Engineering & CS 10 topics
Engineering & CS
Signal processing
10 topics 13 math concepts connects to 7 fields
Signal processing analyses, transforms, and synthesises signals. The Fourier transform is its central tool and connects it to astrophysics, quantum computing, cryptography, meteorology, and geophysics.
Topics in this field
Adaptive Filtering
Filters that update their coefficients online to minimize a cost function, enabling noise cancellation, echo suppression, and channel equalization.
linear algebra optimization random processes
Compressed Sensing
A framework for recovering sparse signals from far fewer measurements than classical sampling theory requires.
convex optimization linear algebra probability theory
Digital Filter Design
Methods for designing FIR and IIR digital filters to meet prescribed frequency-domain specifications.
fourier transform spectral analysis numerical methods
Fourier Transform
Decomposing any signal into its constituent frequencies. One of the most powerful tools in all of mathematics.
fourier transform linear algebra optimization
Kalman Filter
The optimal recursive estimator for linear Gaussian state-space models, fusing predictions with noisy observations.
linear algebra probability theory control theory
Matched Filter
The optimal linear filter for detecting a known signal in additive white Gaussian noise, maximizing output signal-to-noise ratio.
hypothesis testing probability theory spectral analysis
Nyquist-Shannon Sampling Theorem
The fundamental theorem establishing the minimum sampling rate required to perfectly reconstruct a bandlimited continuous signal.
fourier transform spectral analysis probability theory
Power Spectral Density
Describes how the power of a random signal is distributed across frequencies, estimated via periodogram and spectral averaging methods.
fourier transform random processes spectral analysis
Wavelet Transform
A time-frequency analysis tool that overcomes the fixed resolution of the STFT by using dilated and translated basis functions.
fourier transform spectral analysis wavelet transform
Z-Transform
The discrete-time counterpart to the Laplace transform, enabling algebraic analysis of digital filters and LTI systems.
spectral analysis fourier transform dynamical systems