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ECE 401

Discrete-Time Signals and Systems

ECE 401-5 1

Engr. Marion Rey F. Abingosa

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ECE 401-5 2

Relate system input to system output.

Represent through block diagram any discrete time systems.

Interpret the different classifications of discrete time systems.

Analyze the interconnection of discrete time systems.

Intended Learning Outcomes

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ECE 401-5 3

Addition, Multiplication, and Scaling of Sequences

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ECE 401-5 4

Addition, Multiplication, and Scaling of Sequences

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ECE 401-5 5

Input-Output Description of Systems

Example: Draw the following block diagram

representation of the following signals.

a + +

b

c

() ( + ) ( )

( ) ( ) +( )

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Input-Output Description of Systems

Solution:

a + +

b

c

() ( + ) ( )

( ) ( ) +( )

z2

z-1

2

3

y(n)x(n)+

z2

z-4

3

2

y(n)x(n)+-

z-3 y(n)

x(n)+

2

z-2

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ECE 401-5 7

Input-Output Description of Systems

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ECE 401-5 8

Input-Output Description of Systems

Example: The input signal is

a

b

c

d

e

f

+

+ + +

+ , ,

=

+ + +

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ECE 401-5 9

Solution

a

b

c

+

, , , , , , , , , ,

Input-Output Description of Systems

, , , , , , , , , ,

, , , , , , , , , ,

, , , , , , , , , ,

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ECE 401-5 10

, , , , , , , , , ,

Input-Output Description of Systems

d + + + + +

+ +

, , , ,,, ,,,

,,,

e + , , , , , , , ,

. . . . . .

, , , , , , , , , , , ,

Solution (cont.)

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Input-Output Description of Systems

f

Solution (cont.) , , , , , , , , , ,

= + + +

This system is called an accumulator.

= + + +

+ + +

=

+ + + + + + + +

, , , , , , , , , ,

. . . . . .

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Input-Output Description of Systems

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Input-Output Description of Systems

+

< <

Sketch the block diagram representation of the discrete-time system

described by the input-output relation

Example:

Solution:

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ECE 401-5 14

Classification of Discrete-Time Systems

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ECE 401-5 15

Classification of Discrete-Time Systems

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ECE 401-5 16

Classification of Discrete-Time Systems

Time-invariant Systems:

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Classification of Discrete-Time Systems

Time-invariant Systems:

The system is time invariant if

, ( )

Step 1: Delay the input by units

, ( )

Step 2: Delay the output by

units

( )

Step 3: compare , ( )

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Classification of Discrete-Time Systems

Time-invariant Systems:

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Classification of Discrete-Time Systems

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Classification of Discrete-Time Systems

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Classification of Discrete-Time Systems

Example: Determine if the systems shown below

are time invariant or time variant

a + ( )

b ( ) ()

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Classification of Discrete-Time Systems

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ECE 401-5 23

Classification of Discrete-Time Systems

Linear Systems:

Step 1: Find the response of the system to the separate input signals and .

Step 2: Find the response of the system to a linear combination of and

.

+

Step 4: Compare the results of step 2 and step 3. If the same, then the

system is linear.

+

Step 3: Find the linear combination of and . +

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Classification of Discrete-Time Systems

a () [()] ()

b ()()

Examples of linear and nonlinear systems

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Classification of Discrete-Time Systems

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Classification of Discrete-Time Systems

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Classification of Discrete-Time Systems