Digital Signal Processing:

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Nov 24, 2013 (3 years and 9 months ago)

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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)‏


Real-valued
signals vs.
complex-valued
signals


Single channel
vs.
multi-channel
signals

e.g. Blood pressure signal – 128 channel EEG


Deterministic
vs.
random
signal


One-dimensional
vs.
two-dimensional
vs.
multi-dimensional
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 discrete-time signal, commonly referred to as a
sequence
, is only defined at discrete time instances,
where
t
is defined to take integer values only.
- Discrete-time 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 bold-face number
is at t=0.
Applied Signal Processing - Lecture 1
- Discrete-time 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 man-made
(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