Measurement of frequency characteristics using WaveSpectra

Here is a summary of points to note when measuring frequency characteristics by combining WaveSpectra (hereinafter WS) and sister software WaveGene (hereinafter WG).

There are the following methods to measure the frequency characteristics with WS + WG.
(1) A method of using periodic sweep in the user waveform of WG (V1.40).
(2) A method using the sweep signal of the WG directly.(Method using the peak hold function of WS)
Normally,the method (1) is strongly recommended because accurate frequency characteristics can be easily obtained in a short time (at most several seconds).
This method can be used in most cases, such as the characteristics of the sound device itself when connected to a loop, an external circuit such as an amplifier connected to the sound device, or a simple measurement of a speaker via an amplifier microphone.
For details on how to obtain a direct response in real time, refer to the explanation "Measurement of frequency characteristics using periodic sweep" on the WG side .
If (1) cannot be used, for example, if the recording playback characteristics of the recorder do not return in real time, the following method using the general sweep signal + WS peak hold function of (2) should be used. Become. However, in this case, there are some points to be aware of, such as the settings on the WG side.

(1) Setting the sweep signal of the

WG When measuring the frequency characteristics of the sweep signal using the peak hold function of WS in combination with the WG, pay sufficient attention to the sweep speed.

Originally, in order to obtain the correct value in the FFT, the signal must be constant and unchanged for a period of time equivalent to the number of sample data. If it is changing, it means that the true value is not obtained.

In the case of Log sweep, the rate of change increases as the frequency increases, so measurement is performed with characteristics that decrease as the frequency goes up.
(Sometimes I see it in measurement data published on the Web or in magazines (^^;) To eliminate this drop

in the high frequency range, use

Note 1: Use a linear sweep instead of a Log sweep.

It can be a constant drop in the frequency range.

Even with Log sweep, if the number of sample data is reduced or the sweep time is long enough due to the influence of the window function, there will be almost no drop in the high frequency range. However, it is not a correct measurement in the first place.

Before passing through the measurement target, it is recommended to first play the Wave file of the original sweep signal directly to understand the degree of deterioration.

Next, regarding the sweep speed, it is necessary to change it at a sufficiently slow speed for accurate measurement . Then, let's roughly ask for a guideline as to how fast the sweep should be

. If you decide to draw with the original resolution of, for example, the sampling frequency Fs =When 48000Hz and the number of FFT sample data N = 4096 , the frequency resolution is 48000/4096 = 11.72Hz.
When analyzing from 20 to 20000 Hz with this resolution, the analysis time of the FFT is the reciprocal of the frequency resolution of 00853 seconds,
so it is almost good to move at intervals of 11.72 Hz every 0.0853 seconds (20000- 20) 11.72 * 0.0853 = 145 seconds

To summarize the formula,Note 2: Sweep time = Sweep frequency width * N * N Fs Fs

In this case, it takes about two and a half minutes to reach 20kHz. If the number of FFT sample data is 8096 , it will takeabout 10 minutes , which is four times as long. If the number of FFT sample data is 16384 , it will takeabout 40 minutes, which is four times as long.
The following is omitted.

Actually, the resolution of the window function is several times higher than the FFT resolution, so it is possible to plot only with a wider width, so it is not possible to analyze with the above resolution even if it takes a lot of time.

It will take quite a lot of time, but how about it?
(If you do not need that much resolution, you can shorten it even if you know that the original resolution cannot be obtained.)
The following is an actual example of the change in resolution due to the sweep speed.

(2) Resolution at the peak hold of WS due to the difference in the speed of the sweep signal of WG
I put a Twin-T notch filter circuit between the input and output of the sound device and investigated how accurately the dip can be detected... WG Linear Sweep-> Sound Output-> Notch Filter-> Sound Input-> WS Shows the original frequency characteristics of the peak hold filter. (Due to periodic sweep) The dip is about -30dB.

[When the number of FFT sample data and the sweep time are changed]

Is the sweep time the optimum time according to the formula (1)? There is as.
(The blue line is the correct characteristic for comparison. It is intentionally paused at about 1kHz.)

Number of sample data 4096, Hanning window, sweep time is 15 seconds from 10 to 2000Hz (44fps)

Number of sample data 8192, Hanning window, sweep time is 58 seconds from 10 to 2000Hz (38fps)

The number of sample data is 16384, Hanning window, sweep time is 230 seconds (30fps) from 10 to 2000Hz.

Again, the larger the number of sample data (and sweep time), the better the result.
[Enlarged area around the dip to make it easier to see]
In addition to the sweep speed, the resolution also decreases due to the characteristics of the window function. I will show you the difference. Number of sample data 4096, Hanning window, sweep time is 15 seconds from 10 to 2000Hz (44fps)

↑ The green line is the spectrum when paused according to the dip position during the sweep. It seems that almost the correct dip is detected from the level.

However, you can see that the dip is filled and disappears due to the widening of the base of the window function at the rising and falling parts on both sides. Similarly, the number of sample data is 8192, Hanning window, sweep time is 58 seconds from 10 to 2000Hz (38fps)

↑ The green line is the spectrum when paused according to the dip position during the sweep.

Similarly, you can see that the dip is filled and disappears on both sides.

[Differences due to window functions] It is the difference in the degree of dip fill depending on the type of window function.reference

Window function	The number of sample data is 4096, and the sweep time is 15 seconds from 10 to 2000 Hz.	Main lobe width
Hanning		Twice as a rectangular window
Blackman		3 times the rectangular window
Blackman-Harris		Large dip disappearance due to 4 times filling of rectangular window
None (rectangle)		A rectangular window with high resolution is excellent only by detecting a dip of this degree, but it is not normally used because the sidelobes are widened.

Similarly, when the number of sample data is 8192

Window function	Number of sample data 8192, sweep time 58 seconds from 10 to 2000 Hz
Hanning
Blackman
Blackman-Harris
None (rectangle)

Hanning windows seem to be the best for the time being.