Determine and Sketch: The Even and Odd Parts of The Signals Depicted in Figures. Label Your Sketches Carefully

 

1

Determine and sketch the sketch  the even and odd parts of the signals depicted in Figures. Label yo your ur sketches carefully.

a)

 

b)

 

c)

 

d)

 

e)

 

2

components of  of the following signals: Determine the even and odd components

3

Determine whether the following signals are energy signals, power signals, or neither a) Calculate the value of E  for the signal  

Given

b)

 

 

  c)

 

d)

 

e)

f)

g)

 

4

sketch the first derivatives Find and sketch the derivatives of  of the following signals: a)

 b) c)

d)

5

Evaluate the following integrals:

6

Sketch and label each of the following signals a)

 

 

 b)

 

c) 7

Sketch the following signals:

8

a) y(-t+1) b) y(3t+1) c) y(4t-1) d) y(1-3t) e) y(t)δ(t) f) y(t) δ(t-3) g) y(t) δ(-t) h) y(t) δ(3t-5) Represent the signal interms of Step, Impulse and ramp whatever is appropriate.  

 

 

 

 

 

 

 

a)

c)

9

b)

 

d)

Considerr three systems with the following input-output relationships: Conside relationships:

 

 

10

Find the input-output relationship for the overall interconnected system. Is this system linear? Is it time invariant?  Consider the system as shown in Figure. Assume that y[n] that y[n] = 0 for n < 0.

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(a) Sketch the output when x[n] when x[n] = δ[n]. [n].   (b) Sketch the output when x[n] when  x[n] = u[n].  u[n].  Consider the capacitor shown in Figure. Let input x(t) i( t ) and output  y  y(( t ) v cc (t) (  t)

12

(a) Find the input-output relationship. (b) Determine whether the system is (i) memoryless, (ii) causal, ( i i i ) linear, (i v) tim ti me invariant, or (v) stable.  A system has the input-output relation given by

=

 

a)  y[n]  T { x[n]}    x  

 

2



=

x2 

2

 b)  y[n]  T  { x[n]}   x[n ]    

Determine whether system is linear/nonlinear? linear/ nonlinear? 13

14

Determine which of these properties hold and which do not hold for each of the following continuous-time systems. Justify your answers. In each example, example, y(t)  y(t) denotes the syst system em output and x(t) and x(t) is the system input. (1) Memoryless (2) Time invaria invariant nt (3) Linear (4) Causal (5) Stable

Discrete case:

 

  15

Find the input-output relationship