SIGNAL AND SYSTEMQuestion bank

Q:1 Determine following signals are periodic or not. (i) x(t)=10 Sin(200t)-3cos(350t) (ii) x[n]=Cos(10n)Cos(10n)Q:2 Find energy of the following signal. X(t)=Cos(10t )U(t) U(t-2) Q:3 Draw even and odd parts of X(n)=U(n).Q:4 Determine whether the following signals are linear or non-linear. (i) y[n]=x[n2] (ii) y[n]=x2[n]Q:5 Determine and sketch the following for given fig. (i) d/dtX(t) (ii) X(-t) (iii) (-t+2) (iv) X (2t-3)

Q:6 Draw the x(2t-1) and x(4-t/3) from following signal.Q:7 Determine whether the following signals are periodic or not,if signal is periodic then find out its fundamental period.(i) X(n)= Sin (6n/7) (ii) X(n)=Sin(n/8)

Q:8 Show that [n]=U[n]-U[n-1] . Q:9 Determine following signals are periodic or not. (i) x(t)=10 Sin(200t)-3cos(350t) (ii) x[n]=Cos(10n)Cos(10n).Q:10 Find energy of the following signal. x(t)=Cos(10t )U(t) U(t-2)Q11 Determine Laplace transform of the following signals: (i) x(t)=t Sin(t) (ii) x(t)=eat Cos(bt-1)u(bt-1)

Q12 If Laplace transform of x(t) is s+2/(s2 +4s+5) determine Laplace transform of y(t)=x(2t-1)U(2t-1)Q13 Use the convolution theorem of Laplace transform, find y(t)=x1(t)*x2(t), if x1(t)=e-3tu(t) and x2(t)=u(t-2)Q14 Find the inverse Laplace transform of G(s)=10s e-s/(s+1) (s+3)Q15 Determine the unit step response of the system described by the difference equation, y[n]=0.9y[n-1]-0.81y[n-2]+x[n] if y(-1)=y(-2)=0Q16 Determine the Z-transform of following sequences with ROC (i) u[n] (ii) u[-n-1] (iii) x[n]=an u[n]- bn u[-n-1]Q17 Find the convolution of the sequences using z-transform: x1[n]=[1,2,0], x2[n]=[2,2,2]Q18 Using the Z-transform method, solve the difference equation y[n+2]-3/2y[n+1]+1/2y[n]=(1/4)n; for n>0 with initial conditions y(0)=10 and y(1)=4Q19 Determine the Z-transform of following sequences with ROC (i) x[n]=[3(4/5)n-(2/3)2n]u[n] (ii) x[n]=2nu[n+2]-3nu[-n]Q20 Explain the properties of region of convergence Q21 Find and plot the amplitude and phase spectra of the signal x(t)= Ae(-t/T) u(t) where A and T are real-valued constants.Q22 Find the F.T. of x(t)= cost ; -.5