Finding Peak and Valley Values in Vector Dimensions

Identifying peak and valley values in vector dimensions is a fundamental signal processing task in MATLAB, commonly used for analyzing data periodicity and trend variations. The core algorithm involves detecting local extremum points by comparing values between adjacent data points. Peak Detection: A peak is defined as a data point whose value exceeds both its immediate predecessor and successor. This can be implemented through vector traversal using conditional comparisons, typically with a loop structure that checks if the current element satisfies: data(i) > data(i-1) && data(i) > data(i+1). The implementation must handle boundary conditions carefully to avoid index errors. Valley Detection: Conversely, a valley represents a point with values lower than both neighboring points. The detection logic mirrors peak detection but uses the inverse condition: data(i) < data(i-1) && data(i) < data(i+1). MATLAB programmers often utilize vectorization techniques for efficient computation rather than explicit loops. For practical applications, MATLAB provides the built-in `findpeaks` function which automatically identifies peaks and returns their positions and amplitudes. The function supports key parameters like minimum peak height ('MinPeakHeight'), minimum peak prominence ('MinPeakProminence'), and minimum distance between peaks ('MinPeakDistance') to refine detection accuracy. For valley detection, a common approach involves inverting the signal (multiplying by -1), applying `findpeaks`, and then converting the results back to original values. When custom implementation is required, developers can create manual detection algorithms using element-wise comparison operations. This approach offers flexibility but requires robust edge case handling, typically implemented through conditional statements at vector boundaries. Performance optimization can be achieved using MATLAB's diff() function to calculate differences and sign changes. In summary, effective peak and valley detection in MATLAB relies on either leveraging optimized built-in functions or designing efficient comparison algorithms that ensure accurate identification of local extrema while maintaining code reliability and computational efficiency.