Linear Interpolation for Sine Wave Sampling

In MATLAB, we can implement linear interpolation for sine wave sampling through the following procedure:

First, we need to upsample the original signal by increasing the number of sampling points. This can be achieved by inserting zero values between existing samples using MATLAB's array manipulation functions. Next, we apply linear interpolation to the upsampled signal to obtain continuous sampling points and further increase the sampling rate. Linear interpolation is a simple yet effective method that estimates values between two adjacent samples by connecting them with a straight line. Specifically, for each point in the input signal, the algorithm calculates the weighted average of its left and right neighboring samples, where the weights are determined by the relative distance between the target point and its neighbors. This can be implemented using MATLAB's interp1 function with the 'linear' method or through direct mathematical computation of the weighted averages.

Therefore, implementing linear interpolation for sine wave sampling in MATLAB requires two main steps: upsampling through zero insertion and linear interpolation. This approach yields more refined sampling results, enabling better understanding and analysis of sine wave signals, particularly useful in digital signal processing applications where higher resolution is needed for frequency analysis or waveform reconstruction.