Metric spaces

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• Metric spaces
• Vectorial space, distance Pythagoras theorem
• Functional space, distance int f1(x) f2(x)ab

y
f1(x)
f2(x)
x
a
b
The functions that we will deal with belong to
functional metric spaces called Banach spaces
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Signals can be represented as sums of simple
functions (some times of infinite number of
terms)
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It is useful to define a series of functions
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Binomial distribution
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Dirac Delta function (density)
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A particularly popular methods for representin
signal is FREQUENCY
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Discrete representations
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Continuous representation Fourier transform
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Time and frequency are scaled In opposite ways
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The fourier transform of a gaussian is A nother
gaussian
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The importance of windowing
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Relationship Between cross correlation Function
and fourier transform
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