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
.
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
scalar values
. The following are statistics:
(sample mean)
(the data itself)
(order statistic)
(
,
)
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
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.
Must decide
vs.
.
Step 2
Collect data
Step 3
Formulate a useful statistic
If
, guess
. If
, guess
.
Estimation example
Suppose we take
measurements of a DC voltage
with a noisy voltmeter. We would
like to estimate
.
Step 1
Assume a Gaussian noise model
where
.
Step 2
Gather data
Step 3
Compute the sample mean,
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
I'm interested in biological psychology and cognitive psychology
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
it starts up serve and return practice/assessments.it helps find voice talking therapy also assessments through relaxed conversation.
miss
Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
Samuel
I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills
