Advanced Mathematical Methods In DSP

Catalog description

Analog-To-Digital and Digital-To-Analog Conversion, Digital Signals, Difference Equations and Filtering, Convolution and Filtering, Z-Transforms, Fourier Transforms and Filter Shape, Digital Signal Spectra. Mathematical Modeling using MATLAB is employed. Typically offered Fall. Prerequisite(s): (MA 16019 FOR LEVEL UG WITH MIN. GRADE OF D- OR MA 16300 FOR LEVEL UG WITH MIN. GRADE OF D-) AND MA 16021 FOR LEVEL UG WITH MIN. GRADE OF D- (MAY BE TAKEN CONCURRENTLY) Course Learning Outcomes 1. Sketch time domain responses when given various analog signals such as the step function, the ramp function, the exponent function, the sinusoidal function, the damped-sinusoidal function, and the impulse function. 2. Determine Laplace transform given various analog signals such as the step function, the ramp function, the exponential function, the sinusoidal function, the damped-sinusoidal function, and the impulse function. 3. Determine their inversed Laplace Transforms given Laplace transforms of the analog signals based on Laplace table or using the partial fraction expansion. 4. Analyze the circuit response to an input signal using Laplace transforms when given a circuit containing resistors, capacitors, and inductors in various series and parallel combinations. 5. Determine the Laplace transfer function of an analog system; and determine the impulse response, step response, sinusoidal response, steady-state frequency response, the pole-zero plot, and stability of the analog system. 6. Determine the Laplace transfer function that meets the filter specifications using Butterworth and Chebyshev functions when given a set of specifications for an analog filter. Realize the filter using active topologies like the Sallen-Key and Multi-feedback topologies. 7. Realize the filter using passive networks when given a set of specifications for an analog filter. 8. Develop the solutions, construct and demonstrate the working project; and document the design with a formal written report and/or an oral presentation in accordance with the given guidelines when given the practical project specifications such as audio equalizer, crossover, or ECG sensing. View Class Schedule