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Horstmann Full Popular. Mohrig Full Ebook. The resulting waveform depends upon its relative amplitude and phase characteristics, and may be greater, lesser or equal to the individual contributors. It is not possible, post facto, to separate out the original signals with filters or computation. The combined waveform of two amplitude- and phase-matched signals is indistinguishable from that of a single signal at twice the level. Unmatched uncorrelated complex waveforms merge together to create a new waveform with a random association to each of the original parts.
The combination of unmatched complex waveforms multiple frequencies must be evaluated on a moment-to-moment basis. The obvious example of uncorrelated signals is two different music streams: frequencies are in phase one moment and out of phase the next. These could be different songs, different instruments playing the same song or even violins playing the same parts in a symphony.
In all cases the relationship between the signals is unstable and therefore incapable of consistent addition or subtraction at a given frequency. The combination of matched correlated complex waveforms also creates a new waveform, but with an orderly and predictable relationship to the original parts. Phase-matched signals create a combined waveform similar in shape to the individuals but with higher amplitude.
If there is time offset between the signals, the new waveform will be modified in a stable and predictable way, with alternating additions and subtractions to the amplitude response over frequency a. An example is copies of the same music stream combined in a signal processor. Comb filtering is created by time offset between the signals. The interaction of speakers carrying the same signal in a room is more complex because the interaction must be evaluated on a frequency-by frequency and location-by-location basis covered in depth in Chapter 4.
Oscillation is a continuous function. We cannot get from Point A to Point B without passing through all the points in between. That is the essence of analog audio: the motion of a tuning fork, string, phonograph needle, speaker cone and more. If the movement stops, so does the song.
If we can trace this continuous movement on one device and transfer it to another audio device, we will recognize it as the same song, even if one version came from magnetic flux a cassette tape and another came from the mechanical motion of a needle in a groove.
Analog audio is like a continuous drawing exercise, a transcription that never lifts the pencil from the paper. Transferring a waveform between electrical, magnetic and acoustic transmission mediums is like redrawing that pencil sketch with a different medium such as paint, stone or whatever. Digital audio is a non-continuous function.
We can only get from Point 0 to Point 1 without evaluating any points in between. Listening to 0s and 1s sounds pretty boring, even for people at raves. Digital waveforms are copies of analog waveforms, but the operation differs from the transduction process between analog mediums discussed above. Analog-to-digital converters slice the continuous signal into tiny bits ba-da-boom , each of which represent the best fit for the momentary amplitude value.
The faithfulness of the digital rendering depends on how finely we slice both amplitude and phase time. Amplitude resolution is defined by the number of bits bit is the current standard , and temporal resolution a. If you look close enough at the photograph you can see that there are no continuous lines, just lots of little dots. That is the essence of digital.
Audio pixels. The beauty of it is that once we have the digital copy we can send it around the world without changing it. As long as we are very careful, that is. This is not even hypothetically true of an analog signal because all audio mediums have some form of degradation distortion, frequency response variation, phase shift, etc.
Bear in mind that we can never hear digital audio. This time the conversion requires our scribe to pick up the pencil again and draw one continuous connecting line between every dot in our digital photograph of the original line drawing. Analog audio waveforms propagate through a medium.
Within this book air molecules will be the acoustical medium and electronic charge and magnetic flux serve as the electromagnetic medium. Each medium has unique properties such as transmission speed, propagation characteristics, loss rate, frequency response, dynamic range and more.
Digital audio between analog conversions is transmitted over a medium not through it. Propagation through a medium is a chain reaction. Each energy transfer takes time an incremental latency so the more media we go through, the longer it takes.
Propagation speed is constant over frequency but variable by medium. Electromagnetic propagation is so fast we are mostly able to consider it to be instantaneous. Sound propagates through a metal bar very dense faster than water medium density , which is faster than air low density. Sound propagation is the same speed, however, for heavy metal bars and air shows ba-da-boom.
An audio frequency has physical size once it exists within a transmission medium. Wavelength is inversely proportional to frequency becomes smaller as frequency rises.
Why should we care about wavelength? After all, no acoustical analyzers show this, and no knobs on our console can adjust it. In practice, we can be blissfully ignorant of wavelength, as long as we use only a single loudspeaker in a reflection-free environment.
Good luck getting that gig. Wavelength is a decisive parameter in the acoustic summation of speaker arrays and rooms. Once we can visualize wavelength, we can move a speaker and know what will happen. Transduction is the process of waveform conversion between media Fig. Transducers are media converters. Examples include acoustic to electromagnetic microphones , and vice versa speakers. The amplitude values and wavelength in one media e.
Speaker sensitivity relates acoustic output pressure to the input power drive. The standard form is dB SPL 1 meter with 1-watt input. This book is full of charts and graphs, all of which have scales. The sooner we define them the easier it will be to put them to use. Amplitude is all about size. There are a million ways to scale it or should I say there are dB ways.
Linear level units are seldom used in audio even though they correspond directly to electrical and acoustic pressure changes in the physical world our level perception is logarithmic. Many engineers go their entire careers without thinking of linear sound level. Can we do a rock concert with a sound system that can only reach 20 pascals dB SPL? My mix console clips at 10 VRMS.
Is this normal? Voltage is found in many areas outside the audio path, so it helps to have bilingual fluency between linear and log. If we started at V and continued this linear trend we would see V, , and V. The total run from 1 V to 4 V is 12 dB. By contrast, the entire 4-volt sequence starting at V would not even total 0. Linear amplitude scales include volts electrical , microbars or pascals acoustical , mechanical movement excursion , magnetic flux and more.
The log scale characterizes amplitude as a ratio dB relative to a reference fixed or variable Fig. Therefore acoustic levels and the electronics that drive them are best characterized as log.
Successive linear doublings of 1 microbar to 2, 4 and 8 microbars would be successive changes of approximately 6 dB 94, , and dB SPL. One of the most heavily enforced standards in professional audio is to never have just one standard Fig. The dB scale for voltage has at least twenty. The difference between them is a constant 2.
There is an extensive history regarding dB voltage standards going back to the telephone, which you can read somewhere else when you have trouble sleeping. The dB scale is favored because our audio signals are in a constant state of change. We are constantly riding current levels relative to each other, to a moment ago or to the legal level allowed before the police shut us down. The dB scale is complicated but is easier than linear when trying to monitor relative levels that have a 1,, ratio.
We should at least know the maximum voltage level for our equipment, which is usually around 10 volts i. The noise floor should be in the dBV range. This leaves 20 dB of headroom above and the noise dB below. The common term for acoustic level is dB SPL sound pressure level , the measure of pressure variation above and below the ambient air pressure.
The limit of audibility approaches the noise level of the air medium, i. The threshold of pain is around 3 million times louder at dB SPL. The threshold of audio insanity has reached dB SPL by car stereo fanatics. The following values are equivalent expressions for the threshold of hearing: 0 dB SPL, 0. For most optimization work we need only deal with the log form. It takes about ms for the ear to fully integrate the sound level. This setting is used to monitor levels for outdoor concert venues that have neighbors complaining about the noise.
An excessive LE reading can cost the band a lot of money. There are filtered versions of the SPL scale Fig. Easier to spell. LF range is virtually nonexistent. Applicable for noise floor measurements. Often used as a maximum SPL specification for voice transmission. Subwoofers on or off goes undetected with A- weighted readings.
Applicable for measurements using music program material. Close to a flat response. Applicable for maximum-level measurements. Used as a specification for full- range music system transmission levels. Subwoofers on or off will have a noticeable effect when C weighting is used. Note: D weighting is shown here but not typically used for our applications graphic by Lindosland en. Power is derived from a combination of parameters e.
The 10 log10 formula is the log conversion of power ratios also Fig. Phase scaling is circular and therefore very different from amplitude. When we get more amplitude we simply expand the scale.
This is similar to an automobile race where cars on the lead lap are indistinguishable from those a lap behind. Phase serves us poorly as a unit of radial measure. Radians are rarely used by audio engineers for system optimization or in a sentence for that matter.
It is a vestige of a merciful rounding error by ancient Egyptian mathematicians. Linear frequency scaling shows equal spacing by bandwidth unequal spacing in octaves. The linear scale is an annoying, reality-based construction that corresponds to how frequency and phase interact in the physical world.
The spacing between 1 kHz, 2 kHz, 3 kHz and 4 kHz consecutive bandwidths of 1 kHz is shown as equal spacing. Phase, the harmonic series and comb filter spacing all follow the linear frequency axis. The frequency resolution of the Fourier Transform the math engine of our analyzer is linear. A log frequency scale shows equal spacing in percentage bandwidth octaves , and unequal spacing in bandwidth.
This corresponds closely to our perception of frequency spacing. A true log frequency response is made of log spacing of log filters. Instead a series of typically eight octave- wide linear sections are spliced together to make a quasi-log display.
Full details are in Chapter Each octave of the quasi-log frequency response is derived from log spacing of the linear resolution e.
Tick, tick, tick. It seems strange to have to write that time is linear evenly spaced increments and not log proportionally spaced increments. This is only mentioned because the frequency response effects of time offsets are entirely linear but are perceived by our log brains. Fluency in reading these graphs is a mandatory skill in this field. The graphs are 2-D, with an x-axis and y-axis. We generally find frequency and time on the x-axis and amplitude, phase and coherence on the y-axis.
Amplitude vs. The amplitude scale can be linear or log but time is only linear. Absolute level over frequency is used to check the noise floor, the incoming spectrum, harmonic distortion, maximum output and more. The y-axis shows level against a fixed standard. We can observe the individual channels used to make transfer function computations next item.
Relative level over a quasi-log frequency scale is the most common graph in system optimization Fig. This transfer function response is used for level setting, crossover alignment, equalization, speaker positioning and more. The y-axis scales unity level to the center and shows gain above and loss below in dB.
An alternative option, the linear frequency scale can help identify time-related mechanisms such as phase, comb filtering, reflections, etc. This is our standard phase display Fig. A flat phase response horizontal line indicates zero phase shift and zero time offset over the frequency range shown.
Variations from flat phase response indicate some time offset, either full band i. A downward slope left to right indicates positive delay whereas an upward slope indicates negative delay. A constant phase rotation at linear frequency intervals indicates latency frequency-independent delay. A quasi-log display shows the slope steepening with frequency a linear function in a log display.
Comb filtering appears as increasingly narrowing spacing of peaks and dips as frequency rises again, linear function, log display. Filters create frequency-dependent delay. The phase response of a filter with a given Q will maintain the same shape slope as frequency rises. This section is intended to provide just enough info to help read phase traces as we go along. If phase were easy, this book would be five pages long.
Relative phase on a linear frequency scale is less popular, but more intuitive than log. A flat phase response indicates no time difference at any frequency, just as the log display. Latency creates a constant phase slope as frequency rises. Comb filtering appears as consistently spaced peaks and dips as frequency rises.
The impulse response is a favorite of the modern analyzer Fig. We can find delay offsets between speakers with extreme accuracy in seconds. Follow the dancing peak, read the number in ms. And it seems like magic to most of us, even more so when we stop to think about what this computation is. The FFT analyzer impulse response is a mathematical construction of the picture we would see on a hypothetical oscilloscope amplitude vs.
In practice we get relative amplitude vs. For now we will focus on how to read it. Relative level y-axis is not like our amplitude over frequency. The vertical center is silence, not unity gain. Unity gain normal polarity is shown as an upward vertical peak at a value of 1 0 dB and positive gain is a bigger peak and loss is smaller.
A downward peak indicates polarity inversion. Time x-axis is relative, a comparison of output—input arrival times. A centered impulse indicates synchronicity. The peak moves rightward when the output is late and vice versa.
Yes, it is possible to have the output before the input in our measurements, because we can delay signals inside the analyzer. A perfectly flat frequency response amplitude and phase makes a featureless impulse shape straight single line, up and down. Reflections appear as secondary impulses on the display. Like phase, this is enough information to enable us to read the displays going forward. The coherence function is a data quality index that indicates how closely the output signal relates to the input Fig.
Amplitude and phase data are deemed reliable when coherence is high and unreliable when low. Coherence alerts one to take the wooden shipping cover off the speaker front instead of boosting the HF EQ. Yes, a true story. Coherence is derived from averaging dual-channel frequency responses and is indicative of data stability. A value from 0 to 1 is awarded based on how closely the individual samples match the averaged value in amplitude and phase. Details are in section Voltage, electrical pressure, can be characterized linearly in volts or logarithmically in dB dBV, dBu, etc.
The electronic waveform is a tracing of voltage vs. Voltage is analogous to acoustical pressure. Current is the density of signal flow through an electronic circuit.
As current increases, the quantity of electron flow rises. Analog audio transmission between electronic devices except amplifiers to speakers requires minimal current flow.
Resistance restricts current flow in an electronic circuit. As resistance rises, the current flow for a given voltage falls. Resistance is frequency independent impedance is not. Impedance is the frequency-dependent resistive property of a circuit, a combination of resistance, capacitance and inductance.
Impedance ratings are incomplete without a specified frequency. Impedance rises and output level falls at frequencies above its operating range. Capacitors pass signal across conductive, but unconnected, parallel plates. DC cannot flow across the gap in the plate. An AC signal, however, can flow across the plate resistance falls as frequency rises.
Capacitance in series rolls off the LF response resistance is inversely proportional to frequency. Parallel capacitance such as between wires of an audio cable rolls off the HF via a shunt path to ground.
Inductor coils resist voltage changes in the signal. An unchanging signal DC passes freely but the inductor becomes increasingly resistant as frequency rises the rate of electrical change increases. Series inductance increasingly rolls off the HF response. Parallel inductance shunts the LF to ground. Electrical power in watts is the combined product of voltage, current and impedance. Most electronic transmission involves negligible power low voltage, low current and high impedance.
Speaker-level transmission requires substantial power high voltage, high current and very low impedance. Acoustical power, also in watts, is produced by pressure, surface area and acoustic impedance inertance. Our ears and microphones are pressure sensors, not power sensors, which characterize sound level by pressure only SPL. Signal levels are divided into three categories by voltage and impedance. A lucky waveform can experience all three return to Fig. Mic-level signals are typically generated by small passive devices such as microphone coils, guitar pickups, phonograph cartridges, etc.
Mic level is a matter of necessity, not choice. There are few advantages and many disadvantages to operating in the microvolt range. Signals are vulnerable to induced noise and other complications relating to extremely low voltage and current flow e.
The winning strategy is to preamplify mic-level signals to line level as soon as possible. The worst-case scenario, unbalanced, high-impedance mic level e. Active devices, such as consoles, processor, instrument direct outs, playback equipment and more, usually generate line-level signals. This is the standard operating range, with nominal levels in the 1 V range, and maximum levels over 10 V. Power amplifiers are the exclusive generators of speaker-level signals.
Instead, speaker level ratings refer to the maximum power capability watts. Power ratings require two known parameters: voltage and impedance. This is an overview of some relevant standard specifications for professional-grade analog audio devices Fig. There are two main categories for frequency response: range and deviation. Range is the spectral area between the limits, typically the half-power points -3 dB points at the LF and HF extremes.
Any electronic device has a maximum voltage limit: the clipping point, typically specified at 1 kHz. This parameter helps ensure compatibility between interconnected devices to ensure full dynamic swing through the signal chain. It is preferable to have all devices clip at around the same level, lest the voltage swing become limited by the weakest link.
This is typically given as the worst case across the spectrum and falls into two categories: hum harmonic multiples of the line frequency and noise white noise. Dynamic range is the span between the maximum-level capability and noise floor. Devices with a single gain stage have straightforward dynamic range specifications. In other words, cranking up the input while cranking down the output is likely to change the dynamic range through the device. Every device has one of two polarities: right normal or wrong inverted.
Polarity must be specified for any device with unbalanced inputs e. DJ mixers or outputs e. Sound strange? Unity 0 dB is the expected default gain in line-level devices.
Power amplifiers require positive voltage gain, specified directly in dB or as sensitivity, i. This is the maximum amount of power a device output can drive to another device input the load. This specification is only used for power amplifiers and the speakers they drive. Harmonic distortion is the addition of uninvited frequencies to the original waveform. Harmonics are linear multiples of the original transmitted frequency.
Analog electronic devices normally exhibit a fairly consistent percentage THD over level and frequency. Therefore the specification is normally given at 1 VRMS line level or rated output power amplifiers at 1 kHz. Audio signals are generally and hopefully more complex than a simple sine wave. Therefore our system must remain linear while reproducing complex waveforms as well as simple sinusoids. Intermodulation distortion has the potential to arise when two or more sine tones are simultaneously reproduced.
Where harmonic distortion generates spurious frequencies by multiplication, intermodulation does so by addition and subtraction. IMD products are difference tones related to the linear spacing between the signals. In this case 60 Hz is, in essence, modulating 1 kHz, hence the name.
Loudspeaker motion must track complex waveforms so IMD testing is one way to separate the men from the boys or the under-seat FX generators from real speakers. Digital audio is the numerical rendering of an analog waveform constructed from a series of evenly spaced, end-to-end time records.
The data are transmitted in non-continuous packets and reassembled for further processing, re-transmission or conversion to analog. The waveform is traced as a series of numerical values, i. The number can be referred to a fixed-point standard or floating-point. Fixed-point values can be linear or log in dB , relative to the full-scale reference.
Increments are 2nth power, with n being the number of bits. Twenty-four-bit has 16,, iterations. Floating-point numbers have virtually unlimited size, but not unlimited precision. The precision is limited by the resolution of the mantissa the numbers that precede the exponent, e.
There is voltage and current flow between digital devices, but they relate to the transmission of bits, not the waveform. In essence, an electronic digital audio system has two electrical states e. The key is to connect compatible devices with an impedance-matched cable under its specified maximum length. Sample rate sets the frequency range upper limit. The highest usable frequency must not exceed half the sample rate the Nyquist frequency to prevent calculation errors.
Therefore steep filters are employed around the Nyquist frequency to prevent aliasing errors. A 48 kHz sample rate yields a frequency range up to 24 kHz and a 96 kHz sample rate yields 48 kHz of audio bandwidth.
Full-scale digital is equivalent to the analog clip point. Semiconductors and other analog electronic components constantly emit some level of molecular level noise.
Not so with the 1s and 0s of digital. The least significant bit LSB has the difficult task of determining whether to round the tiniest signals up or down. Quantization noise is the sound of flip-flopping, which can be more disturbing to listeners than old- fashioned analog hiss.
Bit depth is the analog for dynamic range. In fixed-point digital this is the level difference between the maximum capability full scale and the noise floor the LSB.
Each time we add a bit to the resolution we are able to slice the finest increment in half, which is equivalent to 6 dB in terms of amplitude. By contrast, a bit system has a potential of dB, a very high bar for an analog circuit to reach. The process has three stages: voltage to number to voltage dBV to full scale to dBV. Confusion on this concept can cost a pile of dynamic range. We can keep it simple by following the industry standard for dBFS, which is.
There are too many to count. There is no such thing as an rms audio waveform, either analog or digital: ONLY peak negative and positive. Rms values are mathematical calculations for heat dissipation or integrations of perceived loudness. Are we worried about cooking the numbers? It is simply a matter of fitting the waveform within the limits of the counter the digital pipe. Our concern is headroom, the remainder between the positive or negative peak and the full-scale number.
Now how do we relate them? The key is to make sure we match the reference points within our terminology. We can reasonably expect to find systems in the range of to dBFS. We now enter the world of acoustics.
Because we are only covering overwater acoustics we can boil this down to two things: air and surfaces. Air, the medium, is the easy one, with relatively few parameters in play. The surface part is the challenge: floors, ceilings, walls, I-beams, movie screens, balcony fronts and even our paying patrons. Anything that the sound hits, bends around, reflects off or pushes its way through before it has decayed below our hearing threshold goes in the category of acoustic surfaces.
Sound moves through the air medium as pressure variations propagating spherically from the source at a speed of approximately 1 meter every 3 ms 1. The surface area increases and sound pressure level falls as the wave propagates outward.
There is no distance limit to the propagation but the frictional and pressure losses eventually decrease the pressure variations to the point of inaudibility and noise floor of the air itself Fig.
Sound pressure level SPL is analogous to voltage in the electronic waveform. The waveform stretches over an increasingly large area as sound propagates outward. Acoustic power remains constant neglecting frictional heat loss so pressure falls as surface area expands. Acoustic impedance is the static pressure resisting the transmission of our waveform through the elastic medium of air. Speakers must generate actual power to overcome this resistance unlike microphones, which can just sense the pressure.
Air impedance varies slightly over temperature and altitude, but not enough to make us design mountaintop sound systems different from valley sound systems. Acoustic power is analogous to electric power derived from the acoustic properties of pressure, surface area and inertance voltage, current and impedance.
The acoustic power generated by a loudspeaker dissipates gradually by friction heat loss but otherwise remains nearly constant as it propagates spherically outward. A stun grenade has almost as much far-field acoustic power as near-field, but proximity makes a big difference in how we experience it dB SPL peak 1 m. The difference in acoustic power between senders and receivers is found in the surface area acoustic current , not the SPL.
By contrast the mic senses the same SPL over the surface area of its diaphragm. The direct sound path is the most important trajectory in sound system design due to its strong effect on perceived uniformity. Analyzers used for system optimization are highly focused on the direct sound response and early reflections, with varying degrees of inclusion of the late reflections.
Although there is only a single direct sound path, the number of reflected sound paths can be almost infinite. They love reflections because they would not have a job without them. Early reflections arrive close behind the direct sound. This small but critical minority of the overall reflections has strong effects on tonal perception and acoustic gain. Their paths are analyzed individually more than collectively especially by sound engineers. Late reflections are the tail end of the sound.
Late reflections only stretch time, which is characterized statistically. The parameters of room acoustics are well established. The numbers are useful to room designers, especially for this endangered species: the room without a sound system. Nonetheless, this is the bottom line for sound system design and optimization: These numbers have very little bearing on our decision-making process.
We still point the speakers at the audience, not the walls. More on this topic as we go Fig. Reverb time is the interval for a signal to decay 60 dB after cessation. This is the oldest and most common singular room characterization metric. The measurement was conducted historically by exciting the room with a loud impulse such as a balloon or acoustic starter pistol and charting the decay response.
This can now be done computationally by a variety of methods and analyzers. We can measure a shorter sample of time and then extrapolate the results to the RT60 time frame. The assumption is that the decay trend of the first 15, 20 or 30 dB would continue with a longer measurement. Early decay time EDT measurements use a different starting point the first reflection than the RT series direct sound arrival.
As the name implies, this is a statistical analysis of the early reflections. The published value is derived from 15 dB of decay and extrapolated to the 60 dB equivalent. EDT highlights the different perspectives of acousticians and sound engineers.
An EDT measurement characterizes a room without direct sound and a free-field speaker measurement characterizes the direct sound without a room. This stands for noise criteria, which relates to its perceived loudness. The weighting is level dependent like the equal loudness contours.
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