Introduction to digital signals
Math preliminaries, complex numbers
Discrete-time systems
Convolution and impulse response
Difference equations and block diagrams
z-transform
z-transform properties
Inverse z-transform
Transfer functions and LTI system response: Part 1
Transfer functions and LTI system response: Part 2
BIBO stability and causality
Convolution as template matching
Fourier analysis
Discrete-time Fourier Transform
Discrete-time Fourier transform properties
Frequency response
Magnitude and phase response
Ideal filters
Ideal analog-to-digital conversion
Ideal digital-to-analog conversion
Aliasing effect
Discrete Fourier transform
DFT properties
Spectral analysis with the DFT
Spectral analysis and window functions
Short-time Fourier transform and spectrograms
Convolution via the DFT
Fast Fourier transform
Downsampling and decimation
Upsampling and interpolation
Practical filter design
FIR filter design
Window method for FIR filter design
Practical sampling and reconstruction of analog signals