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Transforms. Types of Transforms. Translate Rotate Scale Shear. Affine Transform Math. Transforms are cumulative Transforms change the whole world view Order matters!. Rotate 90. Reflect X. Rotate 90. Reflect X. Making Shapes work together.

Transforms. A sine wave. 5*sin (2 4t). Amplitude = 5. Frequency = 4 Hz. seconds. A sine wave signal. 5*sin(2 4t). Amplitude = 5. Frequency = 4 Hz. Sampling rate = 256 samples/second. Sampling duration = 1 second. seconds. An undersampled signal. The Nyquist Frequency.

Fourier Transforms. Fourier transform for 1D images. A 1D image with N pixels is a vector of size N Every basis has N pixels There must be N basis elements n- th element of k- th basis in standard basis n- th element of k- th basis in Fourier basis. Fourier transform for 1D images.

Fourier transforms. Gaussian filter. 21x21, =0.5. 21x21, =1. 21x21, =3. Difference of Gaussians. 21x21, =3. 21x21, =1. Images have structure at various scales. Images have structure at various scales. Let’s formalize this!. A change of basis. Want to write image I as: Basis:

Laplace Transforms. 1. Standard notation in dynamics and control (shorthand notation) 2. Converts mathematics to algebraic operations 3. Advantageous for block diagram analysis. Chapter 3. Laplace Transform. Example 1:. Chapter 3. Usually define f(0) = 0 (e.g., the error).

Fourier Transforms. David Cooper Summer 2014. Signal Processing. The true value in loading data into MATLAB is the ability to manipulate it and further process your signal

Fourier Transforms. Fourier series. To go from f( ) to f( t ) substitute To deal with the first basis vector being of length 2 instead of , rewrite as. Fourier series. The coefficients become. Fourier series. Alternate forms where. Complex exponential notation. Euler’s formula.

Laplace Transforms. 1. Standard notation in dynamics and control (shorthand notation) 2. Converts mathematics to algebraic operations 3. Advantageous for block diagram analysis. Chapter 3. Laplace Transform. Example 1:. Chapter 3. Usually define f(0) = 0 (e.g., the error).

Laplace Transforms. Important analytical method for solving linear ordinary differential equations. - Application to nonlinear ODEs? Must linearize first. Laplace transforms play a key role in important process control concepts and techniques. - Examples: Transfer functions

Laplace Transforms. Math 2306 Dr. Dillon SPSU Mathematics Department. What Are Laplace Transforms?. A Laplace transform is a type of integral transform. Plug one function in. Get another function out. The new function is in a different domain. When. is the Laplace transform of. Write.