1. Prof. Virendra V. Dakhode Department of Computer Engineering SKNCOE Vadgaon Pune-41

2. What is DSP? The Breadth and Depth of DSP. Steven W. Smith
Sr. No
Name of Topics
Name of books
Referred
No of Lecture 1
What is DSP? The Breadth and Depth of DSP.
Steven W. Smith
Digital Signal Proc. 2
What is Signals ? Classification of signals
John Proakis 3
How signals is created?
ADC and DAC, sampling, 4
Statistics, probability and noise 5
Discrete time system
Properties of DT system 6
Mathematical model for representation of DT system 7
Linear system 8
Use of transducers in DSP

3. Digital signal processor
What is DSP
D-(Digital):-Digital generates store and process data in term of two state –ve and +ve. +ve is express as represent by 1 -ve is express as represent by 0 S-(Signal):- A signal is defined as any physical quantity that varies with time, space or any other independent variable or variable . P-(Processing):-To perform operation on data according to programmed instruction.
Digital signal processor
D to A Convertor
A to D convertor
Analog I/P signals
Analog o/P signals
Digital I/P signals
Digital o/P signals

4. Allied areas of DSP
Telecommunication (telephone conversion, telephone signals)
1. Multiplexing
2. Compression
3. Echo control
Audio Processing
1. Music
2. Speech recognition
3.Speech generation
Echo location
1. Radar (Radio detection & ranging)
2.Sonar (Sound navigation & ranging)
3. Reflection seismology

5. Image processing
1. Medical
2. Space
3. Commercial imaging product.

6. The Breadth and Depth of DSP
Space
Space photograph enhancement
Data compression
Intelligent sensory analysis by remote space probes
Medical
Diagnostic imaging (CT, MRI, ultrasound, and others)
Electrocardiogram analysis
Medical image storage/retrieval
Commercial
Image and sound compression
for multimedia presentation
Movie special effects
Video conference calling

7. Telephone
Voice and data compression
Echo reduction
Signal multiplexing
Filtering
Military
Radar
Sonar
Ordnance guidance
Secure communication
Industrial
Oil and mineral prospecting
Process monitoring & control
Non destructive testing
CAD and design tools

8. Scientific
Earthquake recording & analysis
Data acquisition
Spectral analysis
Simulation and modelling

9. What is signal
A signal is defined as a physical quantity that varies with time, space or any other independent variable
The signal may depend on one or more independent variable.
If a signal depends on only one variable then it is known as one dimensional signal.
Ex. AC power signal, speech signal ,ECG signal etc.
If a signal depends on two independent variable then the signal is known as two dimensional signals.
Ex. X-ray , sonograms.
Multi dimensional signal depends on many variables.

10. Classification of signals
Signals are classified according to their characteristics
Continuous time and discrete time signals
Deterministic and random
Periodic and non periodic signals
Even and odd signals
Energy and power signals
Causal and non causal signals

11. Continuous time signals
Continuous time signals are defined for all values of “t” and is represented by x(t) .
Continuous time signals is also called an analog signals.
Ex. AC power supply

12. Discrete time signals
The discrete time signals are defined at discrete instance of time and represented by x(n).
Ex. The amount deposited every month in a savings account is discrete.

13. Deterministic and random signals
A deterministic signal is a signal having certainty of values at any given instance of time. (In medical images like ECG)
A random signal is a signal having uncertainty before its actual occurrence.(noise, seismic signals)

14. Periodic and non-periodic signals
A continuous time signal is said to be periodic if it satisfies the condition
x(t + T) = x(t) for all “t”
A discrete time signal is said to be periodic if it satisfies the condition
x(n) = x (n + N) for all “N”

15. Symmetric (even) and anti- symmetric (odd)
A continuous time signal is said to be symmetric (even) if it satisfies the condition
x(-t) = x(t) for all “t”
A continuous time signal is said to be anti- symmetric (odd) if it satisfies the condition
x(-t) = - x(t) for all “t”

16. Energy and Power Signals
The total energy of a sequence of x[n] is defined by
An infinite length sequence with finite sample values may or may not have finite energy.
The average power of signal given by
Average power of an infinite length sequence may be finite or infinite.

17. Causal and non-causal Signals
A continuous time signal x(f) is said to be causal if
X(f)=0 for t<0
Other wise it is non causal
Discrete time signal is said to be causal if
X(n)=0 for n<0
Otherwise it is non casual

18. Statistics, probability and noise
Statistics and probability are used in DSP to characterize signals and processes that generate them.
The primary use of DSP is to avoid interference, noise and other undesirable components in the acquired data.
All these are produced as unavoidable by product of some DSP operation.
Statistics and probability allows these disruptive features to be measured and classified and to remove that offending components.

19. Mean and standard deviation
Mean indicated by μ=
In words sum the values in the signal
Where “i” is the index run from 0 to N-1 and then divide the sum by N.
This identical to the equation
In electronics, mean is commonly called the DC(direct current)
value the AC (alternating current) refers to now the signal fluctuate around the mean values.

20. Standard deviation It is denoted by In equation form it is given by
The term occurs frequently in statistics and given the name variance.
Standard deviation is a measure of how the away the signal fluctuate from the mean.
Variance represents the power of this fluctuation.
Mean describes what is being measured.
Standard deviation represents noise and other interference.

21. The histogram, PMF and PDF
The Histogram display the number of samples that are in the signal that have each of the possible values.
The sum of all values in the histogram is equal to the number of points in the signal
Where Hi is the signal
N is the number of points in signal
M is number of points in histogram
The histogram can be used to efficiency calculate the mean and std. Deviation of very large data sets.
This is especially important for image which can millions of samples.

22. Histogram groups samples together that have the same values.
Calculation of mean from histogram
Calculation of standard deviation from histogram
Limitation of histogram
Calculating mean and standard deviation is time consuming operations of addition and multiplication.
Histogram algorithm is uses only on few samples.

23. Probability mass function(PMF)
A histogram is always calculated using a finite numbers of samples while PMF is used with an infinite number of samples.
PMF is use for discrete signals.
PDF is use for continuous signals.

24. ADC and DAC
Analog to digital conversion (ADC) and digital to analog conversion (DAC) are the processes that allow the digital computers to interact with everyday signals.
Digital information is different form its continuous counterpart in two important respect it is sampled and quantized.

25. ADC (Analog to digital conversion)
The analog signal get convert into digital signal by performing following operation like Sampling, quantization and encoding.
Most of the analog signal in the form of continuous time signal but in digital signal processing the signal are sampled and quantized at discrete time instance and represented by 0 and 1.This can be done by analog to digital convertor.
Sampling: This is the conversion of a continuous time signal into discrete time signal.
Quantization: this is the conversion of a discrete time continuous valued signal into a discrete time discrete value signal(digital signal)
Encoding: In the coding process each discrete value represented by binary sequence.

26. ADC Fs=1/T Analog signal x(t) Discrete time signals x(n)
Quantized signal xq(n)
Digital signal
X[n]
Sampler
Quantizer
Encoder
Fs=1/T
X(n)=x(nT)
Analog signal
x(t)
Discrete time signal

27. Basic block diagram of DAC
To convert a digital signal into an analog signal A to D convertor is used.
In D to A convertor interpolation of samples performed.
In interpolation it connects successive samples with straight line segment
D to A converter involves a sub optimum interpolator followed by post filter.
Filter
Interpolator
Digital signal
analog signal
Basic block diagram of DAC

28. Discrete time system
Discrete time signals defined at discrete instance of time and represented as x(n).
Discrete time system is a device or algorithm that operates on a discrete time signals.
DT system processes a given input x[n] to generate an output response with more desirable properties.
In most of application discrete time system is a single input single output system.
Various types of discrete time systems are available science the digital computer such as systems used for digital control, robotices,data compression and image processing.
Discrete time system
Y[n] output signal
X[n] input signal

29. Basic properties of discrete time systems
Linearity
Time invariant
Causality
Static and dynamic system.
Linear system
The system is linear if and only if it satisfies superposition principal that is
If it does not satisfy above condition then system is said to be non linear

30. Time invariant
A system is said to be time invariant if its input output characteristics does not change with time
Suppose we have a system T in relax state which, when exited by an input signal x(n) produces an output signal y(n) i.e.
Suppose we delay the input signal by ‘k’ units i.e. X(n-k) then
If the time of system do not change with time the output of the system is same i.e. Y(n-k) then the system is said to be time invariant/shift invariant otherwise time variant system.

31. There fore, A relaxed system (time invariant ) Or shift invariant if and only if Implies that, For every input signal x(n) and every time shift k.

32. That is system is causal if it satisfy
Causal system
A system is said to be causal if the output of the system at any time n [i.e. y(n) depends only on present and past input i.e. X(n),x(n-1),x(n-2) ] and does not depends on future input that is [x(n+1),x(n+2) ] ,
That is system is causal if it satisfy
If the system does not satisfy this question then it is said to be non causal.

33. Both are said to be causal.
Static system
A discrete time system called static/memory less system if its output at any instant “n” depends at most on the same time , but not on past and future samples of the input otherwise system is said to be dynamic.
And
Both are said to be causal.

34. Mathematical model for representation of DT system
Linear constant coefficient difference equation
Difference equation describe a relationships between the input and output rather than an explicit expression for the system output as a function of its input.
A linear constant coefficient difference equation of order N looks like
All solution of y[n] can be expressed as a sum.
Equation 1 can be rewritten as

35. We need to know the input for all ‘n’ as well as a set of ‘N’ auxiliary condition such as
In order to be solve equation
Condition
An input x[n]=0 for leads to output y[n]=0 for
A causal input x[n]=0 for n<0 leads to a causal output y[n]=0
for n<0.

36. Linear convolution Consider unit step input x(n)=u(n) and filter
Filtering is the operation of convolving a signal with the filter impulse response.
Y(n)=0 , n<0
Y(0)=x(0).h(0)=1 (all other terms are zero)

37. Linear System
A signal is any physical quantity that carries information.
OR we can say signal is a description of how one parameter varies with anther parameter.
A system is any process that produces an output signal in response to an input signal.
Linearity : A system is called linear if it has two mathematical properties homogeneity and additive.
Or a system is said to be linear if it obeys superposition theorem.
Homogeneity: It means that a change in amplitude of input signal results in change in amplitude of output signal.
x[n]=y[n]
k x[n]=k y[n] where k is any constt.

38. Additive: A system is said to be additive if added signal pass through it without interfacing.
If x1[n] result in y1[n]
If x2[n] result in y2[n]
then
x1[n]+x2[n]=y1[n]+y2[n]
Examples of linear systems
Wave propagation: Electromagnetic waves
Electrical circuits: resister, capacitor, inductor.
Electronic circuits: Amplifiers and filters.
Unit system: Where output is equal to input signal.

39. Use of transducers in signal processing
Transducers defined as the device which convert one form of energy into other form.
The word transducer is a collective term used for both sensors and actuator.
Sensors which can be used to sense a wide range of different energy forms such as movement electrical signals, radiant energy, thermal energy.
Actuator used to switch voltage or current.
Example 1: Microphone converts sound waves into electrical signals for the amplifiers to amplify.
Example 2: Loudspeaker(output device) convert these electrical signals back into sound.

40. Output device loudspeaker
Controller/System
Amplifier
Input device
Microphone
Thermocouple used to produce an analog signal.
Light sensor used to produce digital signal.
Carbon microphone and piezo electric crystal are used to measure sound.
Thermister/thermostat are used to measure temperature and many more.