Table of Contents

Resampling

Resampling is a critical process in signal processing and data analysis. It involves altering the sampling rate of a signal to either reduce (downsample) or increase (upsample) the number of samples. This is particularly useful when dealing with signals of different sampling rates, reducing data size, or preparing data for further analysis. SignalSharp provides various methods for resampling signals, including downsampling, segment statistics, and approximation techniques.

Overview

The Resampling class includes methods for:

  • Downsampling: Reducing the number of samples in a signal.
  • Segment Statistics: Computing statistics (mean, median, max, min) for segments of a signal.
  • Moving Average: Smoothing a signal using a moving average filter.
  • Chebyshev Approximation: Approximating a signal using Chebyshev polynomials.

Why Resampling?

Resampling is necessary in various scenarios:

  • Data Reduction: Downsampling helps reduce the size of large datasets, making them easier to manage and analyze.
  • Rate Matching: When combining or comparing signals recorded at different sampling rates, resampling ensures consistency.
  • Noise Reduction: Techniques like moving average can help smooth out short-term fluctuations and highlight longer-term trends.
  • Feature Extraction: Segment-based statistics can summarize and simplify signals, making it easier to extract meaningful features for further analysis.
  • Signal Compression: Approximation methods can reduce the complexity of a signal while retaining its essential characteristics, useful in data compression.

Usage Examples

Here are some practical examples demonstrating how to use the resampling methods.

Example 1: Downsampling Heart Rate Data

In wearable devices, heart rate data is often collected at high sampling rates. Downsampling can reduce the data size for storage and further analysis.

double[] heartRateData = {75, 76, 77, 78, 75, 74, 76, 78, 79, 77, 76, 75};
int factor = 3;
double[] downsampledHeartRate = Resampling.Downsample(heartRateData, factor);
Console.WriteLine("Downsampled Heart Rate: " + string.Join(", ", downsampledHeartRate));

Example 2: Computing Segment Statistics for Temperature Data

Segment statistics are useful for summarizing long-term trends in environmental data, such as temperature readings from weather stations.

Segment Mean

double[] temperatureReadings = {20.1, 20.3, 20.5, 21.0, 21.2, 21.3, 21.5, 22.0, 22.1, 22.3};
int factor = 3;
double[] segmentMeans = Resampling.SegmentMean(temperatureReadings, factor);
Console.WriteLine("Segment Means: " + string.Join(", ", segmentMeans));

Segment Median

double[] temperatureReadings = {20.1, 20.3, 20.5, 21.0, 21.2, 21.3, 21.5, 22.0, 22.1, 22.3};
int factor = 3;
double[] segmentMedians = Resampling.SegmentMedian(temperatureReadings, factor, true);
Console.WriteLine("Segment Medians: " + string.join(", ", segmentMedians));

Example 3: Applying a Moving Average Filter to Stock Prices

A moving average filter can smooth out fluctuations in stock prices, helping to identify trends and make trading decisions.

double[] stockPrices = {150, 152, 153, 155, 158, 157, 156, 158, 160, 162, 161, 159};
int windowSize = 3;
double[] smoothedStockPrices = Resampling.MovingAverage(stockPrices, windowSize);
Console.WriteLine("Smoothed Stock Prices: " + string.Join(", ", smoothedStockPrices));

Example 4: Chebyshev Approximation of Audio Signal

Chebyshev approximation can simplify an audio signal, reducing its complexity for storage or further processing while retaining essential features.

double[] audioSignal = {0.2, 0.3, 0.1, -0.1, -0.2, 0.0, 0.1, 0.3, 0.2, 0.0, -0.1, -0.2};
int order = 2;
double[] approximatedAudioSignal = Resampling.ChebyshevApproximation(audioSignal, order);
Console.WriteLine("Approximated Audio Signal: " + string.Join(", ", approximatedAudioSignal));

Understanding the useQuickSelect argument in SegmentMedian

The useQuickSelect argument in the SegmentMedian method determines the algorithm used for median computation:

  • QuickSelect Algorithm (useQuickSelect = true):

    • Efficiency: Has an average-case time complexity of O(n), making it efficient for larger datasets.
    • Purpose: Suitable for processing large signals quickly.
    • Usage: Preferred when performance is critical, especially with large segments.
    • Mechanism: Finds the k-th smallest element in an unordered list, adapted to find the median by selecting the middle element.

  • Sort-and-Select Method (useQuickSelect = false):

    • Simplicity: Has a time complexity of O(n log n) due to the sorting step.
    • Purpose: Simpler to understand and implement.
    • Usage: Suitable for smaller datasets or when algorithmic complexity is less of a concern.
    • Mechanism: Sorts the segment and selects the middle element (or the average of the two middle elements for even-sized segments).

API References

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