc11jT4GsOSLGjV0F+R+RG3+Bperqkd+fn6Jt2bEDzxfkgKcitETzOaju8dcEtIP5vwNi6bw9T86Ohc/7PH8I+xrneMBW6zbht10Od8u5oKdnV5zIM50+fRR6VqKH5jU8PkfsLnuMYP5/D/xPp6uiI6nWmFt0KxPBFhbzDmghVesbrVHrNgQuNNmixHVTesck3RD3jED+09WyaHt8XCQ+3TBtrpG4q7Ohk5Z72fqC/MSQ8FEx6pKnY4GS4u5L687vEIW/XwY1y+WKbaYotml+L16M7Pw+tDdyv5cD537w0yTOuNc2Ea3f2u2Hsiy9nliLPmpv+PTWMYplhZz/n2PnhJduwkrZskzgC2mOCPPf7VcMATPNnQr5nlL51OHy7v7hy3Od1oU13q93kIaT+aeoe7gFvRw7Nbdx2nL9OXrEUsLPVWN/4dyJ+7EuoFdoez63oj/DDjRyIMOVF3gOB6T05e9xSQ/dcT18gxgiyl2PYg9f6XTj4/BHoZuxdzEuxbhoWY6TcopKh8h9uOGYMcPZAnxpzF1U0zzFSu3y4k7M1E+ppBGOH8erHwG/lqBRUfg4Kri6k8qxgyt7dUapu7FaZeZDxpRh5us3CPrI4zFBDuuxo1qcBKLxTLRZAMuwsYl+ZL3XscxE3SxwNzEJzfCogt1mu7It4nL4tSxeO+bqkCwow22Dxxy2rHgF5yzWSScX1cc/kS2nLIVXeo6/jclur6Gl94oSvwHuX9Xl3WDSERLGIsRP1cs9fmZscUk7hrHmK06/cDbWGRcBjc38fsvwr8px1Q/t3XBYcZ78pz1uD26hZUluptIObrpCkbBkR64VC3WUTM+V7ZnMWzeLRdgHzjb4RFv1Q8cdOxWvC46ZSnCWQwmdMTROskW0zQ5G/+iZSxojn1U36MJ6cWfNF1Xp0/DjeabmSZv4yZTn+C++ah+dCzAJH2nlHGMGo/7lIKmHy49X17anSfKVco90XG1lDtw0AflpbeZxwiREcZiX12HteI80sRiscwzWfWkUodP0YPOxTmq79GYm/iufdgrMLKDr37E4+KKuP/ngPffsry6801Wq9dbMJPoPtgxulokVszHZ++SRQuexEMy1XYVLpJ3iBYHRYe9xZzbsLFqwNlvXCV+LBaLZZ7J5t2DM+SFlDT0SF2py7SUWtAbDwTcZJyz5pcP1WmYWosVcki39tC3c2UJ0W+do02ad9GnEirouVXYkvrQd878tzPvPUmN+fwFsCxLDU/cRx0Lc6DZtQfLRgUfZLMuY4utxfbficOLVQ981szLxa+yxWhc5TmOWNp3GZ3HzjO+ofHMtGulOxPROdfbWw5x8k4WzlJqzK7yKdfZHbFiWK3Xe3EjxEK/klv3Kf8ujU/3Uw0V5JxF2kRcfeGW1bTLOp9a03U4U04VOidcREVnXmZ1UFTYW2zz1eL/+mgnrxRssWjZMrB0RpiVhGVZO1/UyRiIZxyVwHiyeOSVbXVhfWRiqKC0sRhxxYhFIvJNa52NgIRY7Lxe6FXhG0IYtQl7xOrxED6kRr9Za2y8A23iqNBNhEP3ZoiNH9KFkZB5T+A3iMXsTWYX+WYP4qV3UyJM5BtrEmCxF1zPLB0dsuq842l8/o/y2hg99YbU6NaylfD5DsUujgpk951vmPu15PQJFdQAFrM1mW3kmxHYV63X/tQTX79fpkKwNFn6WMw8eWPGTl/2cVSy+3ZZY3lSBOBQQadIOIvZmSyCyDeDeqLvga1gLE2W2U3cPo4KNfFJOukjsjgq3MQjJpYmXn/kmwmz8cxXVDLTLBZOYc7e97bTSRP2cVRW7sOOciBeV+hbIo8gjgrBoYIiJmwTtzFZuMg3zgEtPA8iPqKzmWcxC4WdchwVgK4X78R/SYcQRfg4KhwqKBqsmnh9JgtnMeeHI2j48SjiXv+sPZFBFrNQmH+ZrXB83d6HVTKKOCqKRwbj8/4Fao6jEkesmnh9JovAYh/Nxp2z/A02kywW7rJnNxYPF0fFxwdd/J50HEclroSzmJ3JIrBYddPB+Pt+Kp1ZFgsXUsOuidvGUXH+MEl7mI67z7Gzg+wTOI5KnAkbBMXOZCEW0yar/r9tn4scfbHIUfGPTLRY2JAatk3cLo6KuxhblYjlsxva4/jWQj0cRyXehA+CYmuyYItpk2X/goN7CKc0stjbP4jyzLJYfSE1HpqDI6ybuE0cFbqvKaabkPySWv0Fx1GJL/UGQQljMrPF/Cb7fEPNOrIPW4xhGIZhGIZhGIZhGIZhGIZhGIZhGIZhGIZhGIZhGIZhGIZhGIZhGIZhGIZhGIZh4gXA/wND0HsE7yyrAwAAAABJRU5ErkJggg==)
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(i) If system is stable, give ROC condition.
(ii) Find the impulse response.
(iii) Find system response if X(z) = 1/(1-0.2z-1)
(iv) Draw pole-zero diagram.
(i) If system is stable, give ROC condition.
(ii) Find the impulse response.
(iii) Find system response if X(z) = 1/(1-0.2z-1)
(iv) Draw pole-zero diagram.
10 M
7 (a)
Using suitable method obtain the state transition matrix for the system matrix
10 M
7 (b)
The transfer function of the system is given as
Obtain the state variable model.
Obtain the state variable model.
10 M
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