An introduction to 2D circular convolution.
A binary ASK transmitter and receiver is designed to transmit digital information over a "speaker-air-microphone" (SAM) channel. Listening to the channel while making parameter adjustments and viewing plots builds additional insights into the ASK modulation scheme. This project describes the various tradeoffs affecting bandwidth and information rate and provides an application for the pulse shapping transmit filter.
Conclusion of determining room inpulse responses and deconvolving the response out of a recorded signal.
Convolution is a concept that extends to all systems that are both linear and time-invariant (LTI). It will become apparent in this discussion that this condition is necessary by demonstrating how linearity and time-invariance give rise to convolution.
Comparison of deconvolved recorded signal and input. We also compare the theoretical and actual impulse responses.
You will implement a fourth-order, elliptical, low-pass infinite impulse-response (IIR) filter as a cascade of two second-order sections.
You will implement a fourth-order, elliptical, low-pass infinite impulse-response (IIR) filter as a cascade of two second-order sections.
You will implement a fourth-order, elliptical, low-pass infinite impulse-response (IIR) filter as a cascade of two second-order sections.
You will derive the transfer function of a second-order, Direct Form II, infinite impulse response (IIR) filter. Then you will create a fourth-order IIR filter, plot its frequency response, and decompose the fourth-order filter into two second-order sections, choosing an appropriate gain for each stage to prevent overflow.
You will derive the transfer function of a second-order, Direct Form II, infinite impulse response (IIR) filter. Then you will create a fourth-order IIR filter, plot its frequency response, and decompose the fourth-order filter into two second-order sections, choosing an appropriate gain for each stage to prevent overflow.
Infinite impulse response (IIR) filters are an alternative to finite impulse response (FIR) filters. Often, an IIR implementation can meet a given filter specification with less computation than an FIR implementation, but IIR filters induce nonlinear phase
Introduction to the impulse response of a linear system.
An introduction to the impulse response of an LTI system.
Background information regarding the recreation of sound using deconvolution.
Partial differential equations (PDEs) describe the relationships among the derivatives of an unknown function with respect to different independent variables, such as time and position. Experiment and observation provide information about the connections between rates of change of an important quantity, such as heat, with respect to different variables. Upon successful completion of this course, the student will be able to: State the heat, wave, Laplace, and Poisson equations and explain their physical origins; Define harmonic functions; State and justify the maximum principle for harmonic functions; State the mean value property for harmonic functions; Define linear operators and identify linear operations; Identify and classify linear PDEs; Identify homogeneous PDEs and evolution equations; Relate solving homogeneous linear PDEs to finding kernels of linear operators; Define boundary value problem and identify boundary conditions as periodic, Dirichlet, Neumann, or Robin (mixed); Explain physical significance of boundary conditions; Show uniqueness of solutions to the heat, wave, Laplace and Poisson equations with various boundary conditions; Define well-posedness; Define, characterize, and use inner products; Define the space of L2 functions, state its key properties, and identify L2 functions; Define orthogonality and orthonormal basis and show the orthogonality of certain trigonometric functions; Distinguish between pointwise, uniform, and L2 convergence and show convergence of Fourier series; Define Fourier series on [0,pi] and [0,L] and identify sufficient conditions for their convergence and uniqueness; Compute Fourier coefficients and construct Fourier series; Use the method of characteristics to solve linear and nonlinear first-order wave equations; Solve the one-dimensional wave equation using d'Alembert's formula; Use similarity methods to solve PDEs; Solve the heat, wave, Laplace, and Poisson equations using separation of variables and apply boundary conditions; Define the delta function and apply ideas from calculus and Fourier series to generalized functions; Derive Green's representation formula; Use Green's functions to solve the Poisson equation on the unit disk; Define the Fourier transform; Derive basic properties of the Fourier transform of a function, such as its relationship to the Fourier transform of the derivative; Show that the inverse Fourier transform of a product is a convolution; Compute Fourier transforms of functions; Use the Fourier transform to solve the heat and wave equations on unbounded domains. (Mathematics 222)
This section lists the key results of our projects and some final conclusions.
Infinite impulse response (IIR) filters are an alternative to finite impulse response (FIR) filters. Often, an IIR implementation can meet a given filter specification with less computation than an FIR implementation, but IIR filters induce nonlinear phase
Theory behind deconvolution of recorded sound to reproduce an input.
ELEC 301 project by William Howison, Chris Lamontagne, Bryce Luna, and David Newell. Given the output of a system and the system characteristics we can determine the input. We will determine the system characteristics of two rooms by playing an (approximate) impulse and recording the impulse response, and then we will play music into the same rooms and record the output. Using MATLAB we will deconvolve the output with the system response to determine a rough approximation of the input.
Conclusion of determining room inpulse responses and deconvolving the response out of a recorded signal.
