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Digital signal processing

  • Digitalsampled, discrete-time, quantized
  • Signalwaveform, sequnce of measurements or observations
  • Processinganalyze, modify, filter, synthesize

Examples of digital signals

  • sampled speech waveform
  • "pixelized" image
  • Dow-Jones Index

Dsp applications

  • Filtering (noise reduction)
  • Pattern recognition (speech, faces, fingerprints)
  • Compression

A major difficulty

In many (perhaps most) DSP applications we don't have complete or perfect knowledge of the signals we wishto process. We are faced with many unknowns and uncertainties .

Examples

  • noisy measurements
  • unknown signal parameters
  • noisy system or environmental conditions
  • natural variability in the signals encountered

Functional magnetic resonance imaging

Challenges are measurement noise and intrinsic uncertainties in signal behavior.

How can we design signal processing algorithms in the face of such uncertainty?

Can we model the uncertainty and incorporate this model into the design process?

Statistical signal processing is the study of these questions.

Modeling uncertainty

The most widely accepted and commonly used approach to modeling uncertainty is Probability Theory (although other alternatives exist such as Fuzzy Logic).

Probability Theory models uncertainty by specifying the chance of observing certain signals.

Alternatively, one can view probability as specifying the degree to which we believe a signal reflects the true state of nature .

Examples of probabilistic models

  • errors in a measurement (due to an imprecise measuring device) modeled as realizations of a Gaussian randomvariable.
  • uncertainty in the phase of a sinusoidal signal modeled as a uniform random variable on 0 2 .
  • uncertainty in the number of photons stiking a CCD per unit time modeled as a Poisson random variable.

Statistical inference

A statistic is a function of observed data.

Suppose we observe N scalar values x 1 , , x N . The following are statistics:

  • x 1 N n 1 N x n (sample mean)
  • x 1 , , x N (the data itself)
  • x 1 x N (order statistic)
  • ( x 1 2 x 2 x 3 , x 1 x 3 )
A statistic cannot depend on unknown parameters .

Probability is used to model uncertainty.

Statistics are used to draw conclusions about probability models.

Probability models our uncertainty about signals we may observe.

Statistics reasons from the measured signal to the population of possible signals.

Statistical signal processing

  • Step 1

    Postulate a probability model (or models) that reasonably capture the uncertainties at hand
  • Step 2

    Collect data
  • Step 3

    Formulate statistics that allow us to interpret or understand our probability model(s)

In this class

The two major kinds of problems that we will study are detection and estimation . Most SSP problems fall under one of these two headings.

Detection theory

Given two (or more) probability models, which on best explains the signal?

Examples

  • Decode wireless comm signal into string of 0's and 1's
  • Pattern recognition
    • voice recognition
    • face recognition
    • handwritten character recognition
  • Anomaly detection
    • radar, sonar
    • irregular, heartbeat
    • gamma-ray burst in deep space

Estimation theory

If our probability model has free parameters, what are the best parameter settings to describe the signalwe've observed?

Examples

  • Noise reduction
  • Determine parameters of a sinusoid (phase, amplitude, frequency)
  • Adaptive filtering
    • track trajectories of space-craft
    • automatic control systems
    • channel equalization
  • Determine location of a submarine (sonar)
  • Seismology: estimate depth below ground of an oil deposit

Detection example

Suppose we observe N tosses of an unfair coin. We would like to decide which side the coin favors, heads or tails.

  • Step 1

    Assume each toss is a realization of a Bernoulli random variable. Heads p 1 Tails Must decide p 1 4 vs. p 3 4 .
  • Step 2

    Collect data x 1 , , x N x i 1 Heads x i 0 Tails
  • Step 3

    Formulate a useful statistic k n 1 N x n If k N 2 , guess p 1 4 . If k N 2 , guess p 3 4 .

Estimation example

Suppose we take N measurements of a DC voltage A with a noisy voltmeter. We would like to estimate A .

  • Step 1

    Assume a Gaussian noise model x n A w n where w n 0 1 .
  • Step 2

    Gather data x 1 , , x N
  • Step 3

    Compute the sample mean, A 1 N n 1 N x n and use this as an estimate.

In these examples ( and ), we solved detection and estimation problems using intuition and heuristics (in Step 3).

This course will focus on developing principled and mathematically rigorous approaches to detection and estimation,using the theoretical framework of probability and statistics.

Summary

  • DSPprocessing signals with computer algorithms.
  • SSPstatistical DSPprocessing in the presence of uncertainties and unknowns.

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
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Source:  OpenStax, Statistical signal processing. OpenStax CNX. Jun 14, 2004 Download for free at http://cnx.org/content/col10232/1.1
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