Signal Processing Simulation Projects

Introduction

Simulation projects bridge the gap between textbook theory and practical application. By implementing signal processing algorithms in code, you develop intuition for how mathematical concepts translate into working systems. Each project below is designed to reinforce specific course topics while producing a tangible, testable result. These projects can be implemented in MATLAB, Octave, or Python — the algorithms are the same regardless of the language.

The projects are ordered by complexity: start with simpler ones (signal generation, basic filtering) and work toward more sophisticated systems (DTMF decoding, AM radio, adaptive filtering).

Project 1: Signal Generator and Spectrum Analyzer

Concepts: Sampling, DFT/FFT, frequency resolution, windowing

Implementation:

1. Generate a signal containing multiple sinusoids: $x(t) = \sum_k A_k \sin(2\pi f_k t + \phi_k)$
2. Sample at rate $f_s$ and compute the FFT
3. Display magnitude spectrum with correct frequency axis
4. Experiment with different window functions and observe spectral leakage
5. Add white noise and observe how SNR affects spectral peaks

Learning outcomes: Understand the relationship between time-domain samples and frequency-domain representation, effect of observation time on resolution, and windowing tradeoffs.

Project 2: FIR Filter Design and Implementation

Concepts: Convolution, FIR filters, frequency response, linear phase

Implementation:

1. Design a low-pass FIR filter using the windowed-sinc method
2. Implement the filter using direct convolution ($y[n] = \sum b_k x[n-k]$)
3. Plot the frequency response and verify the cutoff frequency
4. Filter a noisy signal and compare before/after spectra
5. Measure group delay and verify linear phase

Learning outcomes: Connect convolution theory to practical filtering, understand FIR design parameters, verify that theory matches implementation.

Project 3: IIR Filter and Stability Analysis

Concepts: Recursive filtering, pole-zero analysis, stability, transient response

Implementation:

1. Implement a second-order IIR filter: $y[n] = b_0 x[n] + b_1 x[n-1] - a_1 y[n-1] - a_2 y[n-2]$
2. Compute and plot the pole-zero diagram
3. Verify stability by checking pole magnitudes
4. Compare impulse response with theoretical prediction
5. Move poles toward the unit circle and observe the effect on resonance

Learning outcomes: Understand recursive structures, stability conditions, and the relationship between pole locations and system behavior.

Project 4: AM Radio Transmitter and Receiver

Concepts: Modulation, demodulation, frequency shifting, filtering

Implementation:

1. Generate a baseband audio signal (or load a WAV file)
2. Modulate: $y(t) = [1 + m \cdot x(t)] \cos(2\pi f_c t)$
3. Simulate the transmission channel (add noise, attenuation)
4. Demodulate: multiply by carrier, then low-pass filter
5. Compare recovered audio with original

Learning outcomes: See multiplication/frequency-shifting theory in action, understand why the low-pass filter is needed, observe the effect of overmodulation.

Project 5: DTMF Tone Decoder

Concepts: DFT, frequency detection, signal classification

Implementation:

1. Generate DTMF signals (dual-tone pairs for telephone keypresses)
2. For each received tone, compute the DFT
3. Identify the two dominant frequencies using peak detection
4. Map frequency pair to keypress using the DTMF frequency table
5. Handle real-world complications: inter-digit silence, noise

Learning outcomes: Apply spectral analysis to a real detection/classification problem, handle practical issues like noise and thresholds.

Project 6: Echo Cancellation

Concepts: Convolution, adaptive filtering, LMS algorithm, system identification

Implementation:

1. Simulate an echo: $y[n] = x[n] + \alpha x[n - D]$ (delayed, attenuated copy)
2. Implement the LMS adaptive filter to estimate and cancel the echo
3. Plot the learning curve (error vs iteration)
4. Test with different delay lengths and echo strengths
5. Challenge: handle multiple echoes (more complex impulse response)

Learning outcomes: Connect convolution (echo as filtering) with inverse system concepts, understand adaptive algorithms that learn system parameters from data.

Project 7: Sampling and Reconstruction

Concepts: Sampling theorem, aliasing, interpolation, reconstruction filters

Implementation:

1. Start with a continuous signal (high sample rate approximation)
2. Subsample at various rates (above and below Nyquist)
3. Demonstrate aliasing by comparing spectra
4. Implement sinc interpolation for reconstruction
5. Compare with zero-order hold and linear interpolation

Learning outcomes: Directly observe the Sampling Theorem in action, see aliasing occur, and compare reconstruction quality.

Key Takeaways

• Simulation transforms abstract theory into working, testable implementations
• Start simple (signal generation, FFT) and build toward complex systems (AM radio, adaptive filtering)
• Every project should include verification: compare simulation results with theoretical predictions
• Use visualization extensively — plot time-domain signals, spectra, and pole-zero diagrams
• Projects develop debugging skills: when theory and simulation disagree, investigate why
• Code is reusable: filter designs and analysis functions become your personal toolbox