# Visualizations on Statistics and Signal Processing

Below you find a collection of widgets to illustrate key concepts in statistics and signal processing.

Bayes Theorem / Dependent Probabilities
A geometric interpretation of Bayes Theorem showing how dependent probabilties relate to each other. Gaußian Estimator
An interactive visusalization that shows how the parameters of a bivariate Gaußian Distribution can be estimated based on a given set of samples. Binary Hypothesis Test
An interactive visusalization that shows how an optimal binary classifier can be derived from two given hypothesis. Function applied to a Random Variable
An interactive example of a function applied to a random variable showing the resulting distribution. Fourier Cuboid
Interactive exploration of the dualities between signals and their corresponding Fourier Transform Complex exponential
Explore how the exponential function can be extended for complex numbers. Sum of two complex exponentials
Explore how the sum of two complex exponentials may result in a real valued Oscillation and how each of the complex exponentials influence the sum. Signal Transformer
Explore how a signal can be transformed by only delay and scaling. Signal Generator
Generate digital 2d signals by moving your mouse and explore the effect of applying and LTI filter. Time Frequency Analysis
A tool for understanding the trade-off between the time and frequency resolution when applying a filter to a signal. Beam Former
Explore how multiple microphones can be used to capture signals from different directions. Linear Quantization
Explore how quantization introduces noise and how the signal to noise ratio depends on the quantization strategy. LTI System impulse reponse
See how the the impulse reponse of a linear time-invariant system determindes the output signal for any input signal. 2D Convolution
See the effects of convolving a 2D image signal with a 2D kernel and applying element-wise non-linear functions Nyquist–Shannon sampling theorem
Explanation of how the minimum sample frequency results from from the convolution of the spectra. # Other Educational Tools

If you found the tools above helpful you might be interested in these other computer science related tools and visualizations.

Interactive Graph Algorithms
Explore Graph algorithms by watching them run step by step. Logic Expressions
Evaluate logical expressions and explore their syntax tree and truth tables. Karnaugh Map Editor
Optimize boolean expressions Binary Integer Encodings
Explore how integer numbers can be binary encoded in different ways 2D Convex Quadrilateral to Ellipse Conversion
Algorithm to fit an ellipse into a quadrilateral Simple Perspective Projection
3D->2D perspective projection Matrix Multiplication
See how two matrices are multiplied. Affine Transformation of Functions
Observe how the asymptotic growth of a function is not affected by affine transformations of their input or output. Marching Squares
See how the Marching Squares algorithm turns a continous shape into a polygon. Cocoa Scroll Physics
Cartoon physics implementation inspired by the iOS scroll view dynamics. Manual SVG ViewBox calculation
This is an experiment to transform coordinates from the viewport space into the local SVG space without using `svg.getScreenCTM()`. PID Controller
An experimental implementation of a PID controller to move an object in a 2D physics simulation. Levenshtein Distance
The Levenshtein Distance or edit distance measures the similarity between two sequences/strings Quantum Bit
See how a Qbit can be modelled as two complex numbers. Halfedge Data Structure
Educational implementation of a HDS to represent geometry meshes. # Bonus

Infinite Impulse Rhapsodie (IIR)
A complex exponential rap song. 