11. Find the CTFT for the following functions. Sketch and label the magnitude response of each...
need help all those questions. 10. Solve the following systems of linear differential equations: 11. Determine the Laplace transform of each of the following functions: (a) fe)-2t+1, 0StcI , 21 (b) f(t) te (c) f(t) = cos t cos 2t (Hint: Examine cos(a ± b).) Determine the inverse Laplace transform of each function: 12. (a) F(s) = 52 +9 is Demin 13. Determine L{kt cos kt + sin kt). 0, t< a 14. Determine L(cos 2t)U(t-r), where U(t-a)={ 15. Use...
4. Find the Nyquist rate for the following signals. For each case sketch the magnitude spectrum of the sampled signal if the sampling rate is 25% higher than the Nyquist rate. a.) ft)sinc E 2T 10 b.) h)=sinc 2T For all the following, use ft) given in part a.) c.) glt)= f(l-7) d.) c(t)- f)cos() 1 e.) x(t)= fit)+ _ sinc (t 4. Find the Nyquist rate for the following signals. For each case sketch the magnitude spectrum of the...
Hollie work #2 (Due April 1 δ) Problem Obtain the Laplace transform of each of the following functions: 2t (a) et cos 3tu(t) (c) e3 cosh 2tu(t) (e) te sin 2tu(t) (b) e2t sin 4tu(t) (d) e4 sinh tu(t) Problem 2. Find the Laplace transform of each of the following functions (b) 3f* e^ut) (c) 2n1(t)-4". δ(t) (e) 5u(t/2) (d) 2e) u(t) 2p-(t-1) (f) 6el3 u(t) d" dt" Problem 3. Find the Laplace transform of the following signals (a) f(t)-(2t...
2. Find the CTFT for the following PERIODIC signals: a. xdt) = sin(2t + π/4)) b. Xb(t) = 2 + cos(2π/3 t) + 4sin(5π/3 t)
2. Determine the CTFT of the following signals, then plot the magnitude spectrum (a) X(t) e2lt| (b) X(t) ea u(t), a > 0 (c) X(t) e4 (d) X(t) 6(t-3) 2. Determine the CTFT of the following signals, then plot the magnitude spectrum (a) X(t) e2lt| (b) X(t) ea u(t), a > 0 (c) X(t) e4 (d) X(t) 6(t-3)
2. Find the Laplace transform of the following functions (a) f(t)3t+4 (b) cos(2Tt) (c) sin(2t T) (d) sin(t) cos(t) "Use Trig. Identity" (e) f(t) te 2t use first shifting theorem
1) Sketch the graph of each of the following exponential functions. Make sure you label at least three points on the graph or include a t-chart with the coordinates. a. S(x)=3 b. y=213 c. g(x)= (3) 3 d. y e. f(x) = "+1
1. In each of the following piece-wise functions: (i) Sketch the graph of the given function, (ii) Express f(t) in terms of the unit step function uc(t) = u(t -c) where 0 u(t) = t<0 t> 0 and (iii) find the Laplace transform of f(t). (a) $(t) = { 2=(1-2), 0<t<2 t> 2 (b) f(t) = t, 2, 7-t, 0, 0<t <2 2 <t<5 5<t<7 t> 7
1. Using appropriate properties and the table of Fourier transforms, obtain and sketch the sin(at) Fourier transform of the signal x()cn(31-4 marks) 2fX(a), determine the Fourier transform of the signal y(t)dx( F.T. dx(2t) dt (3 marks) 3. Find the Fourier transform of x(t)-cos(2t/4). (3 marks) 4. Let x(t) be the input to a linear time-invariant system. The observed output is y(t) 4x(t 2). Find the transfer function H() of the system. Hence, obtain and sketch the unit-impulse response h(t) of...
1. Find the CTFT of the following signals 0 otherwise cos(40rt) sin(10Tt = e-10t (b) x(t) = ) ( c) x(t) u(t) + e10ta(-t + 1)