fardinafdideh / binning-designer

Binning Designer: Binning Parameters Effects on the Frequency Content of the Binned Signal

The sliding window or binning technique, which can be thought of as a form of low-pass filtering that smooths the signal by averaging or weighing the samples within the window, can affect the frequency content of the resulting signal in several ways depending on the size and shape of the window, as well as the overlap between successive windows. The developed toolbox lets us explore the binning parameters, i.e., the window size, shape, and overlap, in order to choose them carefully depending on the specific analysis goals and the characteristics of the signal being processed.

Window Size

The size of the sliding window determines the resolution in both time and frequency domains. A smaller window provides better time resolution, but poorer frequency resolution, and vice versa, hence, there is a trade-off between time and frequency resolution.

Window Shape

The choice of window shape can also impact the frequency content of the resulting binned signal. Common window shapes like the rectangular, Hamming, Hanning, or Blackman windows have different spectral characteristics. Some have narrower main lobes and lower side lobes in the frequency domain, which can reduce spectral leakage.

Window Overlap

Overlapping consecutive windows can improve the trade-off between time and frequency resolution. Overlapping allows for better tracking of rapidly changing frequency components and reduces the impact of frequency leakage.

Other Problem-Specific Parameters

Interpolation

To ensure consistency across windows with different sizes, one can interpolate or resample the data to a common time grid. Here, in the toy example, the simulated time-series is sampled uniformly, $f_s = 1000$, hence the count of within-window values is identical across windows, i.e., no need to within-window interpolation.

Time-Domain Signal Duration

Amplitude and Frequency of Main Oscillations

Frequency of Interest

Signal-to-Noise Ratio

Noise Type

Uniform Noise

It is characterized by a constant probability distribution over a specified range.

Colored Noise

It has a power spectral density (PSD) that is not flat like white noise. The relationship between power spectrum ($𝑃$) and frequency ($𝑓$) follows a power-law function: $P=\frac{1}{f^\alpha}$, where $-2 \leq \alpha \leq 2$, the inverse frequency power determines the type of the noise:

$\alpha$	Noise type
-2	Purple, Violet
-1	Azure , Blue
0	White
1	Pink
2	Red, Brownian, Brown, Random walk