Applied Signal Processing  Lecture 1
Digital Signal Processing:
Mathematical and algorithmic manipulation of
discretized and
quantized
or
naturally digital
signals in order to extract the most
relevant and pertinent information that is carried by the signal.
What is a signal?
What is a system?
What is processing?
Applied Signal Processing  Lecture 1
Examples of signals:
Applied Signal Processing  Lecture 1
Characterization of signals:
Continuous time
signals vs.
discrete time
signals
e.g. Temperature in the building at any time
Continuous valued
signals vs.
digital
signals
e.g. Amount of current drawn by a device; average exam grades
 Continuous time and continuous valued:
Analog signal
 Continuous time and discrete valued:
Quantized signal
 Discrete time and continuous valued:
Sampled signal
 Discrete time and discrete values:
Digital signal
(CD audio)
Realvalued
signals vs.
complexvalued
signals
Single channel
vs.
multichannel
signals
e.g. Blood pressure signal – 128 channel EEG
Deterministic
vs.
random
signal
Onedimensional
vs.
twodimensional
vs.
multidimensional
signals
Applied Signal Processing  Lecture 1
Applied Signal Processing  Lecture 1
 Any physical quantity that is represented as a function
of an independent variable is called a
signal
.
independent varables can be time, frequency, space etc.
 Every signal carries
information
. However, not all that
information is typically of interest to the user. The goal of
signal processing is to extract the
useful information
from the signal
 The part of the signal that is not useful is called
noise
.
Noise is not necessarily noisy. Any part of the signal we are not
interested in is by definition noise.
Applied Signal Processing  Lecture 1
Applied Signal Processing  Lecture 1
Sinusoids play a very important role in signal
processing, because
They are easy to generate
They are easy to work with; their mathematical properties
are well known
Most importantly: all signals can be written as a sum of
sinusoids, through Fourier transforms (later).
In continuous time:
Applied Signal Processing  Lecture 1
 A discretetime signal, commonly referred to as a
sequence
, is only defined at discrete time instances,
where
t
is defined to take integer values only.
 Discretetime signals may also be written as a sequence
of numbers inside braces:
{x[n]} = {..., 0.2,
2.2
, 1.1, 0.2, 3.7, 2.9, ...}
n indicates discrete time, in integer intervals, the boldface number
is at t=0.
Applied Signal Processing  Lecture 1
 Discretetime signals are often generated from
continuous time signals by
sampling
, which can roughly be
interpreted as quantizing the independent variable (time).
{x[n]} = x(nT
S
) =
x
t
∣
t=nT
S
n= ...,2,1,0,1,2,...
T
S
= Sampling interval/period
f
S
= 1/T
S
= Sampling frequency
Applied Signal Processing  Lecture 1
Applied Signal Processing  Lecture 1
Applied Signal Processing  Lecture 1
Applied Signal Processing  Lecture 1
Applied Signal Processing  Lecture 1
Applied Signal Processing  Lecture 1
Applied Signal Processing  Lecture 1
Applied Signal Processing  Lecture 1
Applied Signal Processing  Lecture 1
Applied Signal Processing  Lecture 1
Applied Signal Processing  Lecture 1
Applied Signal Processing  Lecture 1
Applied Signal Processing  Lecture 1
Applied Signal Processing  Lecture 1
Applied Signal Processing  Lecture 1
Applied Signal Processing  Lecture 1
Analysis of ECG Signals
Applied Signal Processing  Lecture 1
Analysis of seismic waves:
study the structure of the
soil by analyzing seismic
waves, wither natural (earthquakes,
volcanic eruptions) or manmade
(explosions etc.)
Useful e.g. for exploration of oil.
Depending on the material in
the soil the reflected waves have
different frequencies (modes).
Applied Signal Processing  Lecture 1
travel
time
Seismic signals as a function of position
Applied Signal Processing  Lecture 1
Dolby Noise Reduction Scheme
A Compressor
Applied Signal Processing  Lecture 1
Dolby Noise Reduction Scheme
Applied Signal Processing  Lecture 1
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