Tutorial 2
1. Evaluate the following discrete-time convolution sums:
(i) y[n] = u[n+3] * u[n-3]
(ii) y[n]= 3nu[-n+3] * u[n-2]
Tutorial 2
EKT 230 Signals & Systems
Tutorial 2
EKT 230 Signals & Systems
(iii) y[n] = (1/4)n u[n] * u[n+2]
(iv) y[n]= (-1)n * 2nu[-n+2]
2. Consider the discrete-time signals depicted in Figure 1(a), Figure 1(b) and Figure 1(c).
Evaluate the following convolution sums:
(a) m[n]= x[n] * y[n]
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Tutorial 2
(b) m[n]= x[n] * f[n]
Tutorial 2
EKT 230 Signals & Systems
Tutorial 2
(c) m[n]= y[n] * f[n]
Tutorial 2
EKT 230 Signals & Systems
Tutorial 2
Tutorial 2
EKT 230 Signals & Systems
Tutorial 2
EKT 230 Signals & Systems
Figure 1(a)
Figure 1(b)
Tutorial 2
Tutorial 2
EKT 230 Signals & Systems
Figure 1(c)
3. A linear time invariant system has an impulse response, h(t) and input signal, x(t). Use
convolution to find the response, y(t) for following signal:
Cross multiplication method
x[n]
h[n]
1
2
3
-1
-1
-2
-3
-1
-1
-2
-3
2
2
4
6
1
1
2
3
1
1
2
3
Ans : y[n] = [-1 -3 -3 2 9 5 3]
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Tutorial 2
EKT 230 Signals & Systems
h[-k]
x[k]
1
0
n=0
2
1
1
3
2
3
4
5
h[0-k]
1
-2
2
-1
0
-1
2
1
-3
1
1
-1
y[0] = -1
-3
-2
-1 0
-1
n=1
1
-1
y[1] = -2-1
= -3
h[1-k]
1
-3
2
1
-2
-1 0
1
-1
n=2
y[2] = -3-2+2
= -3
h[2-k]
1
-3
n=3
-1
2
1
-2
-1 0
1
-1
h[3-k]
1
-3
1
-2
2
-1 0
1
-1
n=4
-1
h[4-k]
1
-3
-2
1
y[4] = 6+2+1
=9
2
-1 0
-1
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y[3] = -3+4+1
=2
-1
1
-1
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EKT 230 Signals & Systems
h[k]
x[k]
1
0
n=5
2
1
3
2
3
4
6
-3
2
1
-2
-1 0
-1
y[5] = 3+2
=5
1
-1
h[6-k]
y[6] = 3
1
-3
2
1
-2
-1 0
1
-1
n=7
-1
y[7] = 0
h[7-k]
1
-3
-2
1
2
-1 0
-1
y[n]=[-1 -3 -3 2 9 5 3]
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7
h[5-k]
1
n=6
5
1
-1
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EKT 230 Signals & Systems
4. According to Figure 2(a), (b), (c), (d), evaluate the following convolution integral:
(a) m(t) = x(t) * y(t)
(b) m(t) = x(t) * z(t)
(c) m(t) = y(t) * w(t)
(d) m(t) = y(t) * z(t)
Figure 2 (a), (b), (c), (d)
ANSWER:
(a) m(t) = x(t) * y(t)
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Tutorial 2
(b) m(t) = x(t) * z(t)
Tutorial 2
EKT 230 Signals & Systems
Tutorial 2
(c) m(t) = y(t) * w(t)
(d) m(t) = y(t) * z(t)
Tutorial 2
EKT 230 Signals & Systems
Tutorial 2
Tutorial 2
EKT 230 Signals & Systems