System and method of noise reduction
A method for signal detection including the steps of: (1) iteratively acquiring sets of signal samples in a time domain N times; (2) iteratively applying a first transform to each iteratively captured samples in the time domain to convert each set of samples in the time domain to a corresponding subsequent set of samples in a frequency domain; (3) iteratively creating array rows using each of the sets of samples in the frequency domain wherein each subsequent array row has a length N; (4) appending each subsequent array row to the array until a second axis representing time reaches length N; (5) applying a second transform to the array to create a plurality of layers of spectral content; (6) determining a location of a signal of interest within the array based on a threshold; and (7) applying a bounding box to the array to isolate the signal of interest.
1. A method for signal detection comprising the steps of:
acquiring a first set of samples of a signal in a time domain;
applying a first transform to the first set of samples in the time domain to convert the first set of samples in the time domain to a first set of samples in a frequency domain;
creating a first row of an array using the first set of samples in the frequency domain wherein the row has a first axis of length N representing frequency;
iteratively capturing subsequent sets of samples of the signal in the time domain N−1 times;
iteratively applying the first transform to each iteratively captured subsequent set of samples in the time domain to convert each subsequent set of samples in the time domain to a corresponding subsequent set of samples in the frequency domain;
iteratively creating a subsequent array row using each of the subsequent sets of samples in the frequency domain wherein each subsequent array row has a length N;
appending each subsequent array row to the array until a second axis representing time reaches length N;
applying a second transform to the array to create a plurality of layers of spectral content;
performing a first analysis on the plurality of layers of spectral content to create a histogram of energy levels;
performing a second analysis on the histogram to determine a location of a signal of interest within the array based on a threshold;
determining a bounding box to apply to the array based on the location of the signal of interest within the array; and
applying the bounding box to the array to isolate the signal of interest.
2. The method according to claim 1 wherein the second transform comprises the steps of:
applying a two-dimensional finite impulse response filter with a basis function to the array.
3. The method according to claim 2 wherein second transform further comprises the steps of:
using a finite impulse response filter with an optimized basis function transfer function to divide a frequency range of the array into an upper frequency half and a lower frequency half; and
passing the lower frequency half to form a first layer of the plurality of layers of spectral content.
4. The method according to claim 3 wherein the second transform further comprises the steps of:
dividing the upper frequency half into a subsequent upper frequency half and a subsequent lower frequency half;
passing the subsequent lower frequency half to form a second layer of the plurality of layers of spectral content;
iteratively dividing each subsequent upper frequency half into subsequent upper frequency and lower frequency halves; and
passing each subsequent lower frequency half to form a subsequent layer of the plurality of layers of spectral content.
5. The method according to claim 4 further comprising the steps of:
creating a number of layers of spectral content equal to the order of the transform.
6. The method according to claim 2 wherein the basis function is a burst function beginning, ending, and oscillating about zero.
7. The method according to claim 1 wherein the second analysis determines the threshold through analysis of the peaks, valleys, or curvature of the histogram.
8. The method according to claim 1 wherein the second analysis determines the threshold based on clustering in the histogram.
9. The method according to claim 1 wherein the second analysis determines the threshold based on entropy of the histogram.
10. The method according to claim 1 wherein content of the plurality of layers below a derived frequency threshold is deprecated to reduce noise.
11. The method according to claim 10 further comprising the step of:
recombining the content of the plurality of layers to create a second array with less noise than the array.