Deterministic and random signal analysis, Slides of Java Programming

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Digital Communication

Faculty of Science

Computer department

Deterministic and

random signal analysis

Outline

Important blocks in communication

systems

• Amplifiers
• (^) Noise
• (^) Signal power units
• Modulation

Deterministic and random signal

analysis

Bandpass and Lowpass Signal

Representation.

Amplifiers

Is the major block on transmitter and

receiver design of amplifier used is gain

governed by number of factors which

includes frequency, bandwidth, noise

allowed, type of transmitter and or

receiver.

• (^) An amplifier is an electronic device that

increases the voltage, current, or power of

a signal. Amplifiers are used

in wireless communications and broadcasting,

and in audio equipment of all kinds. They can

be categorized as either weak-signal

amplifiers or power amplifiers.

Noise

• (^) The signal is also contaminated along the path

by undesirable signals lumped under the

broad term noise which are random and

unpredictable signal it case external or

internal.

• External noise: it includes interface from

signals from transmitted on nearby channels,

man-made noise generated by faulty contact

switches for equipment, by automobile

ignition radiation, fluorescent lights, and

natural noise form lightning, electrical noise

can be minimized or even eliminated.

Signal Power Units

Decibel it defined ten times of

logarithm of two power level (to base

Power in Decibels = / dB

db is a ratio not absolute value: 3db

greater than one.

The power is proportional to square of the

amplitude, the amplitude ratio in decibel:

Amplitude in Decibels = dB

Decibel

P(out) P(in) P1/P2 dB

1 1 1 0

2 1 2 3

10 1 10 10

0.5 1 0.5 -

7.2 1.6 4.5 6.

100 1 100 20

1000 1 1000 30

Power in Decibels = / dB

Large variation in ratio can be expressed

reasonable scale

Bel: it is an earlier of power ratio and

equal to power of 10 to 1. or (1 Bel =

10 dB)

Watt and milliwatt decibel

dBm =

dBW =

Compare dBW to dBm, which is referenced to

one milliwatt (0.001 W).

A given dBW value expressed in dBm is always

30 more because 1 watt is 1,000 milliwatts, and

a ratio of 1,000 (in power) is 30 dB; e.g.,

10 dBm (10 mW) is equal to −20 dBW (0.01 W).

Example: calculate (a) dBm for 1 mW

signal (b) dBw for 1 mW signal and 1 W

signal

Solution:

a. 1 mW in dBm = = 0

b. 1 mW in dBW = =

(1W) in dBW = = 0 dBW

bit error rate ( BER )

The bit error rate ( BER ) is the

number of bit errors per unit time.

The bit error ratio (also BER ) is the

number of bit errors divided by the

total number of transferred bits

during a studied time interval. BER is

a unitless performance measure,

often expressed as a percentage.

Example

• As an example, assume this transmitted

bit sequence:

0 1 1 0 0 0 1 0 1 1

and the following received bit sequence:

0 0 1 0 1 0 1 0 0 1,

• The number of bit errors (the underlined

bits) is, in this case, 3. The BER is 3

incorrect bits divided by 10 transferred

bits, resulting in a BER of 0.3 or 30%.

Deterministic and random signal

analysis

• We describe deterministic signals and

events by analytical expressions for

all times (past, presence, future).

Thus, they are also predictable for

arbitrary times and can be reproduced

identically arbitrarily often.

• (^) They are not able to carry new

information (news), since everything

is already fixed (deterministic,

predetermined).

A deterministic signal is completely

specified at any instant of time t There

is no uncertainty about its value at t.

The transmitter employs deterministic

signals to carry random information.

When the receiver receives a

transmitted signal that has been

corrupted by noise (a random signal),

it attempts to detect the information

by stripping away the deterministic

signals.

• Random signals are also called non

deterministic signals are those signals

that take random values at any given

time and must be characterized

statistically.

• (^) Thermal noise generated random signal.
• (^) A deterministic signal can be

represented using mathematical

equations but random signals cannot be

represented using mathematical

equation.

Random signal

Random signal

• (^) Random signals (random variable, random

quantity, noise signal, probabilistic signal) cannot

be described as such in closed analytical form

(Supplement → Examples "Random Signal

Trajectories"). They originate from real events

with many unknown, non-ascertainable

influences. In most cases, the emergence of the

"random" signals is definitely deterministic but

the human perception and the instrumental

sensitivity make them appear as random in

connection with innumerable other events.