免疫调节数字信号处理(英文版)课后习题答案2

2021年1月20日发(作者：传达室)
(Partial) Solutions to Assignment 2

pp.73-76
1.16
In
each
of
the
following
systems,
let
or
be
the
input
and

or

be
the
output.
Determine
whether
each
systems
is
(1)
linear,
(2)
time
invariant,
(3)
causal,
(4)
BIBO
stable

(g).

(i).
ans: omitted
-------------------------------------- --------------
1.17 A linear time invariant system has impulse response
output sequence
(b)
(f)


(b) ans:

The z-transform of
h
[
n
]

is given by

where ROC1:


for each of the followign input signals:


Determine the


z-transform of
x
[
n
]

is given by


where ROC2:

Therefore, the z-transform of the output
h
[
n
]

is given by


Perform inverse z to get
y
[
n
]




(f) ans:

using the same method as in (b) (details omitted )
----------------------- -----------------------------
1.18.
A
linear
time
invariant
system
is
defined
by
the
difference
equation

b. Determine

the output
c.
Determine

the

of the system when the intpu is
output

ans: omitted

------------------- ---------------------------------
1.19 The following expressions define linear time invariant systems. For each one determine the
impulse respnose
(a)


of
the
system
when

the
input
is
(e)
(a) ans: the impulse response is


(e) ans: the impulse response is

------------------------------------------------- ---
1.20
Each
of
the
following
expressions
defines
a
linear
time
invariant
system.
For
each
one
determine whether it is BIBO stable or not
(g)

(k)



BIBO: Bounded input and bounded output


(g) ans: omitted
(k) ans: omitted
------------------------------------------------- ---
1.21. Using
the
geometric
series,
for
each
of
the
following
sequence
determine
the
z-transform
and its ROC
(d)

(g)
(i)
(d) ans:



where ROC:

(g) ans:


The first part is equal to


where ROC1 is


The second part is equal to


where ROC2 is

Therefore combining both parts:

where ROC={ROC1 and ROC2}:



(i) ans:


where ROC: whole complex domain
---------- ------------------------------------------
1.22.
You
know
what
the
and

are.
Using
the
properties only (do not reuse the definition of

the z-transform.) determine the z-transform of the
following signals
(c)
(g)