Method and apparatus for resolving signals in data

A method for identifying and measuring individual radiation particles comprising:

• receiving a plurality of individual radiation particles in a radiation detector and generating detector output data in the form of a stream of digital samples, the detector output data comprising a plurality of individual pulse signals corresponding to the individual radiation particles, some of which are overlapping, each individual pulse signal having a pulse shape with a rising edge and a falling edge above a baseline;
• receiving the detector output data;
• transforming the detector output data such that the rising edge of each individual pulse signal is compressed in the time domain and the falling edge of each individual pulse signal is extended in the time domain so as to produce digital stepped data comprising a transformed stream of samples approximating an ideal step function, by modeling each of the individual pulse signals using a rising edge variable and a falling edge variable, transforming the rising edge variable such that the rising time of each of the individual pulse signals is substantially zero, and transforming the falling edge variable such that the falling time of each of the individual pulse signals is substantially infinite, wherein the digital stepped data is produced without having previously identified each of the individual pulse signals and without having previously determined an energy of each of the individual pulse signals;
• identifying each of the individual pulse signals using the digital stepped data;
• and
• determining one or more of the energy or the time of arrival of each of the identified individual pulse signals using the digital stepped data,
• wherein the transforming of the detector output data is performed using the following operation:
• y(k)=y(k−1)+x(k)−x(k−1)·(e−a+e−b)+x(k−2)·e−a·e−b
• where:
• x(n) is a value of the received detector output data stream at sample ‘n’,
• a, b determine the falling and rising edges of the pulse shape with a double exponential waveform, and
• y(n) is the digital stepped data.

An apparatus, comprising:

• means for receiving a plurality of individual radiation particles and generating detector output data in the form of stream of digital samples, the detector output data comprising a plurality of individual pulse signals corresponding to the individual radiation particles, some of which are overlapping, each individual pulse signal having a pulse shape with a rising edge and a falling edge above a baseline;
• means for receiving the detector output data;
• means for transforming the detector output data such that the rising edge of each individual pulse signal is compressed in the time domain and the falling edge of each individual pulse signal is extended in the time domain so as to produce digital stepped data comprising a transformed stream of samples approximating an ideal step function, by modeling each of the individual pulse signals using a rising edge variable and a falling edge variable, transforming the rising edge variable such that the rising time of each of the individual pulse signals is substantially zero, and transforming the falling edge variable such that the falling time of each of the individual pulse signals is substantially infinite, wherein the digital stepped data is produced without having previously identified each of the individual pulse signals and without having previously determined an energy of each the individual pulse signals;
• means for identifying each of the individual pulse signals using the digital stepped data;
• and
• means for determining one or more of the energy or the time of arrival of each of the identified individual pulse signal using the digital stepped data,
• wherein the means for transforming is further configured to transform the detector output data using the following operation:
• y(k)=y(k−1)+x(k)−x(k−1)·(e−a+e−b)+x(k−2)·e−a·e−b
• where:
• x(n) is a value of the received detector output data stream at sample ‘n’,
• a, b determine the falling and rising edges of the pulse shape with a double exponential waveform, and
• y(n) is the digital stepped data.