This module offers an introduction to Bayesian networks by means of a worked example of computing a bayesian network from a joint probability distribution (JPD).
This module describes the circular convolution algorithm and an alternative algorithm
A brief explanation of calculation complexity and how the complexity of the discrete Fourier transform is order N squared.
The discrete Fourier transform (DFT) and its inverse (IDFT) are the Primary numerical transforms relating time and frequency in digital signal processing. The DFT has a number of important properties relating time and frequency, including shift, circular convolution, multiplication, time-reversal and conjugation properties, as well as Parseval's theorem equating time and frequency energy.
This module will take the ideas of sampling CT signals further by examining how such operations can be performed in the frequency domain and by using a computer.
The course treats: the discrete Fourier Transform (DFT), the Fast Fourier Transform (FFT), their application in OFDM and DSL; elements of estimation theory and their application in communications; linear prediction, parametric methods, the Yule-Walker equations, the Levinson algorithm, the Schur algorithm; detection and estimation filters; non-parametric estimation; selective filtering, application to beamforming.
This course was developed in 1987 by the MIT Center for Advanced Engineering Studies. It was designed as a distance-education course for engineers and scientists in the workplace. Advances in integrated circuit technology have had a major impact on the technical areas to which digital signal processing techniques and hardware are being applied. A thorough understanding of digital signal processing fundamentals and techniques is essential for anyone whose work is concerned with signal processing applications. Digital Signal Processing begins with a discussion of the analysis and representation of discrete-time signal systems, including discrete-time convolution, difference equations, the z-transform, and the discrete-time Fourier transform. Emphasis is placed on the similarities and distinctions between discrete-time. The course proceeds to cover digital network and nonrecursive (finite impulse response) digital filters. Digital Signal Processing concludes with digital filter design and a discussion of the fast Fourier transform algorithm for computation of the discrete Fourier transform.
The Fourier transform can be computed in discrete-time despite the complications caused by a finite signal and continuous frequency.
The Fourier transform can be computed in discrete-time despite the complications caused by a finite signal and continuous frequency.
How to compute spectra using DFT.
Average stock price as an example of discrete-time filtering.
Definitions and basic algorithms for Fourier analysis for discrete-time signals.
Representation, analysis, and design of discrete time signals and systems. Review of Z-transforms, discrete-time Fourier transforms, and difference equations. Discrete-time processing of continuous-time signals. Decimation, interpolation, and sampling rate conversion. Flowgraph structures for DT systems. Time-and frequency-domain design techniques for recursive (IIR) and non-recursive (FIR) filters. Linear prediction. Discrete Fourier transform, FFT algorithm. Short-time Fourier analysis and filter banks. Multirate techniques. Hilbert transforms, Cepstral analysis, various applications.
The DFT can be reduced from exponential time with the Fast Fourier Transform algorithm.
Investigation of different aspects of filtering in the frequency domain, particularly the use of discrete Fourier transforms.
The ideas of using the DFT to filter a signal and recover a signal from a noisy transmission are addressed based on the ideas of the DFT and convolution.
You will investigate the effects of windowing and zero-padding on the Discrete Fourier Transform of a signal, as well as the effects of data-set quantities and weighting windows used in Power Spectral Density estimation.
Review of linear algebra, applications to networks, structures, and estimation, Lagrange multipliers, differential equations of equilibrium, Laplace's equation and potential flow, boundary-value problems, minimum principles and calculus of variations, Fourier series, discrete Fourier transform, convolution, applications.
This module looks at writing our DTFS equations in matrix form to make calculations and displaying the basis easier.
Two algorithms to detect the fundamental frequency of a signal: one in the time domain (Autocorrelation) and one in the frequency domain (Harmonic Product Spectrum / HPS)
