Filter a signal array with bandpass

@param filter_name: the type of filter to use
@param flattened_array: 1D signal array to be filtered
@param sampling_freq: the sampling frequency with which the signal is collected
@param order:
@param lowcut: lower bound of the frequency band of interest
@param highcut: higher bound of the frequency band of interest

@return y: the signal in frequency band [lowcut, highcut]

Convert trodes timestamps into seconds

@param time_file: trodes timestamps.dat source file

@return np.array(time_data): numpy array of timestamps in seconds 

Apply Hilbert transformation to a power data series to get is magnitude envelope

@param power_data: raw power data array

@return hilbert_magnitude: magnitude envelope of power_data after hilbert transformation

Remove data samples that are labeled as global noise from power series 

@param power_data: data sample array
@param time_data: timestamp array in seconds, match power_data in length
@param noise_label: T/F array of each sample labeled as noise or not, match power_data in length
@param threshold: a maximum value of power to be considered normal activity (instead of noise)

@return denoised: array of samples without noise samples
@retun denoised_time: timestamp array in seconds, match denoised in length

Detect threshold crossing events in a given power series

@param magnitude: power array for threshold-crossing events detection
@param num_std: number of standard deviation above average (of power array) for threshold to be
@param num_wait: the number of samples to wait before stimulating. i.e num_wait consecutive Trues then stimulate

@return stimulation: numpy array of stimulation status (T/F) at each sample point in power array

return the root mean-squared of a given array

@param buffer: any array or list of number

@return: the root mean-squared value of the array as a proxy for its power

Process a given power array with stepwise (i.e online) RMS estimation

@param power_data: array of raw power across time
@param sampling_rate: 
@param time_data: array of power_data's timestamps in seconds
@param buffer_length: number of data samples for RMS estimation
@param lower_bound: lower bound of target frequency range 
@param upper_bound: upper bound of target frequency range
@param threshold: maximum RMS value to be considered

@return rms_magnitude: array of RMS-processed power series
@return rms_time: array of rms_magnitude's timestamps in seconds

Filter the whole given power array, then perform RMS estimation on buffer at each sample 

@param power_data: array of raw power across time
@param time_data: array of power_data's timestamps in seconds
@param buffer_length: number of data samples for RMS estimation
@param threshold: maximum RMS value to be considered

@return rms_magnitude: array of RMS-processed power series
@return rms_time: array of rms_magnitude's timestamps in seconds

Extract timestamps of event onset, offset and duration array from stimulation status array

@param stimulation: array of stimulation status (T/F) at each timestamp
@param timestamps: array of timestamps in seconds that match the stimulation array

@return np.array(changedtime): numpy array of timestamps of event onset and offset (alternative) in seconds
@return np.array(eventduration): numpy array of event durations in milliseconds
@return np.array(truetime): numpy array of timestamps in seconds of event onset only 

Remove the onset timestamps that belong to noise events based on event duration

@param truetime: array of timestamps of event onset
@param eventduration: array of event duration in milliseconds, should match array truetime in length
@param threshold: minimum event duration to be considered a real event

@return np.array(deblipped): array of timestamps in seconds without "blips"

Remove the onset timestamps that belong to noise events based on event frequency

@param truetime: array of timestamps of event onset
@param threshold: minimum time gap between two events for the second one to be considered a real event

@return np.array(deblipped): array of timestamps in seconds without "blips"

detection_series_2 is used as ground truth reference to calculate the accuracy and precision of detection_series_1. 
For a particular event in detection_series_2, if there exists an event in detection_series_1 that matches the one
in series_2, we mark the one in series_2 (ground truth) as detected and the one in series_1 as truepositive (TP). 
If an event in series_1 doesn't match any series_2 event, it's marked as falsepositive(FP).

@param detection_series_1: timestamp (of the starts of events) arrays in seconds 
@param detection_series_2: timestamp (of the starts of events) arrays in seconds
@param window_width: range of detection time difference allowed in seconds

@return accuracy: percentage of series_2 events detected in series_1
@return precision: percentage of correct detections (TP) in series_1
@return (len(detection_series_2)-len(truepositive)): number of series_2 events unmatched by any series_1 event

Calculate general time lag distribution between two time series with cross correlation

@param time_series_1: array of timestamps in seconds
@param time_series_2: array of timestamps in seconds

@return lag_distribution: array of cross-correlated time lags in milliseconds