L10-11+Notes

# Does a dirac delta function exist in real life how

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• Does a Dirac delta function exist in real life? How can we massage the definition and keep the mathematics consistent? • Give a formal mathematical model for digitizing a signal. (Hint: look at the sifting property , • What happens to the delta function if we change the scale of the abscissa?: δ ( ax ) 5. Convolution Filtering • Create a convolution filter to smooth a 1-D signal. A 2-D signal. Create one that will smooth even more. (p. 163) • Outline a simple algorithm to perform unsharp masking. Explain visually why unsharp masking works. • What is the concept of deconvolution? Is it really possible to reconstruct a signal? How? Key Concepts : 1. Linear Shift-Invariant Systems (LSIS) describe the behavior of electrical circuits and optical systems 2. Harmonic Signals can be represented with Complex Numbers, sines and cosines 3. Transfer Functions model the relationship between the input and the output of LSIS 4. Convolution is the math that describes the relationship between the input and the output of LSIS 5. Convolution can be represented in the continuous domain using the “superposition” integral 6. Convolution in the discrete domain is a “fold-shift-multiply-add” operation 7.

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