BME 171
SIGNALS AND SYSTEMS

1. Introduction to BME 171. Concepts related to linear systems and signal processing (analog and digital).

2. Analog and discrete signals. Singularity functions, their properties and applications. Periodic signals, complex representation of sinusoids. Amplitude and frequency modulation. Sampling. Sampling theorem, aliasing, folding, AD and DA conversion.

3. System analysis in the time domain. Impulse and step responses. Convolution, its physical interpretation and evaluation. Relation between impulse and step response, Duhammel's integrals.

4. Classification of signals: power and energy signals. Classification of systems: linear, stationary, causal systems. BIBO stability.

5. Exponential Fourier series. Physical interpretation and computation of Fourier coefficients. Signal reconstruction. Gibbs effect and smoothing by spectral windows. Parseval theorem and power of periodic signals.

6. Fourier transform. Properties of Fourier transform. System analysis with Fourier transform. Frequency response. Amplitude and phase spectra. Energy spectral density. Fourier transform of power signals. Discrete Fourier transform and Fast Fourier Transform.

7. Laplace transform. Properties of Laplace transform. System analysis with Laplace transform. Transfer function. Partial fractions expansion. Bode plots. Conditions for stability in terms of the location of poles.

8. FIR and IIR filters. Difference equations, impulse response and discrete convolution. Frequency response of FIR filters. z-Transform, transfer function of FIR and IIR filters. Relation between s-plane and z-plane.

Prerequisites: BME 153L (or equivalent) and MTH 107 or 111 (or equivalent).

Computer: Assignments require programming in Matlab. Previous experience with Matlab not required.

Grading: quizes: 40% ; homeworks: 40% ; in-class final: 20%