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
A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
