Docstoc

Signal Processing

Document Sample
Signal Processing Powered By Docstoc
					Thomas Dohaney
COT 4810

 SIGNAL PROCESSING
OVERVIEW
 Signal Processing Goals, Needs, Applications.
 What is a signal?
 Types of signals.
 Reasons to process signals.
 Analog to Digital conversion.
 Digital Filters.
 Time domain and frequency domain.
 Discrete Fourier Transforms and Fast Fourier
  Transforms and their properties.
 Image processing and Computer Vision.
SIGNAL PROCESSING
   An area in Computer Science that is unique by the
    type of data it uses, signals.
   Signals are sensory data from physical systems .
   Vibrations
   Visual images
   Voltage
   Sound
SIGNAL PROCESSING GOALS
   Signal Processing is
       Mathematics
       Algorithms
       Techniques
       To manipulate signals
   Lots of goals
       Enhancement of visual images
       Recognition and generation of speech
       Compression of data for storage and transmission
       Object detection
       Image enhancement
SIGNAL PROCESSING NEEDS
   1960s and 1970s
            computers first became available
     Digital
     Computers were expensive
     SP was limited to only a few critical applications.

   Pioneering efforts were made in four key areas.
     RADAR   and SONAR
     Oil Exploration
     Space Exploration
     Medical Imaging
SIGNAL PROCESSING TODAY

 Today SP driven
  by
 Commercial
  marketplace
 Need to transfer
  information
WHAT IS A SIGNAL?

 A signal is a function that conveys information,
  generally about the state or behavior of a
  physical system.
 Analog signals are continuous time, continuous
  amplitude.
 Digital signals are discrete time, discrete
  amplitude.
TIME DOMAIN AND FREQUENCY DOMAIN
   Many ways that information can be contained in a
    signal.
       Manmade signals.
       AM
       FM
       Single-sideband
       Pulse-code modulation
       Pulse-width modulation
   Only two ways that are common for information to be
    represented.
       Information represented in the time domain,
       Information represented in the frequency domain.
THE TIME DOMAIN
   Domain describes when something occurs
       What the amplitude of the occurrence was
   Each sample in the signal indicates
     What is happening at that instant, and the
     Level of the event
     If something occurs at time t, the signal directly
      provides information on the time it occurred, the
      duration, and the development over time.
   Contains information that is interpreted without
    reference to any other part of the sample.
THE FREQUENCY DOMAIN

 Frequency domain is considered indirect.
 Information is contained in the overall
  relationship between many points in the signal.
 By measuring the frequency, phase, and
  amplitude, information can be obtained about
  the system producing the motion.
CONVERTING ANALOG TO DIGITAL SIGNALS

 Converting continuous time, continuous
  amplitude
 To discrete time, discrete amplitude

 To convert to a digital signal we must sample it
  at a rate, so there is enough information to
  reconstruct it, and not leave any information
  out.
SIGNAL SAMPLING
   Why we convert the signal to digital form.
        Software implementations
        Accuracy can be controlled
        Repeatable
        Noise is minimal
        Operations are easier to implement
        Digital storage is cheap
        Security
        Price and performance
   Trade offs.
        Loss of information
        AD and DA conversion requires additional hardware
        Speed of processors is limited
        Round off errors
SIGNAL SAMPLING
   Nyquist sampling theorem.
   The lower bound of the rate at which we should sample
    a signal, in order to be guaranteed there is enough
    information to reconstruct the original signal is 2 times
    the maximum frequency.
   Now in its digital form,
    we can process the signal
    in some way.


                                                      .
TYPES OF SIGNALS.
 1-D signals.
 Sound and Vibrations.
 Signals used to extract statistical characteristics,
  and construct a mathematical model of the signal.
 Output signal is entered into the mathematical
  model, if only white noise is observed it is normal,
  it is abnormal if there is a lack of white noise.
 Typically used to diagnose a system in that they
  are used to detect abnormality and deterioration.
TYPES OF SIGNALS

 2-D signals.
 Considered to be an image signal.

 Signal is distorted in the digitizing process based
  on signal to noise ratio. (blur, movement,
  arithmetic, or color distortion).
 Typically to determine measurement of an object
  in an image, image restoration, visualization to
  extract physical information, pattern recognition,
  image inspection and fault detection.
TYPES OF SIGNALS

 3-D signals.
 Computer vision.

 Signal is obtained by visual sensor composed
  of many two dimensional images, or by
  measuring distance of an object (using
  electromagnetic wave, or laser) and adding this
  information to an object in a 2-d signal.
 Typically used in automation, remote sensing.
1-D SIGNALS
  Seismicvibrations
  EEG and EKG

  Speech

  Sonar

  Audio

  Music               ph - o - n - e -   t - i -   c   - ia -   n
2-D SIGNALS.
   Photographs

   Medical   images
   Radar

   IED detection
   Satellite data

   Fax

   Fingerprints
3-D SIGNALS.
   VideoSequences
   Motion Sensing

   Volumetric data sets
      Computed
       Tomography,
      Synthetic Aperture
       Radar Reconstruction)
WHY DO WE WANT TO PROCESS A SIGNAL?
   Compare a transmitted and reflected signal
      Find characteristics of a remote object
   Recognize what’s in a signal
      Target detection
      Speech recognition
      Image analysis
   Predict a future value of the signal
      Stock market prediction
   Interpolate missing values of a signal
      Conceal lost video packets
   Restore a signal that has been degraded
      Noise removal
      Echo cancellation
WHY DO WE WANT TO PROCESS A SIGNAL?

   Obtain a visual representation of a signal
      Extract information
   Enhance a signal
      Image contrast enhancement
   Compress a signal
      Faster transmission
      Less storage space
   Synthesize a realistic example of a signal
      Speech generation and synthesis
      Image texture generation
   Choose specific input signals to control a process
      Face detection
      Motion detection
TECHNIQUES FOR PROCESSING A SIGNAL
   A system is a function that produces an output signal in
    response to an input signal.
   An input signal can be broken down into a set of
    components, called an impulses.
   Impulses are passed through a system resulting in
    output components, which are synthesized into an
    output signal.
   Convolution is a way of combining two signals to form a
    third.
   Discrete Fourier Transforms
   Properties of Fourier Transforms
DISCRETE FOURIER TRANSFORM

 Given the time domain, the
  process of calculating the
  frequency domain is called
  DFT.
 Given frequency domain the
  process of calculating the
  time domain is inverse DFT.
 O(n2)
DISCRETE FOURIER TRANSFORM

   DFT for continuous signals, not for digital
    signals.          DFT




               Inverse DFT




                           Plug in angular
                           frequency f.




              DFT to get
              frequency.




             Inverse DFT to
             get time t.
DISCRETE F0URIER TRANSFORM

 Convert continuous DFT to discrete DFT.
 Continuous version

 Discrete version



 Let  stand for     (a primitive nth root of
  unity)
 We get
FAST FOURIER TRANSFORM

 The algorithm views the problem as computing
  a polynomial                   for  instead of k.
 The theory of polynomials says P(k) is found
  by the remainder of
 In FFT, For N = 23, finding the remainder for
  P(k) is done by…
FAST FOURIER TRANSFORM
              found by recursively using N/2 factors
  of
 For example N=23, then FFT of           is
                 *
 Then FFT of quotient above is


   Then FFT of quotient above is

   O(nlogn)
PROPERTIES OF FFT
 FFT can apply to 1-d, 2-d, multidimensional
  signals.
 Linearity
 Scaling
 Shifting
 Conjugation
 Convolution
 Differentiation
2-D CONVOLUTION
 Convolution is combining
  two signals to form a third.
 A delta function is a
  “normalized response
  (signal).”
 Example of an image
  convolved with a 3x3 delta
  function.
 Example of an image
  convolved with a 3x3
  impulse response.
MORE 2-D CONVOLUTION

 A is the impulse response
  padded with zeros.
 Output image C is the sum of
  the components of B
  convolved with A.
 Represents overlap between
  the two signals.
IMAGE PROCESSING IN COMPUTER VISION
                                                         Image can be classified as
                                    Input Image               a Night Image
   Algorithms
       Edge Detection
       Texture analysis
       Object recognition
        and image
        understanding

                                          Image can be classified as
                      Input Image               a Day Image
IMAGE PROCESSING IN COMPUTER VISION
   Algorithms
       Image segmentation
       Scale Invariance
       Object recognition and image
        understanding
       Face detection
QUESTIONS

 1) True or False, Discrete Fourier Transforms
  will transform one function in terms of another.
 2) List one instance of signal processing used
  in any field today.
REFERENCES
 BORES. Introduction to DSP.
  http://www.bores.com/courses/intro/index.htm
 Dewdney, A. K. The New Turing Omnibus. 2001.
  New York.
 Irwin, David J. Industrial Electronics Handbook.
 Smith, Steven W. The Scientist and Engineer’s
  Guide to Digital Signal Processing.
  http://www.dspguide.com/
 Wikipedia for some images.

				
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
views:4
posted:11/2/2011
language:English
pages:34