Class SpectralAnalysisOptions<T>
Configuration options for spectral analysis of time series data, which transforms time-domain signals into the frequency domain to identify periodic components and patterns.
public class SpectralAnalysisOptions<T> : TimeSeriesRegressionOptions<T>Type Parameters
TThe data type used in matrix operations for the spectral analysis.
- Inheritance
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SpectralAnalysisOptions<T>
- Inherited Members
Remarks
Spectral analysis is a technique used to decompose a time series signal into its constituent frequency components, revealing periodic patterns that might not be apparent in the original time domain representation. This is typically accomplished using the Fast Fourier Transform (FFT) algorithm, which efficiently computes the Discrete Fourier Transform of a signal. The resulting frequency spectrum shows the amplitude and phase of different frequency components present in the signal. This class provides configuration options for spectral analysis, including the FFT size, window function selection, and overlap settings for spectrograms or short-time Fourier transforms. These options allow fine-tuning of the spectral analysis to balance frequency resolution, time resolution, and spectral leakage based on the specific characteristics of the time series being analyzed.
For Beginners: Spectral analysis helps identify repeating patterns in your time series data.
Time series data shows how values change over time, but sometimes it's hard to see patterns:
- A stock price might fluctuate in ways that look random
- Sensor readings might contain multiple overlapping cycles
- Audio signals contain many frequencies mixed together
Spectral analysis transforms this data from the time domain to the frequency domain:
- Instead of seeing "what happened when"
- You see "which cycles/frequencies are present and how strong they are"
This is like:
- Breaking down a musical chord into individual notes
- Identifying that a stock has both weekly and quarterly patterns
- Finding that a machine vibrates at specific frequencies when it's about to fail
This class lets you configure how this transformation happens, controlling the trade-offs between frequency precision, time precision, and other factors.
Properties
NFFT
Gets or sets the number of points used in the Fast Fourier Transform (FFT).
public int NFFT { get; set; }Property Value
- int
A positive integer, typically a power of 2, defaulting to 512.
Remarks
This property specifies the number of points used in the Fast Fourier Transform (FFT) computation. The FFT is most efficient when the number of points is a power of 2, which is why the default value is 512 (2^9). If the input signal has fewer points than this value, it is typically zero-padded to reach this length. If it has more points, it may be segmented or truncated. A larger FFT size provides better frequency resolution (the ability to distinguish between closely spaced frequency components) but requires more computational resources. A smaller FFT size reduces computational requirements but provides coarser frequency resolution. The appropriate value depends on the specific application requirements, the length of the input signal, and the desired balance between frequency resolution and computational efficiency.
For Beginners: This setting controls the precision of frequency detection and computational efficiency.
The NFFT value determines:
- How many frequency bins the analysis will produce
- The resolution or precision of frequency detection
- How computationally intensive the calculation will be
The default value of 512 means:
- The FFT will use 512 points (ideally a power of 2 for efficiency)
- This provides a good balance between precision and computational cost
Think of it like this:
- Higher values (e.g., 1024, 2048): More precise frequency detection, but more computation
- Lower values (e.g., 256, 128): Faster computation, but less precise frequency detection
When to adjust this value:
- Increase it when you need to distinguish between very similar frequencies
- Decrease it when processing speed is more important than frequency precision
For example, in audio processing, higher NFFT values help distinguish between notes that are very close in pitch, while lower values might be sufficient for detecting broader frequency bands like bass vs. treble.
OverlapPercentage
Gets or sets the percentage of overlap between adjacent segments in spectrograms or short-time Fourier transforms.
public int OverlapPercentage { get; set; }Property Value
- int
An integer between 0 and 99, defaulting to 50 (50% overlap).
Remarks
This property specifies the percentage of overlap between adjacent segments when performing spectral analysis on consecutive portions of a signal, as in spectrograms or short-time Fourier transforms. Overlapping segments helps mitigate the effects of windowing, which reduces the amplitude of the signal at the edges of each segment. The default value of 50 (representing 50% overlap) is a common choice that provides a good balance between computational efficiency and accurate representation of the signal. Higher overlap percentages provide smoother time-frequency representations and better capture transient events but require more computational resources. Lower overlap percentages reduce computational requirements but may miss short-duration events and produce less smooth spectrograms. The appropriate value depends on the specific application requirements and the characteristics of the signal being analyzed.
For Beginners: This setting controls how much consecutive analysis windows overlap when analyzing how a signal changes over time.
When analyzing how frequencies change over time (like in a spectrogram):
- The signal is divided into multiple segments
- Each segment is analyzed separately
- Overlapping these segments improves accuracy and smoothness
The default value of 50 means:
- Each segment shares 50% of its data with the next segment
- This provides a good balance between time resolution and computational efficiency
Think of it like this:
- Higher values (e.g., 75%): Smoother results, better detection of short events, more computation
- Lower values (e.g., 25%): Less computation, but potentially missing short events
- 0%: No overlap, most efficient but lowest quality
When to adjust this value:
- Increase it when analyzing signals with rapid changes or short events
- Decrease it when computational efficiency is more important than capturing every detail
For example, in speech analysis, higher overlap percentages help capture the rapid transitions between phonemes, while in long-term climate data analysis, lower overlap might be sufficient.
SamplingRate
Gets or sets the sampling rate of the time series data.
public double SamplingRate { get; set; }Property Value
Remarks
The sampling rate is the number of samples per unit time (typically seconds). For example, a sampling rate of 1000 means 1000 samples per second (1 kHz). This is used to convert normalized frequencies to actual frequencies in the original units.
For Beginners: The sampling rate tells the model how frequently your data was collected. For example: - For hourly temperature data, the sampling rate would be 1/3600 (one sample per 3600 seconds) - For audio data, common sampling rates are 44100 Hz (CD quality) or 48000 Hz (DVD quality) - For ECG data, sampling rates might be around 250 Hz or 500 Hz
When you provide the sampling rate, the model can express frequencies in real-world units (like Hz or cycles per day) rather than just normalized values between 0 and 0.5.
If you don't specify a sampling rate, the default value of 1.0 is used, meaning frequencies will be expressed as cycles per sample. To get frequencies in Hz, set this to your actual sampling rate in Hz.
UseWindowFunction
Gets or sets whether to apply a window function to the signal before spectral analysis.
public bool UseWindowFunction { get; set; }Property Value
- bool
A boolean value, defaulting to true.
Remarks
This property determines whether a window function is applied to the signal before performing spectral analysis. Window functions help reduce spectral leakage, which occurs when the signal being analyzed is not perfectly periodic within the observation interval. Spectral leakage causes energy from a single frequency component to spread across multiple frequency bins, potentially obscuring weaker components. The default value of true enables windowing, which is recommended for most applications to improve the accuracy of the spectral analysis. However, windowing also modifies the signal, potentially affecting amplitude measurements and time-domain characteristics. In some specialized applications where preserving the original signal characteristics is more important than reducing spectral leakage, windowing might be disabled by setting this property to false.
For Beginners: This setting determines whether to use a special technique to improve frequency analysis accuracy.
When analyzing a signal:
- The FFT assumes the signal repeats perfectly (is periodic)
- Real-world signals rarely meet this assumption
- This mismatch causes "spectral leakage" - frequencies bleeding into neighboring bins
Window functions solve this problem by:
- Gradually tapering the signal at the edges of each analysis segment
- Reducing the artificial discontinuities that cause leakage
- Improving the accuracy of frequency detection
The default value of true means:
- Window functions will be applied before spectral analysis
- This provides more accurate frequency information for most applications
When to adjust this value:
- Keep it true (default) for most applications
- Set it to false only in specialized cases where preserving the original signal amplitude is more important than frequency precision
For example, in audio spectrum analyzers, window functions are almost always used to provide cleaner, more accurate frequency displays.
WindowFunction
Gets or sets the window function to apply to the signal before spectral analysis.
public IWindowFunction<T> WindowFunction { get; set; }Property Value
- IWindowFunction<T>
An implementation of IWindowFunction<T>, defaulting to a Hanning window.
Remarks
This property specifies which window function is applied to the signal before spectral analysis, if UseWindowFunction is set to true. Different window functions have different characteristics in terms of main lobe width, side lobe height, and spectral leakage. The Hanning window (the default) provides a good balance between frequency resolution and amplitude accuracy for many applications. Other common options include the Hamming window (similar to Hanning but with different coefficients), the Blackman window (better side lobe suppression but wider main lobe), and the rectangular window (no windowing, preserves signal amplitude but has poor spectral leakage properties). The choice of window function should be based on the specific requirements of the application, particularly the relative importance of frequency resolution, amplitude accuracy, and side lobe suppression. [0]
For Beginners: This setting selects which specific window function to use for improving spectral analysis.
Different window functions have different trade-offs:
- They all reduce spectral leakage, but in different ways
- Some preserve amplitude better, others provide better frequency separation
- The choice depends on what aspects of the signal you care most about
The default Hanning window:
- Provides excellent frequency resolution
- Has good reduction of spectral leakage
- Works well for a wide range of applications
- Is one of the most commonly used window functions
Other common window functions include:
- Hamming: Similar to Hanning, slightly different trade-offs
- Blackman: Better at suppressing distant frequency leakage
- Rectangular: No windowing (preserves amplitude but poor leakage properties)
When to change this value:
- For most applications, the default Hanning window works well
- Change it only if you have specific requirements or are familiar with the trade-offs between different window functions
For example, in audio analysis, the Hanning window is often used for general spectral analysis, while Blackman might be preferred when trying to detect very quiet sounds in the presence of loud ones. [0]