Chapter 1- Signals and Systems Classification.pptx

Signals and Systems
Classification
1
Sunday, 04 February 2024
Chapter 1

Classification of Signals
• Signals: Signals are variables that carry information
• Examples of signal include:
• Electrical signals
– Voltages and currents in a circuit
• Acoustic signals
– Acoustic pressure (sound) over time
• Mechanical signals
– Mass and spring movement
• Video signals
– Intensity level of a pixel (camera, video) over time
The existence of signal is having a very wide range, therefore, for better understanding
we need to classify the signals in various property/application based category
2

• Before going to classification of the signal few important points we need to revise:
• How is a Signal Represented?
 Mathematically, signals are represented as a function of one or more independent
variables.
For instance a black & white video signal intensity is dependent on 𝑥, 𝑦 coordinates
and time 𝑡, 𝑓(𝑥, 𝑦, 𝑡)
In this subject, we shall be exclusively concerned with signals that are a function of a
single variable: time 𝑡.
3
t
f(t)

4
1. Continuous & Discrete-Time Signals
• Continuous-Time Signals
• Most signals in the real world are continuous
time, as the scale is infinitesimally fine.
• Eg voltage, velocity,
• Denote by x(t), where the time interval may be
bounded (finite) or infinite
• Discrete-Time Signals
• Some real world and many digital signals are
discrete time, as they are sampled
• E.g. pixels, daily stock price (anything that a
digital computer processes)
• Denote by x[n], where n is an integer value that
varies discretely
• Sampled continuous signal
• 𝑥[𝑛] = 𝑥(𝑛𝑘) – 𝑘 is sample time
x(t)
t
x[n]
n
A CT signal is called a function.
A DT signal is called a sequence.

2. Analog and Digital Signals
• Analog Signals
• Human Voice – best example
• Ear recognises sounds 20KHz or less
• AM Radio – 535KHz to 1605KHz
• FM Radio – 88MHz to 108MHz
5

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Digital signals
• Represented by Square Wave
• All data represented by binary values
• Single Binary Digit – Bit
• Transmission of contiguous group of bits is a bit stream
• Not all decimal values can be represented by binary
1 0 1 0 1 0 1 0

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Analogue vs. Digital
Analogue Advantages
• Best suited for audio and video
• Consume less bandwidth
• Available world wide
• Less susceptible to noise
Digital Advantages
• Best for computer data
• Can be easily compressed
• Can be encrypted
• Equipment is more common and less
expensive
• Can provide better clarity
• Analog Message: continuous in amplitude
and over time
• AM, FM for voice sound
• Traditional TV for analog video
• First generation cellular phone (analog
mode)
• Record player
• Digital message: 0 or 1, or discrete value
• VCD, DVD
• 2G/3G cellular phone
• Data on your disk

8
Few other important point
• Analog to Digital conversion (ADC); Digital to Analog conversion (DAC)
• Gateway from the communication device to the channel
• Nyquist Sampling theorem
• From time domain: If the highest frequency in the signal is B Hz, the signal can be
reconstructed from its samples, taken at a rate not less than 2B samples per second
• Quantization
• From amplitude domain
• N bit quantization, L intervals L=2N
• Usually 8 to 16 bits
• Error Performance: Signal to noise ratio

9
Sampling
Quantizing
&
encoding
Continuous-time analog signal
Discrete-time analog signal
Discrete-time digital signal
0001

3. Deterministic and Non-deterministic Signals
• A signal is said to be deterministic if there is no uncertainty with respect to its value at any instant of
time. Or, signals which can be defined exactly by a mathematical formula are known as deterministic
signals.
• A signal is said to be non-deterministic if there is uncertainty with respect to its value at some instant
of time. Non-deterministic signals are random in nature hence they are called random signals. Random
signals cannot be described by a mathematical equation. They are modelled in probabilistic terms.
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 A causal signal is zero for t < 0 and an non-causal signal is zero
for t > 0
 Right- and left-sided signals
A right-sided signal is zero for t < T and a left-sided signal is zero
for t > T where T can be positive or negative.
Causal vs. Non-causal
Sunday, 04 February 2024 11

Bounded vs. Unbounded
 Every system is bounded, but meaningful signal is always
bounded

Energy and Power Signals
A signal is said to be energy signal when it has finite energy.
Energy 𝐸 = −∞
∞
𝑥2
(𝑡)𝑑𝑡
A signal is said to be power signal when it has finite power.
Power 𝑃 = lim
𝑇→∞
1
2𝑇 𝑇
−𝑇
𝑥2
𝑡 𝑑𝑡

Even vs. Odd
Even Signal

Odd Signals
Sunday, 04 February 2024 Abhishek Kumar, Assistant Professor, BIET Hyderabad 15

On the properties of the system we classify the system in different types

Memory System and Causal System

Concepts:
x(n): Present value of the input.
x(n-1): Past value of the input.
x(n+1): Future value of the input.
Y(n): Output of the system
1- Dynamic System: System that can depends on the present, past and future values of the input.
Example: y(n)=x(n+5) +x(2n).
2- Static System: System that can depends on present value of the input.
Example : y(n)= kx(n) +nx(n).
3- Causal System: System that can depends on the present and past values of the input
Example: y(n)=5x(n-2) +x(n).
4- Non-Causal System: System that can depends on the present and future values of the input.
Example: y(n)=3x(n) +kx(n+10).
5- Anti-Causal System: System that can depends only on the future values of the input.
Example: y(n)=kx(n+10).

Chapter 1- Signals and Systems Classification.pptx

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Chapter 1- Signals and Systems Classification.pptx