Linear Interpolation of Sampled Sine Waves

Sine wave sampling and linear interpolation are fundamental operations in digital signal processing. Linear interpolation reconstructs continuous signals by connecting adjacent sample points with straight line segments, making it suitable for simple and fast reconstruction scenarios where computational efficiency is prioritized.

The MATLAB implementation of sine wave sampling and interpolation primarily involves three key steps: First, generate the original sine wave signal using functions like `sin()` and discretize it with an appropriate sampling rate determined by the `sampling frequency` parameter. Second, apply linear interpolation methods such as `interp1` with the 'linear' option to insert new points between sampled data points. Finally, perform upsampling operations using techniques like `resample` or `interp` to enhance the apparent resolution of the signal.

The upsampling process inserts multiple new points between existing samples, and when combined with linear interpolation, effectively smooths the signal waveform. While linear interpolation offers computational simplicity and excellent real-time performance, its high-frequency component recovery is inferior to more sophisticated interpolation methods like cubic or spline interpolation. This technique is commonly employed in audio processing, image scaling, and other applications where computational efficiency is critical.

During implementation, it's crucial to ensure the sampling rate satisfies the Nyquist criterion to prevent aliasing. Post-interpolation, the reconstructed signal quality can be evaluated by comparing its frequency spectrum with the original using `fft` analysis. Although linear interpolation introduces high-frequency harmonic components, it meets basic requirements in numerous practical applications where a balance between performance and quality is necessary.