Signal Processing

Summary

Signal processing plays an important role in many applications, such as consumer electronics (audio and video applications), radar and communication, and biomedical applications. It is one of the major areas in Electrical Engineering.

This course consists of two parts: digital signal processing and stochastic processes. The two parts have separate books and will be taught in parallel.
The part on digital signal processing covers one-dimensional signals and discuss non-ideal sampling, DFT and FFT, spectral analysis, multirate filters, and (quantization) noise propagation in filters, and sigma-delta modulation (ADC).

The part on stochastic processes introduces stochastic models and random processes to describe systems and signals that are not deterministic in nature.

The two parts are combined through course labs.

Statistical signal processing (SSP)

This part introduces stochastic models and random processes to describe systems and signals that are not deterministic in nature.

1. Repetition random variables. Pairs of random variables. Correlations.

2. Random vectors. Conditional probability models

3. Sums of random variables; the moment generating function. Performance bounds: Markov, Chebyshev, Chernoff inequalities. Bias, consistency.

4. Estimation of random variables (MMSE, MAP, ML)

5. Stochastic processes, autocorrelation function, stationarity, wide sense stationarity, estimation of the correlation function

6. Signal processing of stochastic signals, power spectral density functions, white noise.

7. AR processes, linear prediction.

Digital signal processing (DSP)

This part lays out the basic principles of digital signal processing and provides the mathematical description and tools to implement and analyse digital signal processing systems.

1. (Non-ideal) sampling and reconstruction, aliasing

2. Discrete Fourier Transform (frequency domain sampling, properties); circular convolution

3. Spectral analysis and filtering (convolution using DFT)

4. The FFT

5. Multirate filters

6. Quantization and rounding errors and their effect on linear filters

Optional additional topics (if time permits): STFT, applications to bio/audio.

Course labs

The Course Labs are biweekly python exercises on the topics covered in the course.