DSP
48 articles • Complete guide
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Curriculum
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Discrete Signals
Discrete-time signals and sequences
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
Z-transform properties and applications
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.
DFT & FFT
Discrete Fourier Transform and Fast Fourier 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.
FIR Filters
Finite Impulse Response filter design
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 Filters
Infinite Impulse Response filter design
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.
Multirate DSP
Decimation, interpolation, and filter banks
Adaptive Filters
LMS, RLS algorithms
Adaptive Filter Basics
Concept of adjustable coefficients.
LMS Algorithm
Least Mean Squares update rule, convergence.
RLS Algorithm
Recursive Least Squares overview.
Noise Cancellation
Application of adaptive filters in removing noise.
Echo Cancellation
Removing echo in telecommunications.
Channel Equalization
Removing ISI in comms.
DSP Applications
Speech, image, and audio processing