Glossaire

Analog to Digital (A/D) Conversion: The process of "digitizing" an analog signal by sampling its amplitude at regular intervals. This process almost always involves limiting the frequency content of the digitized signal to a maximum of one-half the sampling rate, as this provision enables perfect reconstruction of the original band-limited signal from its samples.

Amplitude: The size of a real number (e.g., a number of volts), in either the positive or negative direction. The term amplitude typically refers to numbers that are not complex or plotted on a logarithmic scale, such as the numbers stored in the A/D process. (Numbers expressed logarithmically are more properly called magnitudes.)

Attenuation: A decrease in the level of a signal. Attenuation can refer to reduction in level for a specified frequency range or a decrease in the overall level.

Coherence Function: In the context of transfer function measurements, Coherence is essentially a measure of the signal to noise ratio in a measurement and the linearity of the system under test. It is calculated by dividing the averaged cross spectrum of the measurement and reference signals by the power spectrum of the reference signal – or to put it another way, for each frequency we multiply the averaged reference signal, by the averaged measurement signal and then divide the result by the square of the reference signal. In a perfect world, or at least a perfectly linear and noise free system or transmission medium, all of the above would be the same number meaning the coherence function would essentially boil down to some number divided by itself, which is to say 1. In the real world, differences between the measurement and reference signals more commonly yield a number somewhere between 0 and 1 which we display as a percentage in Smaart.

Compressor: An electronic device that causes changes in output gain (typically attenuation) as a function of the input level. These devices should NOT be used when making transfer function measurements as they are nonlinear by nature and Transfer Function measurements assume the system under test is a Linear Time-Invariant system.

Crosstalk: Undesired energy in one signal (or channel) introduced from an adjacent signal or channel.

Data Window Function: Any of group of mathematical functions that affect the amplitude of a signal over some period of time. Data windows are commonly used to condition a time-domain signal before performing a Discreet Fourier Transform (DFT) to reduce the ringing artifacts associated with abrupt truncation of the signal. In theory data windows can be virtually any shape. In practice, the most useful windows for transforming audio data are bell shaped windows such as raised cosine (Hann, Hamming, Blackman) or Gaussian windows that smoothly reducing the amplitude of the time domain data at the beginning and end of a finite time/amplitude series to be transformed.

Decay Rate: The rate at which a signal decays (diminishes in magnitude) after being stimulated by an impulse or a terminated stimulus signal. In acoustics, this quantity is usually evaluated on the basis of specified frequency ranges and expressed in either decibels per second, or as the amount of time it would be required for the signal to decay 60 decibels at the observed rate of decay. (see Reverberation Time)

Decay Time: See Reverberation Time.

Decibel: The decibel, often abbreviated as dB, is a logarithmic ratio between two values. In electronics and acoustics, decibels most commonly refer to the ratio between a given amplitude value and the number 1, where some reference value such as the maximum output of an A/D converter (dB Full Scale or dBFS) or the threshold of audibility for human hearing (for dB SPL) is scaled to equal 1. The decibel value for an amplitude is then calculated as: dB = 20 • Log10(A) = 10 • Log10(A^2), where A is linear amplitude. In this case, amplitude values greater than one yield positive decibel values and numbers smaller than one become negative dB values. This is why dB FS values are always negative and SPL values are essentially always positive.

Discrete Fourier Transform (DFT): A mathematical technique for decomposing complex waveforms of finite length into a series of component sine and cosine waves at regularly spaced intervals. The spacing between frequencies or frequency resolution of the DFT is a function is a function of its size and the sampling rate used to capture the data. By plotting the amplitudes of these component sine waves on an x/y graph we can get a picture of the spectral content (spectrum) of the original time-domain signal.

Domain: In signal processing the term "domain" refers to the independent variable of a signal. By convention, when graphing a signal the independent variable is typically placed on the horizontal (x) axis of the plot with the dependent variable on the vertical (y) axis. So in Smaart for example, an impulse response display with time (the independent variable) on the x axis and amplitude (the dependent variable) on the y-axis is referred to as a time domain display. Similarly, Spectrum and Transfer Function displays where magnitude or phase shift are plotted as a function of frequency are called frequency-domain displays.

Dynamic Range: The difference in level between the highest and lowest signal a system can accept or reproduce, for example the range between the noise floor and the clipping voltage of an amplifier, typically expressed in decibels.

Equalizer (EQ):  A device with some number of filters used to change the gain or attenuation of a signal at some frequencies but not others. the term equalizer comes from  the fact that a primary application for this type of device is to "flatten out" (i.e. equalize) the most offending lumps and bumps in the frequency response curve of a sound system to make it more acoustically transparent. Equalizer filters may be "active," providing either boost or attenuation in the filter's passband, or "passive" (attenuation-only). The gain of each filter is usually independently adjustable. The center frequencies and bandwidths of filters can be variable or fixed. A filter bank made up of bandpass filters with fixed frequencies and bandwidths, e.g., on 1/3-octave intervals is commonly referred to as a graphic EQ. When the frequencies and bandwidths for each filter in a filter bank are variable along with the gains, it is called a parametric EQ.

Fast Fourier Transform (FFT): A Fast Fourier Transform is a special case of a Discrete Fourier Transform that is optimized for ease of computation. In practice this typically involves limiting the lengths of time domain signals to be transformed to a power of 2 samples in length (e.g., 16, 32, 64, 128, 256...). This limitation allows some shortcuts to be used in calculating a DFT on a digital computer using binary math that significantly reduce the number of computational operations required.

FFT Time Constant: The amount of time it takes to collect all the samples required for a single FFT frame of a given size at a given sampling rate. The time constant of an FFT, also called the time window, can be calculated by dividing the FFT size by the sampling rate. For example, a 4k FFT sampled at 44.1k samples/second has a time window of 0.09 seconds.

Graphic Equalizer: An equalizer with some number of bandpass filters used to change the gain or attenuation of a signal at pre-selected frequencies. The bandwidths and center frequencies of the filters are typically spaced on octave or fractional octave intervals and usually are not adjustable by the end user. The term "graphic" comes from the fact that a series of linear faders arranged side-by-side are typically used to adjust the gains of individual filters so that the knobs on the faders forms a sort of a rough graph suggestive of the unit's response curve. In practice however, interactions between adjacent filters can often make the term something of a misnomer.

Impulse Response: The response of a system to an impulsive stimulus in the time domain. The impulse response of linear time invariant (LTI) system is also the inverse Fourier transform of its transfer function.

Latency: In signal processing, the delay through a given device or system. Latency is also sometimes referred to as the throughput delay for a device. All digital signal processing devices introduce some amount of latency into a signal chain. In small amounts this may have very little perceptual impact on the performance of a system, but in some cases it can cause problems even in relatively small doses, e.g., for monitoring during a performance. And of course when a signal has to travel though several digital devices between its source and its destination, even small amounts of throughput delay per device can add up.

Linear Scale: A set of values in which values are evenly spaced. On a linear scale, each value (or unit) has equal dimension and integer multiples of any number or unit represent equal strides. So 1, 2 and 3... are even intervals, as are 10, 20, 30... as opposed to a logarithmic scale where each integer increase in the power of a number represents an even stride.

Linear Time Invariant (LTI) System: It's not uncommon for descriptions of linear time invariant systems to run pages in length and include a lot of scary math. But in simple terms, LTI essentially means that a given input will always produce a predictably and proportionally scaled output and should always require the same amount of time to work its way through the system. For example, if you put in a five and get out a 10, then putting in a one should get you a two and throughput delay should be the same in both cases. Gain and latency through the system need not be the same for all frequencies, but they should be consistent for a given frequency. Most of the components in a sound system, with the exception of intentionally nonlinear processors such as compressors, limiters and special effects, are intended to be LTI systems. So one other really useful property of LTI systems from our point of view is that they can be completely characterized by their transfer function in the frequency domain and/or their impulse response in the time domain.

Logarithmic Scale: A scale on which each power of a given number (e.g., ten) is given equal dimension. On a logarithmic scale, orders of magnitude, e.g., 10, 100, 1000, 10,000... (a.k.a., 10^1, 10^2, 10^3, 10^4...), are equal intervals.On a base 10 logarithmic scale, orders of magnitude are often referred to as "decades." On a base 2 scale, each stride is essentially one octave.

Magnitude: A number assigned to a quantity so that it may be compared with other quantities. As a convention in our documentation, we normally use the term amplitude to refer to linearly scaled quantities and magnitude when discussing amplitudes cast in logarithmic units such as decibels or orders of magnitude.

Nyquist Frequency: Named for Harry Nyquist, a pioneer in the field of digital signal processing (although it wasn't called that at the time), the Nyquist frequency is a relative quantity equal to one half of the sampling rate used to record a digitized signal. The Nyquist frequency is important because it represents the theoretical limit for the highest frequency that can be accurately reconstructed from a sampled signal. (In practice, the real-world limit tends to a little lower due to the difficulties associated with creating a perfect brick-wall low pass filter for anti-aliasing and signal reconstruction.)

Octave-Band Resolution: On an octave or fractional octave band display the aggregate power for all the frequencies within each band is summed and displayed as a single value per band. It is a common practice to display octave banded data as a histogram (bar chart), rather than a line trace or scatter plot, to better convey the idea that each value shown on the graph represents the total power across a range of frequencies, not just a single frequency point at the band center. Note that by convention, the nominal center frequencies given for ISO standard octave and 1/3-octave bands are slightly different than the exact band center frequencies in most cases, but they're close.

Overlap: For Smaart's purposes, the term Overlap refers to the amount of data each successive FFT Frame shares in common with the one before. Overlapping FFT frames are analogous to shingles on a roof. When no overlap is used, each new FFT frame begins where the last one stopped, as beads on a string.

Parametric Equalizer: An equalizer or digital filter bank in which the relative gain or attenuation, frequency and bandwidth of individual filters are independently adjustable.

Phase Shift: A timing difference in a signal (relative to some reference) at one or more frequencies, typically expressed in degrees, where 360° = one full cycle at a given frequency.

Pink Noise: A random (or pseudorandom) signal in which, over a given averaging period, each Octave-band (or other logarithmically spaced interval across the frequency spectrum) has an equal amount of energy.

Propagation Delay: The time it takes for sound to travel from one place (typically a loudspeaker) to another place (typically a microphone).

Reverberation Time:  In acoustics, the amount of time required for audio energy introduced into a system (typically a room) to diminish, or decay by 60 decibels following the cessation of a stimulus signal used to excite the system — e.g., a balloon pop, gun shot or terminated pink noise. It is normally stated band-by-band for individual octave bands. By convention, decay times are normalized to the time required for 60 dB of decay at an observed rate of decay, regardless of the amplitude range actually measured. 60 dB decay time is often referred to as "RT60" or "T60", which is sometimes a source of confusion. And just to confuse things a little more ISO 3382 specifies that it should be called T20 or T30, where the "20" and "30" refer to the decay range actually measured. The main thing to remember is that all of the above refer to 60 dB decay time within a stated frequency range. When a single-number reverberation time is given, according to the ISO standard it should be the average of the reverberation times for the 500 Hz and 1kHz octave bands, also called "Tmid."

RT60: See Reverberation Time.

Sampling Rate: The number of times that the amplitude of a signal is measured within a given period of time in an analog-to-digital conversion process. For audio-frequency signals, sampling rate is typically expressed in samples/second or Hertz.

Signal: Strictly speaking a signal can be any set of values that depends on some other set of values. The independent variable in this case, e.g., time or frequency, is said to be the domain of the signal. In audio and acoustics the things we most commonly think of as signals are time domain signals, where voltages or numeric values representing amplitude (the dependent variable) vary over time (the independent variable). But by strict definition, most of the things we see in Smaart could also be called signals, including Transfer Function and RTA displays where amplitude or phase shift are presented as a function of frequency, rather than time.

Sound Pressure Level (SPL): The RMS level of pressure waves in air expressed in decibels, referenced to the threshold of audibility for human hearing where 0 dB is approximately equal to the quietest sound the average human being can detect (and 94 dB = 1 Pascal). SPL is typically integrated over some period of time, e.g. using the Fast and Slow time integration settings found on all standard sound level meters. It is usually weighted by frequency to reflect perceptual characteristics of human hearing using standard A or C weighting curves specified in IEC and ANSI standards related to the measurement of sound levels.

Spectrograph: A three-dimensional data plot, displayed in two dimensions with color representing the third dimension (or z-axis). The spectrograph is a topographical representation of the once-common waterfall display.

Spectrum: The frequency content of a given signal.

Speed of Sound: The speed at which sound waves propagate through a transmission medium such as air or water. This quantity is dependent actors such as temperature and density of the material of propagation. Useful rule-of thumb values for the speed of sound in air at room temperature are 1130 ft/sec, or 344 m/sec. In Smaart the speed of sound is used primarily to calculate distance equivalents for time differences and can be set in Delay Options.

T60: See Reverberation Time.

Transfer Function: The frequency (magnitude and phase) response of the system, function or network. The transfer function of the linear time invariant (LTI) system can be measured directly, using techniques such as TDS or dual-FFT transfer function measurements that compare the output of the system to its input signal in the frequency domain, or indirectly by taking the Fourier transform of its impulse response.

Time Constant: In physics and engineering the term time constant is most commonly used to denote a time span between reference or threshold points in continuous processes, such as rise or decay time in the step response of filters, heating and cooling times in thermal systems and lag times in mechanical systems. In the field of acoustic measurement we often use (or perhaps misuse) the term to mean the total time required for discrete processes, such as the time it takes to collect enough samples for an FFT  and/or the time span of an impulse response measurement. This is to say that we tend to use the term interchangeably with Time Window, which might arguably be a bad thing to do that we should stop doing, but probably won't.

Time Window: The amount of time required for and/or represented by a measurement or other process. Often used (or perhaps misused) interchangeably with Time Constant (see above).

White Noise: A random (or pseudorandom) signal in which over a given averaging period, each frequency has equal energy. White noise is a common test signal electronics. It is seldom used in testing systems that include loudspeakers because it has so much high-frequency energy that it can easily damage HF components of the system and human hearing as well.