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Frequency Respnose

Amit Kulkarni

EC department


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Signal processing application

Wireless Sensor Networks (WSN)

Wireless : Communication part

1/13/2012Amit Kulkarni

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


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.


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,


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)


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?


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


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


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


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


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


Band Pass Filter


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One more example Quadrature Filter:


Time Domain Frequency Domain


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A CT and DT exampleCT DT


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


It is low-pass filter, an integrator, and a phase lag network


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Laplace Transform


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


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


3. Ring-Based Optimal-Level Distributed WaveletTransform with Arbitrary Filter Length for WirelessSensor Networks


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