DSP for Dummies aka

1
DSP for Dummiesaka
How to turn this (actual raw sonar trace)
Into this .. (filtered sonar data)
2
Fundamental property of all analog signals
properties
amplitude
Decompose into summation of sinusoids
phase
frequency
3
Fourier Transform
How do we analyze the frequency components of a
complex signal
Time space x(t)
Frequency space X(w)
single frequency signal w0
w
t
w0
t
w
Some properties

• X(w) is complex -- complex conjugate encodes
  phase
• Fourier transform is invertable

4
Digital Signals
Sample amplitude at discrete time intervals
1,0
.55
.46
-,6
-1.0
Nyquist limit (http//www.medcyclopaedia.com) (H
arry Nyquist, 18891976, Swedish - American
physicist), the maximum frequency of a signal
that can be measured with a method that employs
sampling of the signal with a specific frequency,
the sampling frequency. According to Shannons
sampling theorem, a signal must be sampled with a
frequency at least twice the frequency of the
signal itself. The maximum measurable frequency
the Nyquist limit or frequency is thus half the
sampling frequency. If the signal frequency is
higher than the Nyquist limit, aliasing occurs.
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Discrete Fourier Transform
Given a signal represented as a time sequence of
samples, the DFT gives us a seqence of
frequency/phase amplitudes
1,0
.55
.46
w
w0
-,6
-1.0
w
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Signals and noise

• What is noise?
• Any signal other than the one you are interested
  in!
• Sources of Noise (the usual suspects)
• statistical signals from active electronic
  components
• crosstalk from other channels or other signals
  in the same channel
• signals sensed from external sources (power
  supply, EM radiation)

Trival Example
Signal to Noise ratio The relative amplitude of
the signal of interest o the noise signal
Signal of interest
Noise signal
Noisey Signal
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Filtering out the Noise
Finite Impulse response (FIR) filter
Ideal Pulse (time domain)
Ideal Pulse (frequency domain)
Zero rise/fall time
to inifinity
to inifinity
w
t
Ideal Pulse (time domain)
actual rise/fall time
finite band of component frequencies
w
The number and values of the component freqencies
is related to the rise/fall time of the pulse
http//www.chem.uoa.gr/Applets/AppletFourAnal/Appl
_FourAnal2.html
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How a filter works
FFT
w
?signal
?noise
minus
w
?noise
FFT-1
w
?signal