You should be familiar with the concept of a resonator. This is a system which responds to the input of some excitation signal. A pendulum is a simple resonator, and its response to a "push", that is an impulsive signal, is to respond by vibrating (oscillating) at its resonant frequency. You may also have experienced the excitation of a simple resonator with sinusoidal signals. This is often done to establish the resonant frequency of a resonator. We excite the resonator at different frequencies and determine which input frequency gives the largest output response.
Filtering is just recasting these ideas into the frequency domain. Instead of saying that the pendulum responds to an impulse by vibrating, we can say that the pendulum has "filtered" the input impulse into a damped sinusoidal shape output. Likewise we can say that an input sinusoid to the pendulum has been filtered by a simple resonator; the output is a sinusoid with the same frequency as the input but a different amplitude.
What then is filtering? A coffee filter allows small particles of coffee to pass through, but keeps back the larger coffee grounds. In signal terms, the components are sinusoids rather than particles, and the selection of which to allow through is based on their frequency rather than their size. Furthermore, we have the concept that the selection can be "partial", that is affects the amplitude of the component rather than just to accept or reject it. Thus a low-pass filter is a system that tends to pass sinsusoidal signals of relatively low frequency, while tending to hold back (attenuate) sinusoidal signals of relatively high frequency (much like the coffee filter lets through small particles and holds back large ones). However in signal terms we can build many other kinds of filter, for example a "high-pass" filter lets through high frequencies and attenuates low ones; these have less familiarity in the coffee domain.
Coming back to our pendulum, we can say that the inpulse signal contains sinusoids at every frequency, and a simple resonator selects those which are close in frequency to its resonant frequency; the damped sinusoidal output signal consists of sinusoids from a limited frequenc range about the resonant frequency of the pendulum. When we apply a single sinusoid to the pendulum, all it can do is to change the amplitude (and possibly phase) of the input to produce a filtered sinusoidal output of the same frequency.
We can make a four-way division among signals. Firstly there is the distinction between Periodic and Aperiodic signals. Periodic signals have a waveform shape that repeats in time. That is it is possible to predict the future of the waveform by looking at its past. One can isolate a region of the signal, called its period, which occurs over and over again in time. Periodic signals thus have a clear fundamental period, and hence a clear fundamental frequency (or repetition frequency). These sounds also give us a clear sensation of pitch. Aperiodic signals have waveform shapes that do not repeat, that is it is impossible to predict the future of the waveform by looking at its past.
Each of these categories can be further subdivided: Periodic signals can be divided into Simple and Complex. Simple periodic signals are just sinusoids, while complex periodc waveforms are combinations of sinusoids. Aperiodic signals can be divided into Impulsive and Noise. Impulsive signals are aperiodic because they only occur once, with a concentration of energy at a particular time, while noise signals are aperiodic because they are generated by random or chaotic processes.
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