Signal Processing Course

Lesson 1 • Signals and Their Classifications

Defines continuous, discrete, periodic, and aperiodic signals with real-world examples. Establishes the vocabulary used throughout the entire course.

Lesson 2 • Basic Signal Operations

Covers time-shifting, scaling, reversal, and addition of signals. These operations underpin convolution and system analysis in later chapters.

Lesson 3 • Linear Time-Invariant Systems

Defines linearity and time-invariance properties and tests systems for compliance. Provides the theoretical basis for convolution and frequency analysis.

Lesson 4 • Convolution and Impulse Response

Derives convolution as the fundamental LTI output operation using the impulse response. Connects system characterization to practical filtering concepts.

Lesson 1 • Fourier Transform Properties

Surveys convolution, differentiation, duality, and scaling properties of the CTFT. Simplifies complex transform computations in filter design and analysis.

Lesson 2 • Spectral Interpretation and Visualization

Teaches magnitude and phase spectrum plotting and physical interpretation. Prepares students to diagnose signal content and system behavior visually.

Lesson 3 • Discrete-Time Fourier Transform

Introduces the DTFT for sequences and its periodic frequency-domain representation. Bridges continuous Fourier theory to digital signal processing.

Lesson 4 • Continuous-Time Fourier Transform

Extends Fourier analysis to aperiodic signals via the CTFT. Enables spectral analysis of real-world non-periodic waveforms.

Lesson 1 • Sampling Theorem and Nyquist Rate

Proves the Nyquist-Shannon theorem and defines the minimum sampling rate. Establishes the theoretical limit for lossless analog-to-digital conversion.

Lesson 2 • Aliasing and Anti-Aliasing Filters

Explains spectral overlap from undersampling and its perceptual effects. Introduces anti-aliasing lowpass filters as the standard mitigation strategy.

Lesson 3 • Quantization and Analog-to-Digital Conversion

Analyzes uniform quantization, quantization noise, and signal-to-noise ratio. Provides the foundation for understanding digital audio and data acquisition systems.

Lesson 4 • Multirate Signal Processing Basics

Introduces downsampling, upsampling, and their spectral effects. Prepares students for efficient filter bank and compression system design.

Lesson 1 • Difference Equations and System Realization

Connects linear constant-coefficient difference equations to Z-domain transfer functions. Introduces direct-form I and II block diagram realizations.

Lesson 2 • Transfer Functions and Frequency Response

Defines the system transfer function H(z) and evaluates it on the unit circle. Links Z-domain analysis to the DTFT frequency response.

Lesson 3 • Pole-Zero Analysis and Stability

Analyzes pole and zero locations and their effect on system behavior. Determines BIBO stability using the unit-circle criterion.

Lesson 4 • Z-Transform Definition and Properties

Derives the bilateral and unilateral Z-transform and its region of convergence. Establishes the discrete-domain counterpart to the Laplace transform.

Lesson 1 • Filter Specifications and Types

Defines passband, stopband, transition band, and ripple specifications. Establishes the design targets used in all subsequent filter design methods.

Lesson 2 • FIR Filter Design Methods

Covers windowed sinc, frequency sampling, and optimal equiripple FIR design. Emphasizes linear phase property and its importance in signal integrity.

Lesson 3 • IIR Filter Design via Analog Prototypes

Derives IIR filters from Butterworth, Chebyshev, and elliptic analog prototypes. Applies bilinear transform and impulse invariance for digital conversion.

Lesson 4 • Filter Performance Evaluation

Assesses filters using frequency response, phase linearity, group delay, and step response. Guides selection between FIR and IIR designs for specific applications.

Lesson 1 • DFT Properties and Theorems

Covers linearity, circular convolution, Parseval's theorem, and symmetry properties. Enables efficient manipulation of DFT results without recomputation.

Lesson 2 • Spectral Analysis Using the DFT

Applies the DFT to estimate power spectra, detect frequencies, and analyze transients. Addresses windowing, zero-padding, and resolution trade-offs.

Lesson 3 • Fast Fourier Transform Algorithms

Derives the Cooley-Tukey radix-2 decimation-in-time FFT and its butterfly structure. Reduces DFT complexity from O(N²) to O(N log N) for practical use.

Lesson 4 • Discrete Fourier Transform Fundamentals

Defines the N-point DFT and its inverse, deriving them from the DTFT. Establishes the computational basis for all practical spectral analysis.

Lesson 1 • LTI Systems with Random Inputs

Derives output PSD and autocorrelation when a random signal passes through an LTI system. Enables noise analysis in filter and communication system design.

Lesson 2 • Nonparametric Spectral Estimation

Covers periodogram, Bartlett, Welch, and Blackman-Tukey estimation methods. Addresses variance and bias trade-offs in practical spectrum estimation.

Lesson 3 • Autocorrelation and Cross-Correlation

Derives autocorrelation and cross-correlation functions and their properties. Connects time-domain correlation to power spectral density via the Wiener-Khinchin theorem.

Lesson 4 • Power Spectral Density

Defines PSD as the Fourier transform of the autocorrelation function. Interprets PSD as the distribution of signal power across frequency.

Lesson 1 • Parametric Spectral Estimation

Covers AR, MA, and ARMA model-based spectral estimation methods including MUSIC and ESPRIT. Achieves higher resolution than nonparametric methods for short data records.

Lesson 2 • Short-Time Fourier Transform

Analyzes non-stationary signals using the STFT and its spectrogram representation. Balances time and frequency resolution through window design choices.

Lesson 3 • Signal Processing in Communications

Applies modulation, demodulation, and matched filtering concepts from a signal processing perspective. Connects spectral analysis and filtering to practical communication systems.

Lesson 4 • Wavelet Transform Fundamentals

Introduces continuous and discrete wavelet transforms as multi-resolution analysis tools. Compares wavelet and STFT approaches for transient signal analysis.