Calculating the Spectrum of One-Dimensional Non-Uniformly Sampled Signals

In MATLAB, Doppler signals can be represented through multiple approaches. One common method involves using MATLAB's built-in `doppler` function to generate simulated Doppler signals. This function accepts user-defined parameters such as velocity and frequency offset to create realistic Doppler signal models that mimic real-world scenarios where signal frequency shifts occur due to relative motion between transmitter and receiver.

For spectral analysis of one-dimensional non-uniformly sampled signals, MATLAB provides the `fft` (Fast Fourier Transform) function as a primary tool. The FFT algorithm efficiently computes the discrete Fourier transform of a signal, converting it from time domain to frequency domain representation. This transformation reveals the frequency components and their respective magnitudes within the signal, which is crucial for understanding its spectral characteristics.

Important consideration: When dealing with non-uniformly sampled signals, pre-processing steps such as interpolation or resampling are essential before applying FFT. Since standard FFT requires uniformly spaced samples, techniques like cubic spline interpolation or least-squares resampling can be employed to create a uniform sampling grid. This ensures accurate frequency domain analysis and prevents spectral leakage or distortion that might occur with irregular sampling intervals.

The implementation typically involves: 1) Pre-processing the irregularly sampled data using interpolation functions like `interp1` with appropriate methods (e.g., 'spline' or 'pchip'), 2) Applying `fft` to the resampled signal, and 3) Using `fftshift` to center the spectrum for better visualization. For advanced non-uniform FFT (NUFFT) applications, specialized toolboxes or custom implementations may be required for optimal performance with irregular sampling patterns.

This information should provide a solid foundation for working with non-uniformly sampled signals in MATLAB environments.