Signals & Systems

What you'll learn

• Classify signals as continuous- or discrete-time, periodic, even or odd, and energy or power signals, and apply shifting, reversal and scaling to the time variable.
• Test systems for memory, causality, linearity, time invariance, stability and invertibility, and explain why LTI systems are described by their impulse responses.
• Compute discrete-time convolution by flip-and-slide and by code, and read causality, stability and step response from an impulse response.
• Set up and evaluate continuous-time convolution integrals, including the response of an RC filter, and relate step and impulse responses.
• Solve linear constant-coefficient differential and difference equations, separate zero-input and zero-state responses, and implement first-order digital filters.
• Find Fourier series coefficients of periodic signals, use symmetry and Parseval's relation, and predict how an LTI system changes each harmonic.
• Apply Fourier transform pairs and properties, including convolution, modulation and time scaling, and explain the trade-off between duration and bandwidth.
• Read and sketch frequency responses and Bode plots in decibels, and specify low-pass, high-pass, band-pass and Butterworth filters for a practical system.
• Apply the sampling theorem, calculate alias frequencies, and specify anti-aliasing, reconstruction and decimation filters.
• Use the DTFT and DFT to analyze sampled signals, choose block lengths and windows to control resolution and leakage, and explain the speed of the FFT.
• Use the Laplace transform to solve differential equations with initial conditions, find transfer functions, poles and zeros, and judge stability from pole locations.
• Use the z-transform to analyze digital filters, place poles and zeros to design a notch filter, and convert analog filters to digital form with the bilinear transform.