The "basic tone", i.e. the lowest frequency and most dominant sine wave, determines to a large extent how high or low a sound is perceived.The composition of the high-frequency sine waves (the so-called harmonic spectrum) he recognizes the timbre and can distinguish a guitar from a triangle.
*click* The details of time and frequency are explained here *click*
Fourier has left behind a helpful, albeit somewhat unwieldy formula (=glasses) with which signals can be transformed from frequency to time domain. The Fourier transformation named after him or the inverse Fourier transformation. The corresponding formula then looks as follows:
Calculating with the equation requires basic knowledge of higher mathematics, a short explanation of the formula, however, I do not want to remain guilty at this point.
- The left side of the signal is the Fourier transform of the signal in the frequency domain, the expert speaks of the "spectrum" or "spectral range". This spectrum consists of the sum of all (!) sinusoidal oscillations that make up the signal.
- The sum-thing is packaged in the equation in the form of an integral - the crooked line left of the f(t).
- If a simple sum is hidden in this unwieldy operator, it is no wonder that the sinusoidal oscillations also get a rather strange-looking clausulation. This consists of the e term which carries a "-j2πft" in the exponent.
- The time domain signal which should be viewed through another pair of glasses is the "f(t)".
For complex signals the equation is quite unwieldy even for mathematically trained persons. Therefore there is a Fast Fourier Transform (FFT) which can be calculated by computer software. This function is implemented in many programs, even e.g. Excel has a possibility for a corresponding data analysis.
Impulse response + glasses = frequency response
If the Fourier transform is applied to the step response, the so-called complex frequency response is obtained. The impulse response in the time domain is a mathematically complete description of the signal theoretically considered system, the complex frequency response is also a complete system description.
Unfortunately, it is virtually impossible to map the complex frequency response. The complex frequency response gets quite exotic properties - e.g. negative frequencies. And it contains complex frequency components. Complex numbers result if one takes the root from negative numbers - which a commercial calculator immediately acknowledges with an error message, but is actually calculable. These complex numbers contain the phase response, i.e. the temporal shift of the sinusoidal oscillations to each other.
Negative frequencies and roots of negative numbers are at best extremely unwieldy and funny. Even for those who have understood the underlying mathematics.
For a meaningful representation of the complex frequency response, it must be freed from everything that is funny. Mathematically, an amount formation is necessary for this. The result is the so-called amplitude frequency response which describes the loudspeaker in a highly accurate and easily understandable way.
Figure 3: Amplitude frequency responses of a loudspeaker in different radiation directions (axial = forward)
The amplitude frequency response describes the response of a loudspeaker to a Dirac pulse in the frequency domain. The spectrum of a Dirac is a straight line. The measured loudspeaker is (axially) a relatively straight line at least between 100Hz and 20,000Hz. Below 100Hz the loudspeaker drops off which means an error in the reproduction (= bass weakness). The slight waviness of the frequency response is also an error (over- and underemphasis of individual frequency ranges, tonal discoloration).
The sideways radiated sound of loudspeakers at high frequencies clearly falls away from the ideal (= bundling) is representative for commercially available loudspeakers - and a problem. The reflected sound in normal living rooms is louder than the direct sound from the loudspeaker, therefore a resulting fundamental-heavy discoloration is audible.
The essential statement about the sound of hi-fi systems is: The loudspeaker speaks, the room responds! This mixture is the sound of your system.
The bundled radiation at high frequencies has a clear advantage: there are fewer reflections in the room and the sound image becomes clearer. However, the reflective sound in the room lacks the high tones, so the sound impression is dull. Many materials such as concrete walls or carpets absorb high tones more than low tones. The impression is thus additionally ensiled.
It makes sense to simply raise the tweeter using an equalizer to compensate for this effect. However, the hearing takes the direct incoming sound and the reflections were mostly separated, an accentuation of the tweeter in direct sound would cause an unnaturally shrill sound impression.
A balanced and neutral bundling is desirable - however technically very problematic in the conversion.
Further display forms of the impulse response
Even today, the impulse response is still often recorded with Dirac impulses. When testing the room acoustics of a listening room, professionals often clap their hands to get a first impression of the reverberation. In large concert halls, even alarm guns have been used as Dirac generators with a similar aim. Modern tests of loudspeakers, however, are usually carried out with more complex signals and evaluated with the help of software-supported correlation methods. The measurement signals are much less sensitive to interference - but the goal is still the impulse response.
There are different forms (=glasses) of displaying the impulse response. In the following, some display variants are described and evaluated with regard to their significance. Caution: None of the display variants can describe non-linear behavior!
Impulse response:
- Mathematically complete representation
- Response of the loudspeaker to a Dirac
- Display type: Time domain
- Expressiveness: If the viewer of the diagram cannot perform an FFT in the head very low, other display options are easier to interpret.
Step response:
- Can be derived matematically (integral) from the impulse response
- Display type: Time domain
- Contains the complete information from the impulse response.
- Meaningfulness: Analogous to impulse response: Low because difficult to evaluate
Phase response:
- Display type: Frequency range
- Indicates the degree to which the phases are shifted relative to each other in degrees.
- Completeness of the representation: There are no statements about the amplitude frequency response.
- Significance: Low, the hearing is quite insensitive to phase errors, conspicuities only occur with extremely steep separating crossovers in the midrange, at low frequencies the tonal effects (e.g. by bass reflex) are higher.
Group delay times:
- Can be calculated from the phase response
- Display type: Frequency range
- Completeness of the representation: There are no statements about the amplitude frequency response.
- Indicates the degree to which the frequencies arrive at the listener shifted to each other, but is not given here in degrees but in seconds.
- Meaningfulness: Medium, higher than with phase response. Strong time shifts are particularly noticeable in the bass, where phase shifts, e.g. through crossovers or bass reflex ports, are noticeable due to the bass lagging behind.
Amplitude Frequency Response
- Fourier transform of the impulse response, complex information components are omitted
- Display type: Frequency range
- Completeness of the presentation: incomplete, phase information missing
- Expressiveness: Very high, a strongly aurally correct representation of the impulse response
An dieser Stelle nochmals in aller Deutlichkeit: Innere Phasendrehungen sind weitgehend unhörbar und wirken sich nicht auf die Lokalisierbarkeit und Raumabbildung aus, nur sprunghafte Änderungen der Phase sind hörbar. Phasenfehler sind in den meisten Fällen nur dann hörbar, wenn Mitteltöner und Hochtöner im Übergangsbereich unterschiedliche Phasen haben und es daher zu Interferenzen (Kammfiltereffekten) kommt.
Der Amplitudenfrequenzgang wird auch in anderen Darstellungsvarianten gezeigt, z.B. in der Isobarendarstellung (besser bekannt als Tannenbaumdiagramm). Mehr dazu an anderer Stelle.
Data sheet information of manufacturers
At this point again in all clarity: Inner phase rotations are largely inaudible and have no effect on the localizability and spatial mapping, only jerky changes of the phase are audible. In most cases, phase errors are only audible if the midrange driver and tweeter have different phases in the transition range and interference (comb filter effects) therefore occurs.
The amplitude frequency response is also shown in other display variants, e.g. in the Isobar display (better known as the fir tree diagram). More about this can be found elsewhere.
Data sheet data of common large manufacturers
Loudspeakers are complex technical systems that are not easy to assess in combination with acoustics. Let's look at the anonymized technical data for a 150 Euro/piece floorstanding loudspeaker of a well-known major manufacturer.
- 3 ways bass reflex
- 220 / 450 Watt
- 4-8 Ohm
- 18-38.000 Hz
Is the speaker good? Let's evaluate these points:
- 3-way speakers are still effective in advertising. Was that a technical decision? Would a 2.5 way speaker have been better?
- 450 watts sounds good at first glance. But the question of what happens to the power in the loudspeaker remains unanswered. Does the loudspeaker only get warm at the power input - or can it really reproduce high levels?
- The impedance between 4 and 8 ohms is standard on the market. Any conventional amplifier should be able to handle this.
- 18Hz lower cut-off frequency is fantastic. But what does the speaker do at this frequency? Can a low-frequency whisper just be measured with highly sensitive measuring instruments? Or is the frequency response linear up to this frequency?
- 38,000Hz upper frequency limit sounds sufficient. Usually all frequencies above 20,000Hz are filtered out in CD recordings to avoid aliazing effects when digitizing. What the loudspeaker should do at 38.000Hz remains a mystery
But the real questions are: What happens between 18 and 38,000Hz - how does it sound? To answer to this question we will have to know: What is the frequency response? Distortion values? Radiation behavior? The data sheet does not give us any answers to this.
Let's summarize the offer: A large-series manufacturer supplies a low-cost entry-level loudspeaker for 150 euros. As a 3-way construction, it should also be possible to achieve slightly higher bass levels. Loudspeakers in this price region usually have slightly higher treble and bass to make it easier to jump off the seller's shelf, which is probably the case here as well. For a closer evaluation measurements and/or test listening would be desirable.
If you want to see serious and complete manufacturer's information, please visit the following page
http://www.neumann-kh-line.com/neumann-kh/home_de.nsf/root/prof-monitoring_studio-monitors_midfield-monitors_O410#
recommended by the manufacturer Neumannl. Under the menu item measurement curves complete measurements of a technically very good loudspeaker can be seen. If the manufacturer handles measurements so freely, you can actually judge the loudspeakers on the basis of the data sheet. More caution is required with brochures in the usual electrical wholesale markets.
*click* Next section *click*