What topics are covered in Signal Processing?

We cover filter design (FIR, IIR, and analog filters), Wiener filters (optimal linear filters), Kalman filters (recursive optimal estimation), signal generation (waveforms, noise, and modulation), impulse response measurement, and spectral analysis (GHA).

Signal Processing

Notes on analysis and processing of continuous-time and discrete-time signals.

Filter Design

Design methods for digital and analog filters. FIR filters (Parks-McClellan, window method), IIR filters (Butterworth, Chebyshev, elliptic), and more.

Wiener Filter

The optimal linear filter in the minimum mean square error (MMSE) sense. Derivation in the frequency and time domains, and Wirtinger derivatives.

Kalman Filter

Recursive optimal estimation based on state-space models. An adaptive filter capable of handling time-varying and non-stationary systems.

Signal Generation

Basic waveforms such as sine, square, and sawtooth waves. Noise generation, chirp signals, DDS (direct digital synthesis), and modulation techniques.

Impulse Response Measurement

Impulse response measurement using inverse MLS. Generation of signals with flat amplitude spectra across all frequencies, and measurement principles via time-reversed convolution.

Spectral Analysis (GHA)

Spectral analysis methods centered on Generalized Harmonic Analysis (GHA). Fast discrete-time GHA, complex-frequency GHA, pitch-glide GHA, Newton method fusion, and more.

Key Topics

Filter Design

Chebyshev Filter - An analog filter with equiripple characteristics in the passband/stopband