🎯 Exploring Digital Signal Processing Concepts Using Python & SymPy! Over the past few sessions, I worked on a series of practical DSP experiments to better understand the fundamentals of discrete-time systems, Z-transform, and filter design — all implemented using Python 🧠 Here’s what I explored 👇 🔹 1️⃣ Z-Transform Calculations Computed Z-transforms of common signals like aⁿu[n] and δ[n] using SymPy, along with their Region of Convergence (ROC). 🔹 2️⃣ Inverse Z-Transform Derived the time-domain signal from a given X(z) expression such as z/(z-2) — reinforcing how poles define system behavior. 🔹 3️⃣ Partial Fraction Expansion Used SciPy’s residuez() to perform partial fraction expansion of rational functions, identifying residues, poles, and direct terms — key in understanding system realization. 🔹 4️⃣ Poles and Zeros Visualization Found poles and zeros of transfer functions like (1 - 0.5z⁻¹) / (1 - 0.8z⁻¹) to analyze stability and frequency response characteristics. 🔹 5️⃣ System Properties & Testing (FIR System) Implemented a discrete-time system y[n] = 0.5x[n] + 0.8x[n−1] and verified: • Impulse & Step responses • Linearity and Time-Invariance tests • Frequency, Magnitude, and Phase responses • Stability check (BIBO) All visualized using Matplotlib 📈 🔹 6️⃣ Low-Pass Filter Design Designed a 2nd-order Butterworth low-pass filter, plotted its magnitude response, and expressed its transfer function H(z) symbolically. 🧩 Technologies Used: Python, NumPy, SciPy, SymPy, Matplotlib These experiments strengthened my understanding of Z-transforms, filter design, system stability, and signal analysis — bridging the gap between theoretical DSP and real-world implementation. #DigitalSignalProcessing #Python #SignalProcessing #Engineering #DSP #ZTransform #FilterDesign #SymPy #SciPy #LearningByDoing #Palaniappan Thillainathan #QIS College Of Engineering and Technology #ByteXplora Technology

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