DSP
Discrete Time Signals
Sequences, operations, energy/power.
Standard Sequences
Impulse, step, exponential, sinusoidal.
LTI Systems
Linearity, Time-invariance, causality.
Convolution Sum
Linear convolution calculation.
Difference Equations
Describing discrete systems, recursive solving.
Correlation
Auto and Cross correlation.
Z-Transform Definition
ROC, properties, standard pairs.
Properties of ROC
Effect of causality and stability.
Inverse Z-Transform
Partial fractions, power series, residue method.
Transfer Function
Poles, zeros, stability analysis.
System Response
Solving difference equations using Z-transform.
DTFT Overview
Discrete Time Fourier Transform properties.
DFT Basics
Discrete Fourier Transform definition, bins.
Properties of DFT
Periodicity, symmetry, circular convolution.
Circular vs Linear
Using DFT for linear convolution.
FFT Algorithms
Radix-2 DIT and DIF algorithms.
Computations in FFT
Butterfly diagram, bit reversal.
Goertzel Algorithm
Tone detection efficiency.
Filter Types
LPF, HPF, BPF, BSF, Allpass.
FIR Characteristics
Linear phase, stability, implementation.
FIR Filter Design
Fourier series method, Gibb's phenomenon.
Window Functions
Rectangular, Hamming, Hanning, Blackman windows.
Kaiser Window
Adjustable beta parameter logic.
FIR Structures
Direct form, cascade, linear phase.
IIR Basics
Feedback, infinite impulse response.
Impulse Invariance
Mapping s-plane to z-plane, aliasing.
Bilinear Transform
Frequency warping, pre-warping.
Butterworth Filters
Maximally flat response design.
Chebyshev Filters
Type I and Type II ripple.
IIR Structures
Direct Form I/II, Parallel, Cascade.
Interpolation
Upsampling, anti-imaging filter.
Sampling Rate Conversion
Rational factor transformation.
Polyphase Decomposition
Efficient filtering structures.
Adaptive Filter Basics
Concept of adjustable coefficients.
RLS Algorithm
Recursive Least Squares overview.
Decimation
Downsampling, anti-aliasing filter.
Filter Banks
Analysis and synthesis banks, subband coding.
Noise Cancellation
Application of adaptive filters in removing noise.
Echo Cancellation
Removing echo in telecommunications.
Channel Equalization
Removing ISI in comms.
Speech Processing Basics
Vocal tract modeling, LPC.
Image Processing Basics
2D convolution, edge detection.
DSP Processors
Harvard architecture, MAC units, circular buffers.
Fixed vs Floating Point
Quantization noise, dynamic range.
LMS Algorithm
Least Mean Squares update rule, convergence.
Audio Compression
Perceptual coding, MP3 basics.
Radar Signal Processing
Pulse compression, target detection.
Wavelet Transform
Short-time Fourier transform limitation, wavelets.