Academic Domain: Signals, Systems & DSP
The Signal
The Mathematics of Information in Motion
The Architecture of Transformation
A signal is information changing through time or space. A system is what transforms it. Here, we cross the mathematical bridge from continuous physical reality into the discrete, calculable domain of Digital Signal Processing—allowing us to extract meaning from the noise of the universe.
REALITY →
SIGNAL →
SYSTEM →
TIME DOMAIN →
FREQUENCY DOMAIN →
FOURIER →
LAPLACE / Z-TRANSFORM →
SAMPLING →
DIGITAL REPRESENTATION →
DSP →
FILTERING →
FFT →
ANALYSIS
The 15 Realms of Processing
Signals, Systems & DSP Architecture
REALM 01
Signal Foundations
- Continuous vs Discrete-time
- Deterministic vs Random Signals
- Energy & Power Signals
- Signal Scaling, Shifting & Reversal
Systems & LTI
- Linearity & Time Invariance
- Causality, Stability, Memory
- Impulse Response (h(t))
- Continuous & Discrete Convolution
Frequency Analysis
- Sinusoids & Complex Exponentials
- Magnitude & Phase Response
- Continuous & Line Spectra
- Ideal vs Practical Filters
Fourier's World
- Trigonometric/Exponential Fourier Series
- Continuous-Time Fourier Transform (CTFT)
- Transform Properties (Time/Freq Shift)
- Bandwidth & Spectral Content
The Laplace Domain
- Bilateral & Unilateral Transform
- Region of Convergence (ROC)
- Poles, Zeros & Transfer Function
- Stability Analysis in s-Domain
The Z-Domain
- Z-Transform Definitions
- ROC for Discrete Systems
- Difference Equation Solutions
- Pole-Zero Stability Interpretation
Sampling & Quantization
- Nyquist-Shannon Sampling Theorem
- Aliasing & Anti-aliasing Filters
- Quantization Error & Resolution
- ADC/DAC Conversions
DSP Fundamentals
ADC
DSP
DAC
- Digital Signal Processing Chain
- Delay, Addition, Accumulation
- Discrete-Time Fourier Transform (DTFT)
- System Realization (Direct/Cascade)
Digital Filters (FIR/IIR)
- FIR vs IIR Filter Structures
- Windowing Methods (FIR Design)
- Bilinear Transform (IIR Design)
- Passband/Stopband Specifications
The DFT & FFT
- Discrete Fourier Transform (DFT)
- Fast Fourier Transform (Radix-2 FFT)
- Decimation in Time / Frequency
- Frequency Bins & Spectral Computation
Digital Convolution
h
h
h
x
x
x
- Linear vs Circular Convolution
- Sequence System Output
- DFT-based Fast Convolution
- Zero-padding & Filtering
Operations & Analysis
- Auto & Cross Correlation
- Power Spectral Density
- White vs Colored Noise Models
- Signal-to-Noise Ratio (SNR) Analysis
Multirate DSP
- Decimation (Downsampling)
- Interpolation (Upsampling)
- Anti-alias/Anti-imaging Filters
- Sample-Rate Conversion
Advanced DSP
AUDIO | IMAGE | RADAR | BIO
- Short-Time Fourier Transform (STFT)
- Wavelets & Multiresolution
- Adaptive Filtering (LMS/RLS)
- Audio, Image & RADAR Processing
15 — The Signal Laboratory
[1] VISUALIZATION [2] LTI ANALYSIS [3] TRANSFORMS [4] SAMPLING [5] FILTER DESIGN [6] FFT COMPUTATION
The convergence of mathematical theory and computational practice. Utilizing software environments to visualize spectra, analyze pole-zero stability, design discrete filters, and process real-world signals.