MATLAB Code Implementation for Harmonic Analysis

Harmonic analysis is a crucial technique in signal processing and power systems, used to analyze the frequency components of signals. In MATLAB, we can implement harmonic analysis for input and output sine waves through a series of steps involving signal generation, Fast Fourier Transform (FFT) processing, and spectral visualization. First, we need to generate an input sinusoidal signal. A sine wave is typically defined by frequency, amplitude, and phase parameters. MATLAB provides built-in functions like `sin()` for generation, where we can specify these parameters programmatically. For example, we can define the sampling frequency (`fs`), time vector (`t`), and create the signal using `x = A*sin(2*pi*f*t + phi)` with amplitude `A`, frequency `f`, and phase `phi`. Next, assuming the output signal is also sinusoidal but may contain harmonic distortion (additional higher-frequency components beyond the fundamental frequency), we use Fourier Transform (FFT) to convert time-domain signals to frequency-domain representations. MATLAB's `fft` function efficiently performs this transformation, returning complex frequency data that we process by taking the absolute value (`abs(fft_result)`) to obtain magnitude spectra. We apply FFT separately to both input and output signals, then plot their spectra using `plot()` or `stem()` functions to visualize frequency components, including fundamental waves and harmonics like 2nd or 3rd orders. For precise analysis, we compute amplitudes at each frequency bin, detect prominent harmonics through peak detection algorithms (e.g., `findpeaks()`), and compare spectral differences to evaluate system nonlinearity or distortion levels. Finally, we visualize time-domain waveforms and frequency spectra side-by-side using subplots (`subplot()`) for intuitive observation of harmonic distribution. If required, we calculate Total Harmonic Distortion (THD) by summing harmonic powers relative to the fundamental, implementing it with MATLAB's mathematical operations to quantify distortion severity. In summary, MATLAB offers robust signal processing tools, making harmonic analysis straightforward and efficient. Through FFT-based spectral analysis and built-in visualization functions, we can effectively detect and analyze harmonic components in signals for various applications.