Glossary of Terms
Prompt
```linenums="0" Create a glossary of terms for a class on signal processing. Some terms will also have an abbreviation. The definitions should be precise, concise, distinct and non-circular. Return the results in a single raw markdown file in alphabetical order. The term name is in level 4 markdown heading. For each term use the following format:
Term (Abbreviation)
Text of the definition of the term.
Example: Example of use of the term in the course.
Fast Fourier Transform (FFT)
An efficient algorithm that computes the discrete Fourier transform (DFT) and its inverse, reducing the computational complexity. This transformation decomposes a time-domain signal into its constituent frequencies, enabling rapid analysis and processing of frequency components.
Example: We use the FFT to analyze audio signals by converting a time-domain recording into its frequency spectrum. This allows them to identify dominant frequencies, filter out noise, and visualize the signal's frequency content for applications such as music analysis or noise reduction.
Include definitions for the following terms:
Complex numbers Euler's formula Phasors Vectors Matrices Linear algebra Calculus Differential equations Integration Differentiation Probability Random variables Statistics Mean Variance Standard deviation Signals Systems Continuous-time signals Discrete-time signals Analog signals Digital signals Sampling Quantization Aliasing Nyquist theorem Convolution Impulse response LTI systems Causality Stability Frequency response Fourier series Fourier Transform (FT) Inverse Fourier Transform (IFT) Laplace Transform Z-Transform Discrete Fourier Transform (DFT) Fast Fourier Transform (FFT) Window functions Spectral analysis Time domain Frequency domain Signal decomposition Filtering Low-pass filter (LPF) High-pass filter (HPF) Band-pass filter (BPF) Band-stop filter (BSF) FIR filters IIR filters Filter design Bilinear transform Butterworth filter Chebyshev filter Elliptic filter Bessel filter Digital Signal Processing (DSP) Modulation Amplitude Modulation (AM) Frequency Modulation (FM) Phase Modulation (PM) Pulse-Code Modulation (PCM) Adaptive filtering Least Mean Squares (LMS) algorithm Recursive Least Squares (RLS) algorithm Noise cancellation Signal detection Autocorrelation Cross-correlation Power Spectral Density (PSD) Energy Spectral Density (ESD) Random processes Stationarity Ergodicity White noise Colored noise Signal estimation Kalman filter Wiener filter Time-frequency analysis Short-Time Fourier Transform (STFT) Spectrogram Wavelet Transform (WT) Continuous Wavelet Transform (CWT) Discrete Wavelet Transform (DWT) Multiresolution analysis Signal compression Lossless compression Lossy compression Huffman coding Entropy coding Quantization noise Sampling rate conversion Interpolation Decimation Multirate signal processing Polyphase filters Filter banks Subband coding Oversampling Undersampling Compressed sensing Sparse representation Machine Learning (ML) Supervised learning Unsupervised learning Feature extraction Pattern recognition Classification Regression Neural Networks (NN) Deep Learning (DL) Convolutional Neural Networks (CNNs) Recurrent Neural Networks (RNNs) Autoencoders Generative Adversarial Networks (GANs) Signal reconstruction Signal prediction Digital communications Modulation schemes Digital modulation Quadrature Amplitude Modulation (QAM) Phase Shift Keying (PSK) Frequency Shift Keying (FSK) Orthogonal Frequency Division Multiplexing (OFDM) Channel coding Error detection Error correction Communications signal processing Radar signal processing Sonar signal processing Image processing Edge detection Image filtering Image segmentation Audio signal processing Speech recognition Speech synthesis Voice over IP (VoIP) Multimedia signal processing Virtual Reality (VR) Augmented Reality (AR) Cognitive signal processing Quantum signal processing Biosignal processing Brain-Computer Interfaces (BCI) Internet of Things (IoT) Big data analytics Ethical considerations in AI