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Sony Vegas 5 Manual

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    							APPENDIX BGLOSSARY
    329
    Clipboard
    The Clipboard is where data that you have cut or copied in Vegas software is stored. You can then paste the 
    data back into Vegas software at a different location, or paste it into other applications. Some data, such as 
    audio, cannot be pasted into applications such as Microsoft Word or Notepad, but the text data from the 
    Edit Details window can be pasted. This allows you to then print or format the data. The Video Preview 
    window also lets you capture still frames to the Clipboard for use in any image editing program. For more 
    information, see Understanding the Video Preview window on page 253.
    Clipping
    Clipping is what occurs when the amplitude of a sound is above the maximum allowed recording level. In 
    digital systems, clipping is seen as a clamping of the data to a maximum value, such as 32,767 in 16-bit data. 
    Clipping causes sound to distort.
    Codec
    An acronym for COmpressor/DECompressor. A codec is an computer algorithm that is used to compress 
    video and audio data, shrinking file sizes and data rates.
    Compositing
    Compositing is the term used to describe the way separate video sources are mixed together. Overlay titles 
    are composited onto a background video sequence.
    Crossfade
    Mixing two pieces of overlapping audio or video by fading one out as the other fades in.
    Cutoff frequency
    The cutoff frequency of a filter is the frequency at which the filter changes its response. For example, in a 
    low-pass filter, frequencies greater than the cutoff frequency are attenuated while frequencies less than the 
    cutoff frequency are not affected.
    DC Offset
    DC Offset occurs when hardware, such as a sound card, adds DC current to a recorded audio signal. This 
    current causes the audio signal to alternate around a point above or below the normal -infinity dB (center) 
    line in the sound file. To see if you have a DC offset present, you can zoom all the way into a sound file and 
    see if it appears to be floating over the center line.
    Decibel (dB)
    A unit used to represent a ratio between two numbers using a logarithmic scale. For example, when 
    comparing the numbers 14 and 7, you could say 14 is two times greater than the number 7; or you could say 
    14 is 6 dB greater than the number 7. Where did we pull that 6 dB from? Engineers use the equation dB = 20 
    x log (V1/V2) when comparing two instantaneous values. Decibels are commonly used when dealing with 
    sound because the ear perceives loudness in a logarithmic scale.
    In Vegas software, most measurements are given in decibels. For example, if you want to double the 
    amplitude of a sound, you apply a 6 dB gain. A sample value of 32,767 (maximum positive sample value for 
    16-bit sound) can be referred to as having a value of 0 dB. Likewise, a sample value of 16,384 can be referred 
    to having a value of -6 dB.
    Device Driver
    A program that enables Microsoft Windows to connect different hardware and software. For example, a 
    sound card device driver is used by Microsoft Windows software to control sound card recording and 
    playback. 
    						
    							330
    GLOSSARYAPPENDIX B
    Digital Signal Processing (DSP)
    A general term describing anything that alters digital data. Signal processors have existed for a very long 
    time (tone controls, distortion boxes, wah-wah pedals) in the analog (electrical) domain. Digital Signal 
    Processors alter the data after it has been digitized by using a combination of programming and mathematical 
    techniques. DSP techniques are used to perform many effects such as equalization and reverb simulation.
    Since most DSP is performed with simple arithmetic operations (additions and multiplications), both your 
    computer’s processor and specialized DSP chips can be used to perform any DSP operation. The difference is 
    that DSP chips are optimized specifically for mathematical functions while your computer’s microprocessor is 
    not. This results in a difference in processing speed.
    DirectX Application Programming Interface
    A set of interfaces designed by Microsoft for multimedia development. A DirectX® plug-in, such as the Sony 
    Pictures Digital Noise Reduction™ DirectX plug-in, uses the DirectX Media Streaming Services (DMSS) 
    API. Because DMSS is a standard API, a DirectX plug-in can be used in any application that supports 
    DMSS.
    Dithering
    The practice of adding noise to a signal to mask quantization noise (see also Noise Shaping).
    Drag and Drop
    A quick way to perform certain operations using the mouse. To drag and drop, you click and hold a 
    highlighted selection, drag it (hold the left-mouse button down and move the mouse) and drop it (let go of 
    the mouse button) at another position on the screen.
    Dynamic Range
    The difference between the maximum and minimum signal levels. It can refer to a musical performance 
    (high volume vs. low volume signals) or to electrical equipment (peak level before distortion vs. noise floor). 
    For example, orchestral music has a wide dynamic range, while thrash metal has a very small (always loud) 
    range.
    Emphasis
    A rudimentary noise reduction process that involves a boost in the high frequencies during the recording of 
    the CD and a complimentary cut in the same frequencies during the playback of the CD. The result reduces 
    high frequency noise without disrupting the natural frequency response of the source material. If the 
    emphasis flag is set for a track, any CD player that has a de-emphasis circuit will impart the high frequency 
    cut on the track. Be aware that Vegas software cannot impart the pre-emphasis boost on a track; it can only 
    set the emphasis flag.
    Endian (Little and Big)
    Little and Big Endian describe the ordering of multi-byte data that is used by a computer’s microprocessor. 
    Little Endian specifies that data is stored in a low to high-byte format; this ordering is used by the Intel® 
    microprocessors. Big Endian specifies that data is stored in a high to low-byte format; this ordering is used by 
    the Motorola® microprocessors. 
    Envelopes (Audio and Video)
    Envelopes, as used by Vegas software, are a way of automating the change of a certain parameter over time. 
    In the case of volume, you can create a fade out (which requires a change over time) by adding an envelope 
    and creating an extra point to the line that indicates where the fade starts. Next, you pull the end point of 
    the envelope down to -inf. For more information, see Working with track envelopes on page 126. 
    						
    							APPENDIX BGLOSSARY
    331
    Equalization (EQ)
    The process by which certain frequency bands are raised or lowered in level. EQ has various uses. The most 
    common use in Vegas software is to simply adjust the subjective timbrel qualities of a sound.
    Event
    Media files that have been dragged onto the timeline in Vegas software are referred to as events. An event is 
    actually a window into a media file and is a reference, or pointer, to the file. It can display all or part of a 
    media file and can be edited without altering the source media (nondestructive). 
    Field Order
    Video that is displayed on a television is interlaced. This means that every frame of video is actually 
    composed of two fields, each of which is made up of half of the lines that make the final frame. These two 
    fields are woven together in alternate lines, but which of the two fields is displayed first (the field order) can 
    be important. You can set the field order for video in the Project Properties dialog or, when rendering a 
    project, in the Custom Template dialog. For more information, see Interlacing and field order on page 322.
    File Format
    A file format specifies the way in which data is stored on your floppy disks or hard drive. In Windows for 
    example, the most common audio file format is the Microsoft WAV format. However, Vegas software can 
    read and write to many other file formats so you can maintain compatibility with other software and 
    hardware configurations.
    Frame Rate (Audio)
    Audio uses frame rates only for the purposes of synching to video or other audio.
    Frame Rate (Video)
    The speed at which individual images in the video are displayed on the screen. A faster frame rate results in 
    smoother motion in the video. However, more times than not, frame rate is associated with SMPTE standard 
    frame rates for video: 29.97 for NTSC (used in US, North and Central America, parts of South America, 
    and Japan), 25 for PAL (used in many parts of the world, including Europe and much of Asia), or 24 for film. 
    Frequency Spectrum
    The frequency spectrum of a signal refers to its range of frequencies. In audio, the frequency range is basically 
    20 Hz to 20,000 Hz. The frequency spectrum sometimes refers to the distribution of these frequencies. For 
    example, bass-heavy sounds have a large frequency content in the low end (20 Hz - 200 Hz) of the spectrum.
    Hertz (Hz)
    The unit of measurement for frequency or cycles per second (CPS).
    Insertion Point
    The insertion point (also referred to as the cursor position) is analogous to the cursor in a word processor. It 
    is where pasted data is placed or other data is inserted, depending on the operation. The insertion point 
    appears as a vertical flashing black line and can be moved by clicking the left mouse button anywhere in the 
    timeline. 
    Inverse telecine
    Telecine is the process of converting 24 fps (cinema) source to 30 fps video (television) by adding pulldown 
    fields. Inverse telecine, then, is the process of converting 30 fps (television) video to 24 fps (cinema) by 
    removing pulldown. 
    						
    							332
    GLOSSARYAPPENDIX B
    Markers
    Saved locations in the sound file. Markers can be displayed in the Trimmer window for sound files that 
    contain them, but more often, markers and regions are used at the project level to mark locations or sections 
    in the project. 
    Media Control Interface (MCI)
    A standard way for Microsoft Windows programs t o communicate with multimedia devices like sound cards 
    and CD players. If a device has a MCI device driver, it can easily be controlled by most multimedia Microsoft 
    Windows software.
    Media File
    A media file, or multimedia file, is any image, audio or video file on a computer. In Vegas software, you can 
    browse for these files in the Explorer window. You can drag media files to the timeline or insert them into 
    the Media Pool. Media files that have been dragged to the timeline are referred to as events. 
    MIDI Clock
    A MIDI device specific timing reference. It is not absolute time like MIDI timecode (MTC); instead, it is a 
    tempo-dependent number of ticks per quarter note. MIDI clock is convenient for synchronizing devices that 
    need to do tempo changes mid-song.
    MIDI Port
    A MIDI Port is the physical MIDI connection on a piece of MIDI gear. This port can be a MIDI in, out or 
    through. Your computer must have a MIDI port to output MIDI timecode to an external device or to receive 
    MIDI timecode from an external device.
    MIDI Timecode (MTC)
    MTC is an addendum to the MIDI 1.0 Specification and provides a way to specify absolute time for 
    synchronizing MIDI-capable applications. Basically, it is a MIDI representation of SMPTE timecode.
    Mix
    The process of combining multiple audio events and effects into a final output. The analogous process of 
    combining video events together is called compositing.
    Musical Instrument Digital Interface (MIDI)
    A standard language of control messages that provides for communication between any MIDI compliant 
    devices. Anything from synthesizers to lights to stage equipment can be controlled via MIDI. Vegas software 
    utilizes MIDI for synchronization purposes.
    Noise-shaping
    Noise-shaping is a technique that can minimize the audibility of quantization noise by shifting its frequency 
    spectrum. For example, in 44,100 Hz audio, quantization noise is shifted towards the Nyquist Frequency of 
    22,050 Hz. See also Dithering.
    Nondestructive Editing
    A type of editing used by Vegas software that involves a pointer-based system of keeping track of edits. 
    When you delete a section of audio in a nondestructive system, the audio on disk is not actually deleted. 
    Instead, a set of pointers is established to tell the program to play the active sections during playback.
    Nonlinear Editing (NLE)
    A method of editing video non-sequentially or in random order. Editing video in Vegas software is nonlinear 
    as opposed to editing video tape, which is linear. 
    						
    							APPENDIX BGLOSSARY
    333
    Normalize
    Refers to raising the volume so that the highest level sample in the file reaches a user-defined level. Use this 
    function to make sure you are fully utilizing the dynamic range available to you.
    Nyquist Frequency
    The Nyquist Frequency (or Nyquist Rate) is one-half of the sample rate and represents the highest frequency 
    that can be recorded using the sample rate without aliasing. For example, the Nyquist Frequency of 44,100 
    Hz is 22,050 Hz. Any frequencies higher than 22,050 Hz produce aliasing distortion in the sample if an anti-
    aliasing filter is not used while recording.
    OPT Plug-In
    A plug-in that uses Open Plug-in Technology (OPT) standard from Yamaha™. OPT plug-ins provide tools 
    for working with MIDI such as edit views, effect processors and filters, arpeggiators, and real-time panel 
    automation.
    Pan
    To place a mono or stereo sound source perceptually between two or more speakers.
    Peak File (.sfk)
    Vegas software displays the waveform of audio files graphically on a computer monitor. This visual 
    information must be generated by Vegas software when the audio file is opened and can take a few seconds. 
    Vegas software then saves this information as a peak file (.sfk). This file stores the information for displaying 
    waveform information so that opening a file is almost instantaneous. The peak file is stored in the directory 
    in which the file resides and has an .sfk extension. If the peak file is not in the same directory as the file, or is 
    deleted, Vegas software regenerates it the next time you open the file.
    Pixel Aspect Ratio
    Computers display pixels as squares: 1.0. Televisions display individual pixels as rectangles: 0.9091 
    (NTSC DV, D1), 1.0926 (PAL DV, D1), or other rectangular variations. Using the wrong pixel aspect ratio 
    can result in distortions or stretching of the video. You can set the pixel aspect ratio in the Project Properties 
    dialog or, when rendering, in the Custom Template dialog. You should choose the aspect ratio based on the 
    final movie’s destination. Consult your hardware manual if you are in doubt about the appropriate ratio. The 
    pixel aspect ratio is unrelated to the frame’s aspect ratio.
    Plug-In
    An effect that can be added to the product to enhance the feature set. Vegas software supports DirectX 
    compatible plug-ins. The built-in EQ, Compression and Dithering effects are also considered plug-ins 
    because they work in other DirectX-compatible applications.
    Plug-In Chain
    Plug-ins can be strung together into a chain so that the output of one effect feeds into the input of another. 
    This allows for complex effects that couldn’t otherwise be created.
    Pre-roll/Post-roll
    Pre-roll is the amount of time elapsed before an event occurs. Post-roll is the amount of time after the event. 
    The time selection defines the pre- and post-roll when recording into a selected event.
    Preset
    A snapshot of the current settings in a plug-in. Presets are created and named so that you can easily get back 
    to a sound or look that you have previously created. 
    						
    							334
    GLOSSARYAPPENDIX B
    A preset calls up a bulk setting of a function in Vegas software. If you like the way you tweaked that EQ, but 
    do not want to have to spend the time getting it back for later use, save it as a preset. Presets appear in the 
    top of plug-in windows in Vegas software.
    Pulldown
    In telecine conversion, fields are added to convert 24 fps film to 30 fps video.
    In 2-3 pulldown, for example, the first frame is scanned into two fields, the second frame is scanned into 
    three fields, and so on for the duration of the film. 2-3 pulldown is the standard for NTSC broadcasts of 24p 
    material. Use 2-3 pulldown when printing to tape, but not when you intend to use the rendered video in 
    Vegas software. Removing 2-3 pulldown is inefficient because the pulldown fields that are created for frame 
    3 span two frames:
    Use 2-3-3-2 pulldown when you plan to use your rendered video in Vegas software as source media. When 
    removing 2-3-3-2 pulldown, Vegas software simply discards frame three and merges the pulldown fields in 
    the remaining frames:
    Pulse Code Modulation (PCM)
    PCM is the most common direct binary representation of a level of an uncompressed audio signal. This 
    method of coding yields the highest fidelity possible when using digital storage.
    Punch-In
    Punching-in during recording means automatically starting and stopping recording at user-specified times. In 
    Vegas software, shorter events can be punched into longer ones.
    Quadraphonic
    A mixing implementation that allows for four discrete audio channels. These are usually routed to two front 
    speakers and two back speakers to create immersive audio mixes.
    Quantization (Audio)
    The process by which measurements are rounded to discrete values. Specifically with respect to audio, 
    quantization is a function of the analog-to-digital conversion process. The continuous variation of the 
    voltages of a analog audio signal are quantized to discrete amplitude values represented by digital, binary 
    numbers. The number of bits available to describe these values determines the resolution or accuracy of 
    quantization. For example, if you have 8-bit analog-to-digital converters, the varying analog voltage must be 
    quantized to 1 of 256 discrete values; a 16-bit converter has 65,536 values. Quantization is to level as 
    sampling rate is to time.
    24 fps film (top) and resulting NTSC video with 2-3 pulldown fields (bottom)
    24 fps film (top) and resulting NTSC video with 2-3-2-2 pulldown fields (bottom) 
    						
    							APPENDIX BGLOSSARY
    335
    Quantization Noise
    A result of describing an analog signal in discrete digital terms (see Quantization). This noise is most easily 
    heard in low resolution digital sounds that have low bit depths and is similar to a hiss while the audio is 
    playing. It becomes more apparent when the signal is at low levels, such as when doing a fade out. See also 
    Dithering.
    Quantizing (MIDI)
    The correction of rhythms to align with selected note lengths or beats in a MIDI sequence.
    Quantizing (Video)
    Limiting all editing to frame boundaries. For more information, see Quantizing to frames on page 89.
    Red Book specification
    The Red Book defines the specifications of every audio compact disc in every music store throughout the 
    world. Red Book specifications define not only the information within the disc (digital audio recorded at 
    44.1 kHz), but also the disc size itself and the way in which the audio is arranged. 
    Region
    A subsection of a sound file denoted by a start and end point. You can define any number of regions in a 
    sound file.
    Rendering
    The process by which Vegas software saves the project to a specific file format like AVI or WMA.
    Resample
    The act of recalculating samples in a sound file at a different rate than the file was originally recorded. If an 
    audio file is resampled at a lower rate, Vegas software decreases sample points. As a result, the file size and 
    the frequency range are reduced. When resampling to a higher sample rate, Vegas software interpolates extra 
    sample points in the sound file. This increases the size of the sound file but does not increase the quality. 
    When down-sampling, one must be aware of aliasing (see Aliasing). Vegas software automatically resamples 
    all audio to the project’s sample rate.
    Ripple; Ripple Editing
    A type of editing where events are moved out of the way to make room for newly inserted events as opposed 
    to simply being overwritten. When a one minute event is ripple inserted into a project, the duration of a 
    project lengthens by one minute. If ripple editing is turned off, the same operation would not affect the 
    overall duration of the project.
    Roll
    Originally, a conventional studio typically had two source decks that were used to play back video to a final 
    destination or output deck. These two source decks were commonly referred to as the A and B rolls. In Vegas 
    software, a video track can be configured to display an A and a B roll, which appear as sub-tracks. The 
    concept is extended further in Vegas software to include a transition roll between the A and B rolls. For more 
    information, see Understanding track layers on page 234.
    Ruler
    The ruler is the area above the tracks that shows the horizontal axis units.
    Sample
    The word sample is used in many different (and often confusing) ways when talking about digital sound. 
    Here are some of the different meanings: 
    						
    							336
    GLOSSARYAPPENDIX B
    A discrete point in time which a sound signal is divided into when digitizing. For example, an audio CD-
    ROM contains 44,100 samples per second. Each sample is really only a number that contains the 
    amplitude value of a waveform measured over time.
    A sound that has been recorded in a digital format; used by musicians who make short recordings of 
    musical instruments to be used for composition and performance of music or sound effects. These 
    recordings are called samples. In this manual, we try to use sound file instead of sample whenever referring 
    to a digital recording.
    The act of recording sound digitally (i.e., to sample an instrument) means to digitize and store it.
    Sample Rate
    The sample rate (also referred to as the sampling rate or sampling frequency) is the number of samples per 
    second used to store a sound. High sample rates, such as 44,100 Hz provide higher fidelity than lower sample 
    rates, such as 11,025 Hz. However, more storage space is required when using higher sample rates. Sampling 
    rate is to time as quantization is to level.
    Sample Size
    See Bit Depth.
    Sample Value
    The sample value (also referred to as sample amplitude) is the number stored by a single sample. In 16-bit 
    audio, these values range from -32768 to 32767. In 8-bit audio, they range from -128 to 127. The maximum 
    allowed sample value is often referred to as 100% or 0 dB.
    .sfap0
    Sony Pictures Digital audio proxy file. For more information, see Audio proxy files (.sfap0) on page 322.
    .sfk
    See Peak File.
    Shortcut Menu
    A context-sensitive menu that appears when you right-click certain areas of the screen. The functions 
    available in the shortcut menu depend on the object being clicked on as well as the state of the program. As 
    with any menu, you can select an item from the shortcut menu to perform an operation. Shortcut menus are 
    used frequently in Vegas software for quick access to many commands. An example of a shortcut menu can 
    be found by right-clicking any event along the timeline.
    Signal-to-Noise Ratio
    The signal-to-noise ratio (SNR) is a measurement of the difference between a recorded signal and noise 
    levels. A high SNR is always the goal.
    The maximum signal-to-noise ratio of digital audio is determined by the number of bits per sample. In 16-bit 
    audio, the signal to noise ratio is 96 dB, while in 8-bit audio, the ratio is 48 dB. However, in practice, this 
    SNR is never achieved, especially when using low-end electronics.
    Small Computer Systems Interface (SCSI)
    A standard interface protocol for connecting devices to your computer. The SCSI bus can accept up to seven 
    devices at a time including CD-ROM drives, hard drives and samplers. 
    						
    							APPENDIX BGLOSSARY
    337
    SMPTE
    SMPTE is the acronym for the Society of Motion Picture and Television Engineers (SMPTE). SMPTE 
    timecode is used to synchronize time between devices. The timecode is calculated in 
    Hours:Minutes:Seconds:Frames, where Frames are fractions of a second based on the frame rate. Typical 
    frame rates for SMPTE timecode can be 24, 25, 29.97 or 30 frames per second, depending on your local 
    standards.
    SMPTE Drop Frame Timecode
    A method of measuring time in video. Drop frame involves skipping two frame numbers (no frames are 
    actually dropped) every ten minutes to compensate for the difference between NTSC 29.97 fps video and 30 
    frame counts per second.
    Te l e c i n e
    The process of creating 30 fps video (television) from 24 fps film (cinema). See inverse telecine and pulldown.
    Te m p o
    Tempo is the rhythmic rate of a musical composition, usually specified in beats per minute (BPM).
    Time Format
    The format in which Vegas software displays the ruler and selection times. These include: time, seconds, 
    frames and all standard SMPTE frame rates. 
    Time Signature
    See Beats Per Measure.
    Timecode
    For more information, see Timecode on page 324.
    Tr a ck
    A discrete timeline for audio or video data. Events are placed on tracks and determine when sound or images 
    start and stop. Multiple audio tracks are mixed together to give you a composite sound that you hear. 
    Multiple video tracks are composited on top of each other to create the final video output.
    Track List
    The track list appears at the left side of the Vegas workspace and contains the master controls for each track. 
    From here you can adjust track volume or transparency, add track effects, mute or solo tracks, and reorder 
    tracks.
    Track View
    The track view, or timeline, is the space events appear on tracks.
    µ-Law
    µ-Law (mu-Law) is a companded compression algorithm for voice signals defined by the Geneva 
    Recommendations (G.711). The G.711 recommendation defines µ-Law as a method of encoding 16-bit 
    PCM signals into a nonlinear 8-bit format. The algorithm is commonly used in European and Asian 
    telecommunications. µ-Law is very similar to A-Law, however, each uses a slightly different coder and 
    decoder. 
    						
    							338
    GLOSSARYAPPENDIX B
    Undo Buffer
    This is the temporary file created before you do any processing to a project. This undo buffer allows the 
    ability to revert to previous versions of the project if you decide you don’t like changes you’ve made to the 
    project. This undo buffer is erased when the file is closed or when you choose 
    Clear Edit History from the Edit 
    menu.
    Undo/Redo
    These commands allow you to change a project back to a previous state when you don’t like the changes you 
    have made, or reapply the changes after you have undone them. The ability to undo/redo is only limited by 
    the size of your hard drive. See Undo Buffer.
    Undo/Redo History
    A list of all of the functions that have been performed to a file that are available to be undone or redone. 
    The undo/redo history gives you the ability to undo or redo multiple functions. To display the history list, 
    click the down-arrow on the 
    Undo () or Redo ( ) button.
    Video for Windows (AVI)
    See AVI.
    Virtual MIDI Router (VMR)
    A software-only router for MIDI data between programs. Vegas software uses the VMR to receive MIDI 
    timecode and send MIDI clock. No MIDI hardware or cables are required for a VMR, so routing can only be 
    performed between programs running on the same PC.
    WAV
    A digital audio file format developed by Microsoft and IBM. One minute of uncompressed audio requires 
    10 MB of storage.
    Waveform
    A waveform is the visual representation of wave-like phenomena, such as sound or light. For example, when 
    the amplitude of sound pressure is graphed over time, pressure variations usually form a smooth waveform.
    Waveform Display
    A section inside of the Trimmer window or on an audio event that shows a graph of the sound data 
    waveform. The vertical axis corresponds to the amplitude of the wave. For 16-bit sounds, the amplitude 
    range is -32,768 to +32,767. For 24-bit sounds, the range is -8,388,607 to +8,388,607. The horizontal axis 
    corresponds to time, with the left-most point being the start of the waveform. In memory, the horizontal axis 
    corresponds to the number of samples from the start of the sound file.
    Zero-crossing
    A zero-crossing is the point where a fluctuating signal crosses the zero amplitude axis. By making edits at 
    zero-crossings with the same slope, the chance of creating glitches is minimized. Vegas software simulates 
    zero crossings by applying short (10 mS default) fades to trimmed audio.
    Zipper noise
    Zipper noise occurs when you apply a changing gain to a signal, such as when fading out. If the gain does not 
    change in small enough increments, zipper noise can become very noticeable. Vegas software fades are 
    accomplished using 64-bit arithmetic, thereby creating no zipper noise. 
    						
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