Department: Comm.& Electronics Eng,
th
Level: 4
Sheet ( 1 )
Fall 2020
MINISTRY OF HIGHER
EDUCATION
OCTOBER HIGH INSTITUTE
FOR ENGINEERING AND
TECHNOLOGY
Course Name:
Lecturer/
Digital Signal Processing
ELE 471
Dr/Ebtehal
Eng: Abdallah
Assignment #1
1.1. By using appropriate tests, check the filters characterized by the following equations for
time invariance, causality, and linearity:
(a) y(n)= 2x(n-g) where g>0
(b) y(n)= (n+3)x(n-3)
(c) y(n)= 5nx2 (n)
(d) y(n)= 3x(n+3)
(e) y(n)= x(n)sinwn
(f) y(n)= x2(n+1)e-nsinwn
1.2. Analyze the filter networks shown in fig.1,using the operator method.
x(nT)
T
y(nT)
+
T
-1/2
X
Figure 1.a
T
x(nT)
y(nT)
+
T
a1
-b1
X
+
X
a2
T
b2
X
+
X
Figure 1.b
1.3. (a) Find the impulse response of the filter in Fig.2 using the induction method. The filter
is initially relaxed, that is, y(nT) = 0 for n<0.
(b) find the unit-step response of the filter.
x(nT)
y(nT)
+
eα
T
X
Figure.2.
1.4. The filter shown in fig.3 is initially relaxed. Find the time-domain response using the
induction method for n=0,1,2,3,…,6 if
= ,
0,
≥ 0
ℎ Where w=π/6T and T=1.
x(nT)
T
T
+
3
X
r(nT)
m
X
T
Figure.3.
y(nT)
1.5. The unit-step response of a filter is
,
= 0,
≥ 0 < 0
(a) Using the convolution summation, find the unit ramp response.
(b) Check the filter for stability.