Introduction (2 hours)
	integral transforms (e.g. Fourier, Radon, ...)
	sound and waves
	basis functions (transforms as a change of basis)

Continuous time Fourier Transform (2 hours)
	basics: simple functions, signal terminology (e.g. power)
	Fourier series recap
	transform properties
	examples
	convolution (continuous)

Discrete time Fourier Transform (DFT) (4 hours)
	direct measurement of spectra
	discrete data (Moore's law)
	   sampling (time, and quantization effects, aliains, Nyquist)
	DFT and its properties
	Discrete signal transforms: padding, and packing, upsampling
	2D signals and transforms
	applications: 
	   compression
	   steganography (digital watermarks)

Filters and linear systems (4 hours)
	terminology (FIR, IIR, high-pass, low-pass)
	filters and the Convolution Theorem
	z-transforms
	Gibb's phenomena
	ARMA filters
	application: noise reduction, anomaly detection
	block diagrams and linear systems
	2D filters and image processing
	application: tomography
	   backprojection algorithm
	   Radon transform	
	FT and its relationship to linear systems

Theory and algorithms (2 hours)
	Fast Fourier Transform (FFT)
	Random process
          white and filtered noise
          spectral density and autocovariance
        Parceval, Rayleigh and Plancheral theorems
          generalized Fourier transform

Windowing (2 hours)
        leakage and windows
	transient signals (e.g. chirps)
	uncertainty principle
	short time Fourier Transform (and spectrogram)
	regularity, compactness and decay

Wavelets and multiresolution analysis (4 hours)
	Gabor functions and transform
	wavelets as sub-band filters
	multiresolution approximation
	pyramidal decomposition algorithm
	2D wavelets
	Applications: fingerprint compression, tonebursts, edge detection

Optional material (primarily for masters students)		      
	wavelets for the analysis of 1/f noise and self-similarity
	irregular sampling
	lifting schemes, basis pursuit, and other generalizations

The Laplace transform are ommitted, as most students are typically
familiar with this. PGFs are discussed in conjunction with
z-transforms. Laplace- and Fourier-Stietjes transforms are also
ommitted.