Generally, what parameters are used to compare the magnitude (or strength) of time-waveform signals?
Should I use this? Simply put, the peak value or maximum value of the time waveform is one
While these are evaluation values, in the world of measuring instruments, RMS values are commonly used.
The RMS value is a representative quantity that represents the magnitude (strength) of a periodic AC signal. Originally, it was related to power...
In the world of electricity, it represents the voltage of alternating current. For example, the electricity supplied to homes in Japan is actually
This is an AC signal with an effective value of 100V. Therefore, the definition of effective value is related to power and is as follows:
It can be defined as follows.
"If the applied AC voltage (E volts) consumes power equivalent to the power consumed when a DC voltage (E volts) is applied to a DC resistor R, then the effective value of the applied AC voltage is defined as E volts."
To illustrate with an illustration, comparing Figure 1 and Figure 2, when the amount of heat generated by DC resistors R of the same size is equal, the effective value of the AC signal in Figure 2 is E volts.
This relationship can be expressed by an equation. First, the power in Figure 1 (DC side) is E 2 This is /R. Intersection of period T
If the current signal is V(t), then the instantaneous power (or rather, energy) is V(t). 2 /R
Therefore, when we integrate over one period and average it (to obtain the power amount by averaging over time), the power P is:
And so, we can calculate that, and since this value is equal to E² /R, the RMS value E of the AC signal is;
This is the result. Equation ② is the defining formula for finding a periodic AC signal.
Looking at the square root on the right side of equation ②, we see an AC signal. V (t) The time-mean (mean square) of the squared value of
Therefore, the effective value is called the Root Mean Square (rms).
They've found out.
Let's redefine the mean square and RMS values of the time signal x(t).
In the world of signal processing, the mean square of equation 3 is called the power of the time signal x(t).
This is because it can be associated with the physical quantities mentioned above, such as electricity, and is physically clear, and reliable.
Because it allows for easy addition and subtraction of the size (strength) of a number, it is a very important quantity.
The power spectrum in an FFT analyzer can also be viewed as a spectral decomposition of this power.
Therefore, the overall value obtained by adding up the power divided into the spectrum is power
—It becomes that very thing.
Next time, we'll continue discussing how to calculate the effective value.
(Excerpt from the email newsletter issued on December 20, 2007)
