The present invention provides a waveform detection
system and a state-
monitoring system. The waveform detection
system features a
signal-
processing function that characterizes and detects non-cyclic transient variations and performs 1 / f fluctuation conversion for input waveforms to derive output waveforms. The waveform detection
system characterizes signs of
state variation, incorporates multiple digital filters in the
digital filter calculator of the computer, uses coefficient patterns derived from non-integer n-time integration as elemental patterns for multiplication coefficient patterns, and incorporates a manner of changing the phase of at least one of the elemental patterns, input
signal data, and
digital filter output so that the outputs of digital filters that use the elemental patterns are synthesized in a state where a portion of the phases of the characteristic extracting and
processing function is changed. The state-
monitoring system of the present invention monitors states based on the
signal processing of the waveform detection system.