Chandra Shekhar Azad Institute Of Science & Technology
intro to pro
QW 231

Fall 2015
Tutorial No. 9 & 10
Signal & Systems (ELL205)
Laplace Transform
1.
Consider a stable and causal system with real impulse response h(t) and system
function H(s). It is known that H(s) is rational, one of its poles is at 1 + j, one of its zero is
at 3 +j,
Chandra Shekhar Azad Institute Of Science & Technology
intro to pro
QW 231

Fall 2015
Tutorial #1 and #2Signals and System EEL 205 N
1. Compute the values of P and Efo the signals a) x1(t) = e
x[n] = e j ( /2n + /8) d) x [n] = cos ( n /4)
ANS
a)
u(t), b) (1 / 2) n u [n], c)
2t 2
E  e
 d t 1/4, P 0

b)
2t
n 2
E  ( 1/2)  4/3
c) This
Chandra Shekhar Azad Institute Of Science & Technology
intro to pro
QW 231

Fall 2015
Tutorial #3 and #4
Signals and System ELL 205
1. Let x [n] = [n] + 2 [n  1]  [n  3] and h [n ] = 2 [n + 1] + 2 [n  1]
y [n] = x [n] * h [n] = h [n] * x [n]. That means we are looking for the output for a pulse
located in h[n] at nk = 1 or k = n+1 an
Chandra Shekhar Azad Institute Of Science & Technology
intro to pro
QW 231

Fall 2015
Tutorial Fourier Transform
Tutorial #5
1.
Evaluate the Fourier transforms of the following time functions:
(i)
2.
(t+1) + (t1)
d / dt cfw_ u (  2 t) + u ( t 2)
(ii)
Find the Fourier transform of the following periodic signals
a) Sin (2 t + /4)
3.
b) 1
Chandra Shekhar Azad Institute Of Science & Technology
intro to pro
QW 231

Fall 2015
1. Cnnaputc thc s‘alucs an'DD and Eat ﬁt: this signals a)x_1[:ﬂ= c J t u (t). b) [l .’
2) n 11[n].
H1151 n+ 1:3)
c)1s[n] =c (1)3[11] =cns (um’4}
2. Lct x[n] h: a signal with x[n] =0 for n:1 1 and n34. For the signals a} K [n—
3]: h) K [—11], c} a; [—n
Chandra Shekhar Azad Institute Of Science & Technology
intro to pro
QW 231

Fall 2015
Tutorial #7
Signals and System ELL 205
1. A discrete time periodic signal x[n] is real valued and has fundamental period N=5.
The non Fourier series coefficients for x[n] are: a0 = 2 , a2=a*2 = ej/4, a4 = a*4 =
2e j /3. Express x [n] Ao A sin ( n )
k
k
Chandra Shekhar Azad Institute Of Science & Technology
intro to pro
QW 231

Fall 2015
Tutorial #3 and #4
Signals and System ELL 205
1. Let x [n] = [n] + 2 [n  1]  [n  3] and h [n ] = 2 [n + 1] + 2 [n  1]
b) y3 [n] = x [n] * h [n+2]
2. Consider an input x[n] = n u [n] and a unit impulse response h [n] = u[n]. Find the
convolved output.
Chandra Shekhar Azad Institute Of Science & Technology
intro to pro
QW 231

Fall 2015
Tutorial #5 and #6
Signals and System ELL 205 N
1. A continuoustime real valued signal x(t) is real valued and has the fundamental
period T=8. the non zero Fourier series coefficients for x(t) are:
a1 = a1 = 2, a3 = a 3* = 4j
Express x(t) in the from: