2. UNIT I INTRODUCTION
Classification of systems: Continuous, discrete, linear, causal, stability, dynamic, recursive,time variance;
classification of signals: continuous and discrete, energy and power;mathematical representation of
signals; spectral density; sampling techniques, quantization,quantization error, Nyquist rate, aliasing
effect.
UNIT II DISCRETE TIME SYSTEM ANALYSIS
Z-transform and its properties, inverse z-transforms; difference equation –Solution by
ztransform,application to discrete systems - Stability analysis, frequency response –Convolution –
Discrete Time Fourier transform , magnitude and phase representation
UNIT III DISCRETE FOURIER TRANSFORM & COMPUTATION
Discrete Fourier Transform- properties, magnitude and phase representation -Computation of DFT using
FFT algorithm – DIT &DIF using radix 2 FFT – Bu
UNIT IV DESIGN OF DIGITAL FILTERS
Need and choice of windows – Linear phase characteristics. Analog filter design –Butterworth and
Chebyshev approximations; IIR Filters, digital design using impulse invariant and bilinear transformation
Warping, pre warping.
UNIT V DIGITAL SIGNAL PROCESSORS
Introduction – Architecture – Features – Addressing Formats – Functional modes -Introduction to
Commercial DS Processors
SYLLABUS
3. TEXT BOOKS:
1. J.G. Proakis and D.G. Manolakis, ‘Digital Signal Processing Principles, Algorithms and
Applications’, Pearson Education, New Delhi, PHI. 2003.
2. S.K. Mitra, ‘Digital Signal Processing – A Computer Based Approach’, McGraw Hill
Edu, 2013.
3. Lonnie C.Ludeman ,”Fundamentals of Digital Signal Processing”,Wiley,2013
REFERENCES
1. Poorna Chandra S, Sasikala. B ,Digital Signal Processing, Vijay Nicole/TMH,2013.
2. Robert Schilling & Sandra L.Harris, Introduction to Digital Signal Processing using
Matlab”, Cengage Learning,2014.
3. B.P.Lathi, ‘Principles of Signal Processing and Linear Systems’, Oxford University
Press, 2010 3. Taan S. ElAli, ‘Discrete Systems and Digital Signal Processing with
Mat Lab’, CRC Press, 2009.
4. SenM.kuo, woonseng…s.gan, “Digital Signal Processors, Architecture,
Implementations & Applications, Pearson,2013
5. DimitrisG.Manolakis, Vinay K. Ingle, applied Digital Signal
Processing,Cambridge,2012
4. Define signal
A signal is a description of how one parameter varies with another parameter.
For instance, voltage changing over time in an electronic circuit, or brightness
varying with distance in an image. A system is any process that produces
an output signal in response to an input signal.
5. Cont/.,
• flow of information
• measured quantity that varies with time (or position)
• electrical signal received from a transducer
• (microphone, thermometer, accelerometer, antenna,
etc.)
• electrical signal that controls a process
• Continuous-time signals: voltage, current, temperature,
speed, . . .
• Discrete-time signals: daily minimum/maximum
temperature,
6. Define Digital,Signal,Processing
&System
• Digital: In digital communication, we use discrete signals to represent data
using binary numbers.
• Signal: A signal is anything that carries some information. It’s a physical
quantity that conveys data and varies with time, space, or any other
independent variable. It can be in the time/frequency domain. It can be one-
dimensional or two-dimensional.
• Processing: The performing of operations on any data in accordance with
some protocol or instruction is known as processing.
• System: A system is a physical entity that is responsible for the processing.
It has the necessary hardware to perform the required arithmetic or logical
operations on a signal.
7. Difference between Analog and digital
signal
• Analog Signals
• The analog signals were used in many systems to produce signals to carry
information. These signals are continuous in both values and time. The use
of analog signals has been declined with the arrival of digital signals. In
short, to understand the analog signals – all signals that are natural or come
naturally are analog signals.
• Digital Signals
• Unlike analog signals, digital signals are not continuous, but signals are
discrete in value and time. These signals are represented by binary numbers
and consist of different voltage values.
9. Signal processing
Signals may have to be transformed in order to
Amplify or filter out embedded information
Detect patterns
Prepare the signal to survive a transmission channel
Prevent interference with other signals sharing a medium
Distortions contributed by a transmission channel
Compensate for sensor deficiencies
Find information encoded in a different domain
10. Digital signal processing
• Digital Signal Processing is the process of representing signals
in a discrete mathematical sequence of numbers and analyzing,
modifying, and extracting the information contained in the
signal by carrying out algorithmic operations and processing
on the signal
12. Digital signal processing
Advantages:
• noise is easy to control after initial quantization
• highly linear (within limited dynamic range)
• complex algorithms fit into a single chip
• flexibility, parameters can easily be varied in software
• digital processing is insensitive to component tolerances, aging,
• environmental conditions, electromagnetic interference
Applications:
• Communication systems
• Consumer electronics
• Music
• Medical diagnostics
• Aviation
13. Continuous Time (CT) Signals
• Most of the signals in the physical world are CT signals, since the time
scale is infinitesimally fine (e.g., voltage, pressure, temperature,
velocity).
• Often, the only way we can view these signals is through a transducer, a
device that converts a CT signal to an electrical signal.
• Common transducers are the ears, the eyes, the nose… but these are a
little complicated.
• Simpler transducers are voltmeters, microphones, and pressure sensors.
15. Discrete-Time (DT) Signals
• We can write a collection of numbers (1, -3, 7, 9) representing a
signal as a function of a discrete variable, n. x[n] represents the
amplitude, or value of the signal as a function of n, which takes
on integer values
• Many human-generated signals are discrete (e.g., MIDI codes,
stock market prices, digital images).
• In this course, we will show that most of the properties that apply
to CT signals apply in a similar manner to DT signals
25. Classification of Discrete-time
Systems
• Static and dynamic systems
• causal and non causal systems
• Linear and non linear systems
• Time in variant and time varying systems
• stable and unstable systems
• Invertible and non invertible systems
• FIR and IIR systems
26. • Memoryless systems: If the output of the system at an
instant n only depends on the input sample at that
time (and not on past or future samples) then the
system is called memoryless or static,
e.g. y(n)=ax(n)+bx2(n)
Otherwise, the system is said to be dynamic or to
have memory,
e.g. y(n)=x(n)−4x(n−2)
Static and dynamic systems
28. • In a causal system, the output at any time n only
depends on the present and past inputs.
• An example of a causal system:
y(n)=F[x(n),x(n−1),x(n− 2),...]
• All other systems are non-causal.
• A subset of non-causal system where the system
output, at any time n only depends on future inputs is
called anti-causal.
y(n)=F[x(n+1),x(n+2),...]
Causal vs. Non-causal Systems
30. • Unstable systems exhibit erratic and extreme
behavior. BIBO stable systems are those
producing a bounded output for every bounded
input:
Example:
i)y(n)=x(n2)---------stable
ii)y(n)=n.x(n)-------unstable
Stable vs. Unstable Systems
y
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32. • Example:
• Solution:
Example:
Linear vs. Non-linear Systems
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Useful Hint: In a linear system, zero input results in a zero
output!
34. • Time-invariant example: differentiator
• Time-variant example: modulator
Time-invariant vs. Time-variant Systems
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y(n-1)= x(n-1).Cos(w0.(n-1))
¹ y(n-1)
36. • LTI systems have two important characteristics:
– Time invariance: A system T is called time-invariant or shift-
invariant if input-output characteristics of the system do not
change with time
– Linearity: A system T is called linear iff
• Why do we care about LTI systems?
– Availability of a large collection of mathematical techniques
– Many practical systems are either LTI or can be approximated by LTI
systems.
Linear Time-Invariant (LTI) Systems
36
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T[ax1(n)+bx2(n)]=aT[x1(n)]+bT[x2 (n)]
37. Impulse Response of LTI Systems
h(n): the response of the LTI system to the input unit sample (n), i.e. h(n)=T((n))
An LTI system is completely characterized by a single impulse response h(n).
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Convolution
sum
37
Hossein Sameti, CE, SUT, Fall 1992
38. Sampling techniques
• There are three types of sampling techniques:
• Impulse sampling.
• Natural sampling.
• Flat Top sampling.
39. Quantization
• Quantization, in mathematics and digital signal
processing, is the process of mapping input values from
a large set (often a ontinuous set) to output values in a
(countable) smaller set, often with a finite number of
elements. Rounding and truncation are typical
examples of quantization processes
• Quantization error is the difference between the
analog signal and the closest available digital value at
each sampling instant from the A/D
converter. Quantization error also introduces noise,
called quantization noise, to the sample signal.
Editor's Notes
- If the processing is done offline, it is possible to use non-causal signals such as processing of images.
