Sine Wave, Square Wave, and White Noise Signal Generation and Analysis

1. Generate sine wave, square wave, and white noise signals using MATLAB programming. Display their time-domain waveforms using plot functions with proper labeling and scaling. For sine waves, use the sin() function with specified frequency and amplitude. For square waves, implement using the square() function or logical operations. White noise can be generated using randn() function for Gaussian distribution.

2. Perform Fast Fourier Transform (FFT) using fft() function to convert time-domain signals to frequency domain. Display magnitude spectrum plots using abs(fft()) and proper frequency axis scaling based on the sampling rate. Allow customizable parameters including sampling frequency (fs), signal frequency, and data length (N) for flexible analysis.

3. Compute and display three types of spectral analysis: Root Mean Square (RMS) spectrogram using rms() function or manual calculation, power spectrum using periodogram() function or squared magnitude of FFT results, and logarithmic RMS spectrogram by applying 20*log10() to RMS values. Implement windowing techniques and averaging for improved spectral estimation.

4. Reconstruct original signals using Inverse Fast Fourier Transform (IFFT) with ifft() function. Apply proper scaling and real-part extraction to recover time-domain signals. Display the reconstructed sine wave waveform comparing it with the original signal to verify reconstruction accuracy. Include error analysis and reconstruction quality metrics.

5. Additional implementation details: Include code structure for signal generation parameters (amplitude, frequency, duration), FFT size optimization recommendations, window function applications (Hamming, Hanning) for spectral leakage reduction, and plotting configurations for professional visualization. Explain computational considerations for real-time applications and memory management for large data sets.