Bandpass phase response speaker
The present invention relates to a multi-way speaker system comprising a woofer, a squawker and a tweeter, and more particularly to a speaker system having flat sound pressure-frequency and linear phase-frequency characteristics to improve a waveform transmission characteristic. In a prior art multi-way speaker system, a plurality of speakers have been arranged in a plane and constant K-type filters have frequently been used as crossover networks to divide an input audio signal so as to be assigned to a frequency band of each of the speakers. In this type of multi-way speaker system, while it has been designed to have a substantially flat sound pressure-frequency characteristic, a phase-frequency characteristic has not been considered and hence the phase-frequency characteristic has not been linear, resulting in a very poor waveform transmission characteristic. Although a crossover network which assures flat amplitude-frequency and linear phase-frequency characteristics over the entire response range has been proposed from a standpoint of a network, it also has not considered the phase-frequency characteristic of the speakers. Thus, prior art systems have not at all considered making flat both sound pressure-frequency and linear phase-frequency characteristics of the entire speaker system.
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Zero Phase In Studio Monitors
I have correct in quotes above because for a given magnitude response there are an infinite number of equally valid phase responses. This is due in part to what is called propagation delay. This is simply the time of flight of a signal through the air or any other medium.
It can also be caused by the latency of a DSP unit. An increase in propagation delay, or any frequency independent delay for that matter, increases the phase shift of a signal at the receiver location compared to when it originated. This is shown in Figure 1. The same device was measured three different times with a different propagation delay for each measurement.
This could have been due to different microphone location or different DSP latency. In this case a different signal delay was applied to illustrate the point. In each case the magnitude response is the same but the phase response is different.
The reason for this can be understood by looking Figure 2. This shows the impulse response, in the time domain, of these same measurements. The progressively later arrival of each impulse more propagation delay causes more phase shift. But exactly how much time compensation receive delay should be used? If we remove too much propagation delay the phase response will increase, again predominantly in the high frequency region. Both of these conditions are shown in Figure 3. This latter condition indicates that energy came out of the DUT before it went into it.
This is referred to as an a causal response meaning that the output was not caused by the input. A loudspeaker can be modeled as a band pass filter. At low frequency the magnitude response will be very low in level and increasing with increasing frequency until it reaches its pass band level and flattens out.
At a higher frequency the magnitude response will begin to decrease with increasing frequency. This is shown in Figure 5. The phase response for this DUT is also shown. In this example, a 1 kHz corner frequency is selected as the high frequency limit to illustrate a concept detailed in a paper by Richard Heyser1. This two page paper is highly recommended reading. Its brevity greatly belies its substance. This is exactly what is beginning to occur in Figure 5 at approximately 8 kHz and higher.
The phase response is asymptotically approaching a horizontal line. Notice also that in the higher frequency region of the pass band and just beyond — 2, Hz the phase response is not flat. It is erroneous, albeit possible, to set a receive delay to yield a nearly horizontal phase response in this frequency region. This is a very common error and one that was formerly perpetrated by the author with some regularity.
Now that we know what to look for in the phase response, how do we achieve it? We can look at Figure 2 or Figure 4 and conclude that the correct receive delay to apply is some time between the initial perturbation of the impulse response from a magnitude of 0 or out of the noise floor and its maximum value.
We could iteratively try each incremental data point sample of the IR and look at the phase to see if we had it right. This may become quite time consuming, however. Alternatively, we can use group delay to help us determine the correct receive delay. This is just the mathematical way of saying that the negative slope of the phase response gives us the group delay response.
This means that if the slope of the phase response is constant, i. In real time the phase response always slopes down with increasing frequency. This means the slope is negative.
To see the constant slope of the phase response we must view it on a linear frequency scale. When viewed on the more common logarithmic frequency scale the phase response appears to curve down more in the high frequency region.
This is simply a result of viewing phase on a log frequency scale. The phase response curves of Figure 1 are shown on a linear frequency scale in Figure 6. Here we see that progressively greater propagation delay results in a straight line in the high frequency region with progressively greater downward slope compare Figure 6 with Figure 2. The group delay for these phase responses is shown in Figure 7.
The group delay in the very high frequency region of each of these curves approaches the actual propagation delay for each measurement. This has a much lower cutoff frequency high frequency limit than the example in Figure 1. Since it has less high frequency output and more phase shift as seen in the frequency domain, the impulse response or the ETC in the time domain will have a longer rise time. This makes it more difficult to determine its true propagation delay from these time domain graphs.
The cursor in Figure 8 shows the peak arrival at However, the cursor at 8 kHz on the group delay response shown in Figure 9 indicates the propagation delay to be This is the true propagation delay for this measurement.
If we had used This would have resulted in the phase response turning up and increasing with increasing frequency. This is shown in Figure 10 along with the phase response using a Comparing this to Figure 5 should be convincing.
We have seen that the proper receive delay to be used for removing propagation delay is not the time corresponding to the maximum value peak of the IR or ETC but typically a bit earlier.
We have also seen that this time can be located fairly accurately by looking at the group delay. Using these techniques we have also seen that the phase response of a system with a band pass response, typically of loudspeakers, does not have flat phase response in the high frequency region of its pass band.
It is only at higher frequencies, well above its pass band, that the inherent phase response of a device begins to approach a flat, horizontal line. Heyser , pp. Today we more accurately refer to this as signal delay. Stay connected with email updates! You might also like Roll your own acoustic source for STI testing. The Amplifier-to-Loudspeaker Interface.
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MartinLogan Subwoofer Control App

When studying and practicing music production or audio engineering, you will certainly come across band-pass filters. Band-pass filters are powerful tools that are used in equalization and in general audio design. What is a band-pass filter in audio? The study of electronic filters is rather dense. However, this is by no means meant to be a complete study of band-pass filter.
Basics of audio filters
Lansing Sound, Inc. Most practical loudspeaker systems do not exhibit minimum phase performance. It is this phase error that we would like to minimize. As long as any loudspeaker behaves like a band-pass filter, it will exhibit a unique phase response that is related to its amplitude response. If the loudspeaker is ideal, then the phase response will exhibit the minimum possible deviation from flat phase response — hence the term minimum phase. A more convenient way to examine the same phenomenon is through the group delay response of the system.
Audibility of group delay at low frequencies
I have correct in quotes above because for a given magnitude response there are an infinite number of equally valid phase responses. This is due in part to what is called propagation delay. This is simply the time of flight of a signal through the air or any other medium. It can also be caused by the latency of a DSP unit. An increase in propagation delay, or any frequency independent delay for that matter, increases the phase shift of a signal at the receiver location compared to when it originated.
For very long FIR filters, segmented frequency-domain and multi-rate methods help to reduce the computational load, but these methods come with increased algorithmic complexity. This article aims to answer these questions, but doing so first requires covering a number of basic concepts in digital audio. Forgive me for skipping some of the details and simplifying some of the more complex concepts.
In signal processing , group delay is the time delay of the amplitude envelopes of the various sinusoidal components of a signal through a device under test , and is a function of frequency for each component. Phase delay , in contrast, is the time delay of the phase as opposed to the time delay of the amplitude envelope. All frequency components of a signal are delayed when passed through a device such as an amplifier, a loudspeaker, or propagating through space or a medium, such as air. This signal delay will be different for the various frequencies unless the device has the property of being linear phase. The delay variation means that signals consisting of multiple frequency components will suffer distortion because these components are not delayed by the same amount of time at the output of the device. This changes the shape of the signal in addition to any constant delay or scale change.
A Crossover Network or Circuit consists of separate subcircuits; each one being an electrical filter connected to a loudspeaker. All filters of a Crossover Network are connected to the Speaker System's input terminals. All filters receive the same electrical signal coming from the amplifier. The LowPass Filter allows for low frequencies to be sent to the Woofer Driver; frequencies higher than a specific limit are attenuated. The BandPass Filter allows for mid frequencies to be sent to the Midrange or Squawker Driver; frequencies outside a specific range are attenuated. In a similar sense the HighPass Filter allows for high frequencies to be sent to the Tweeter Driver; frequencies lower than a specific limit are attenuated too.
This project was designed as an Open Source alternative to Gold Line's TEF system and other similar expensive software and hardware bundles. These systems use Time Delay Spectrometry to achieve frequency response measurements of loudspeakers, rooms, audio circuits, and many other minimal-phase systems without the need of an anechoic chamber. This project benefits from being capable of taking measurements using any modern consumer-grade audio interface, while TEF and other systems require you to purchase their proprietray hardware.
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