In the previous discussion, we talked about various types of signals, including periodic signals, transient signals, and random signals. Let's start by considering periodic signals. The simplest and most fundamental type of periodic signal is the sine wave signal. Expressed mathematically,
x(t)=Asin(ωt+θ) ・・・・（1）
It will be.
Here, A: Amplitude representing the magnitude of the signal
ω: Angular frequency (angular velocity) representing the rate of repetition.
θ: Phase (more precisely, phase difference) representing the time difference.
First, regarding amplitude, for physical quantities such as sound, vibration, and pressure, it will be the physical unit of that quantity. For voltage signals, it will be voltage (V). In particular, for sinusoidal signals like the one described above, A is called the single-amplitude value (0 minus peak value), and 2A is called the double-amplitude value (peak to peak value).
ω: Angular frequency is the angle (in radians) that travels per second, and its unit is rad/s.
By the way, 360 degrees is equal to 2π (radians).
Furthermore, frequency is the number of repetitions per second, expressed in cycles/s, and in the SI unit system it is expressed in Hz. If frequency is f, the relationship between the two is:
ω＝2πf
Therefore, equation (1) is
x(t)=Asin(2πft+θ) ・・・・（2）
It can be expressed as follows.
The frequency f is the rate at which the periodic waveform repeats per second.
Furthermore, the period is the time (in seconds: s) required for that periodic waveform to repeat once, so if we let the period be T,
T=1/f
Therefore, the period T and frequency f are reciprocal.
Phase can be used to indicate the time difference between two signals or to understand the time difference from a certain reference timing. For example, by looking at the phase difference between the vibration waveform of one point and the vibration of another point relative to that point, we can understand how the vibration is occurring. The waveform itself of a single channel does not have much meaning as information.
Thus, amplitude, frequency, and phase are called the three elements of a signal waveform.
Periodic signals can take many forms, such as square waves, triangle waves, sawtooth waves, and repeating pulse waves, but the fundamental basis for all of them is the sine wave shown in equation (1) (or equation (2)).
Generally, if the fundamental frequency of a periodic signal is f, then any periodic signal can be represented as a superposition of sine waves that are integer multiples of f.
(Excerpt from the email newsletter issued on November 22, 2002)
