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Frequency Respnose
Amit Kulkarni
EC department
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Signal processing application
Wireless Sensor Networks (WSN)
Wireless : Communication part
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Sensor : Sensing and processing part
Networks : Information transfer over interconnectedsensor
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Collaborative processing By signal we understand 'something' that signifies
some occurrence of events of our interest. It may be
deterministic in nature or may not be. But it conveyssome information
Processing means understanding that signal, or to
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mo y rans orma on, se ec ve re en on asignal in order to extract the information that itcarries
Collaboration means co-operation or workingtogether . Hence, collaborative signal processingmeans to process the signals received by a group ofelements which are sensors in case of WSN.
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Why it is needed in Sensor Network? In case of WSN, the 'goal' is to detect, identify and
track any target.
Again sensors are powered by fixed energy sourceswhich are supplied at the time of network forming.So, 'limited power' is key factor here.
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In order to achieve a bigger goal, information mustbe shared.
Receiving, transmitting, and processing of data is to
be done with that limited power for a certain timeperiod
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Applications The goal of DSP is usually to measure, filter and/or
compress continuous real-world analog signals
Audio and Speech signal processing Sonar and radar signal processing,
Sensor array processing,
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pec ra es ma on, s a s ca s gna process ng, Digital image processing
Signal processing for communications,
Control of systems,
Biomedical signal processing,
Seismic data processing, etc.
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Signal modifications/operations Both in time and in frequency domain
1. Amplitude scaling
2. Shifting ( Delay or advancement)3. Time and frequency scaling ( compression or
expansion)
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4. eversa p ase s5. Convolution
6. Correlation
All the above operations can be done if we knowor understand the behavioral characteristics of asystems (frequency response)
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Signals and their respective spectra?
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Signal Type Spectrum
Continuous + Periodic Discrete + Aperiodic
Continuous + Aperiodic Continuous + Aperiodic
Discrete + Periodic Discrete + Periodic
Discrete + Aperiodic Continuous + Periodic
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What a spectrum means? Why ideal filters are impossible to realize?
Fourier spectra:
1. Amplitude Vs Frequency plot known as anam litude s ectrum
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2. Phase Vs Frequency Plot known as a phasespectrum
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Frequency Response Frequency response is the quantitative measure of
the output spectrum of a system or device in
response to a stimulus, and is used to characterizethe dynamics of the system.
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Frequency Response Plots The frequency response is characterized by the
magnitude of the system's response, typically
measured in dB or as a decimal, and the Phase,measured in radians or degrees, versus frequency inradians/sec or Hertz (Hz).
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Related Plots1. Bode Plot: by plotting the magnitude and phase
measurements on two rectangular plots as
functions of frequency
2. Nyquist Plot: by plotting the magnitude and phase
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angle on a single polar plot with frequency as aparameter
3. Nichols Plot: by plotting magnitude and phase on asingle rectangular plot with frequency as aparameter
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Tools to determine frequency response Practically using an oscilloscope, which is not that
accurate and it also difficult especially in the
presence of noise and non-linear distortions in theout-put.
Another method is Correlation that generally
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mu p es e ou -pu y e es s gna an enintegrates over a time duration lets say (-, ) insec.
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ESD and PSD
Since the correlation function for energy signal and
its CTFT are transform pairs also
The correlation function for ower si nal and its
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CTFT are transform pairs
So transform comes into picture such as CTFT,
Laplace Transform, and Z-transform.
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An LTI/LSI system
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A typical Responses
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Band Pass Filter
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One more example Quadrature Filter:
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Time Domain Frequency Domain
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A CT and DT exampleCT DT
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For this case Z-transform can helpby which we can fine H(Z) and bytaking inverse Z-transform we canfind h(n)
Now magnitude and phasecan be determined and can beplotted.
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The Response
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It is low-pass filter, an integrator, and a phase lag network
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Laplace Transform
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System Function or a well known Transfer Function
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Pole-Zero plot
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Significance of Poles an Zeros Zeros : Magnitude of a response
Poles : Time Variations
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AnswerFrequency Domain Time Domain
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But for physically realizable system h(t)must be causal, meansFrequency response of an ideal LPF
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Some research topicsFor real-signal processing for WSN
1. Distributed Signal Processing Techniques for
Wireless Sensor Networks2. Energy-Constrained Optimal Quantization for
Wireless Sensor Networks
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3. Ring-Based Optimal-Level Distributed WaveletTransform with Arbitrary Filter Length for WirelessSensor Networks
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