TheFast Fourier Transform" (FFT) is an important measurement method in the science of audio and acoustics measurement. It converts a signal into individual spectral components and thereby provides frequency information about the signal. FFTs are used for fault analysis, quality control, and condition monitoring of machines or systems. This article explains how an FFT works, the relevant parameters and their effects on the measurement result.
Strictly speaking, the FFT is an optimized algorithm for the implementation of the "Discrete Fourier Transformation" (DFT). A signal is sampled over a period of time and divided into its frequency components. These components are single sinusoidal oscillations at distinct frequencies each with their own amplitude and phase. This transformation is illustrated in the following diagram. Over the time period measured, the signal contains 3 distinct dominant frequencies.
It can be seen that condition 2. would apply only to very few signals. The sampling of a signal whose frequencies are not an integer multiple of df would begin and end within a block of 2^n samples with different values. This results in a jump in the time signal, and a "smeared" FFT spectrum. (aka Leakage)
In order to prevent this smearing, in practice "windowing" is applied to the signal sample. Using a weighting function, the signal sample is more or less gently turned on and off. The result is that the sampled and subsequent "windowed" signal begins and ends at amplitude zero. The sample can now be repeated periodically without a hard transition.
The portable audio and acoustic analyzer XL2 is ideally suited for fast and simple FFT analysis up to 20 kHz. For multi-channel and more detailed analysis or calculations, a more powerful system with large bandwidth and fast signal processors such as the FLEXUS FX100 Audio Analyzer is required. In conjunction with the FX-Control PC software, the FFT can be easily and quickly adapted and visualized according to the requirements of the measurement. The larger internal memory of the FLEXUS FX100 allows significantly longer blocklengths to be processed, resulting in a much finer frequency resolution.
This second part of this article deals with specific aspects that are helpful in the practical application of FFT measurements. FFT measurements are used in numerous applications. The results are usually presented as graphs and are easy to interpret. For accurate FFT measurements, there are some things to look out for. This article provides valuable tips.
As explained in the first part, the sampling rate fs of the measuring system and the block length BL are the two central parameters of an FFT. The sampling rate indicates how often the analog signal to be analyzed is scanned. When recording wav files via a commercially-available PC sound card, for example, the audio signal is usually sampled 44,100 times per second.
Harry Nyquist was the discoverer of a fundamental rule in the sampling of analog signals: the sampling frequency must be at least double the highest frequency of the signal. If, for example, a signal containing frequencies up to 24 kHz is to be sampled, a sampling rate of at least 48 kHz is required for this purpose. Half the sampling rate, in this example 24 kHz, is called the "Nyquist frequency".
But what happens if signals above the Nyquist frequency are fed in to the system?
For the most, a signal is sampled with a more-than-sufficient number of samples. With a 48 kHz sampling rate, for example, the 6 kHz frequency is sampled 8 times per cycle, while the 12 kHz frequency is only sampled 4 times per cycle. At the Nyquist frequency, only 2 samples are available per cycle.
With 2 samples or more it is still possible to reconstruct the signal without loss. If, however, less than 2 samples are available, artifacts which do not occur in the sampled (original) signal are generated.
In the FFT, these artifacts appear as mirror frequencies. If the Nyquist frequency is exceeded, the signal is reflected at this imaginary limit and falls back into the useful frequency band. The following video shows an FFT system with 44.1 kHz sampling rate. A sweep signal of 15 kHz to 25 kHz is fed in to this system.
These unwanted mirror frequencies are counteracted with an analog low-pass filter (anti-aliasing filter) before the scanning. The filter ensures that frequencies above the Nyquist frequency are suppressed.
In the case of periodically-continuous signals, the time windowing serves to smooth the undesired transitional jumps at the end of the scanning (see part 1). This prevents smearing in the spectrum. There are numerous types of windows, some of which differ only slightly. When selecting the time window, the following rule applies: Each window requires a compromise between frequency selectivity and amplitude accuracy.
Modern high-resolution FFT analyzers offer the possibility to decouple the number of measurement results from the FFT block length. This results in an increase in measurement performance time, especially for high-resolution FFTs. Thus, for example, with a 2MB block length it is no longer necessary to measure and represent more than 1 Million points (bins), but only the number necessary for the display, e.g. 1024.
The value chosen for each FFT bin can be defined in two ways:
FFTs are mainly used to visualize signals. However, there are also applications where FFT results are used in calculations. For example, very simple levels of defined frequency bands can be calculated by adding them via an RSS (Root Sum Square) algorithm.
Another application is the comparison of spectra. The example below shows an acoustic measurement of a cordless screwdriver. The measured spectrum is subtracted from a defined reference spectrum. This difference is compared against an upper and lower tolerance. The upper spectrum shows a functional cordless screwdriver. In the lower, the acoustic spectrum suggests that the test specimen is defective.
Ok so to jump right into it, a couple of friends and I picked up an 2014 Audi RS7 and plan to make a commercial/teaser-esque video of it. I have three GoPro hero4 black editions so the video portion of this is more than set. Now for the question, GoPros aren't notoriously known for the best audio, but I'm looking to get professional sounding engine & car sounds, like deep rich sounds from the exhaust that I'm going to overlay over the video audio.
1.) What would be the best way to record these sounds, harnessing the ultimate sound quality to then later piece together. Currently I have a Azden shotgun mic for my DSLR, but only one of them. And if need be I have a Blue Yeti microphone if i could use that too.
Taping lavalier omni mics to the back of the car, with these little furry wind protection balls will produce very usable and consistent exhaust noise. There will be something missing, because part of the exhaust noise can be captured only about a meter behind the tailpipes, which can only be captured on a dyno. Combine that with mics in the engine bay and roadside mics for passbys and you can create stunning results.
I know this is almost 5 years old... However, I stumbled upon something that supports EMV's answer.RDE made a hot lap recording of a GTR and also showed a setup for consumers without a massive budget.
The shotgun you have will do just fine and all you really need to do is capture the audio in a static situation (unless you want audio of the car passing buy). The way I would go about this is to shoot the video and patch in some dummy audio of the engine after the fact. FWIW it will much easier to capture the engine noise with the car not moving and you will get the tone you are looking for. An engine revved up while parked is pretty similar to when its under load. In this case you can use any mic you like, a condenser, small or large diaphragm will work as will the range of popular dynamics. Cars have a pretty high SPL output so you don't need something super sensitive. You should keep in mind (although this is a newer car) exhaust is a dirty thing and you should keep the mic out of the direct line of the tailpipe as well as the spray of gasses that come out.
Most of the audio you want is going to come out of the tailpipe and thats where I would focus my efforts. The key is to try and record on a day with not a lot of wind so you can reduce issues from it. Since you are just going for audio you can chose a day that may not be great for video recording.
I have owned and driven a wide variety of cars and frankly the movie car audio you often hear is a poor representation of what engines really sound like. the vast majority of cars dont make some fancy air compression release noise when they shift (fast and the furious). Cars dont shift 25 times in a 1/4 mile drag race.
To get good in-motion audio you will need a chase car (something quiet, an electric if you can get it). You will have a wind issue but you can get a variety of wind screens for this which may help. I have tried this a few times and never gotten a solid result so I wont offer much more than that.
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