In order to determine what information in an audio signal is perceptually irrelevant, most lossy compression algorithms use transforms such as the modified discrete cosine transform ( MDCT ) to convert time domain sampled waveforms into a transform domain.

More generally, lossy compression can be thought of as an application of transform coding – in the case of multimedia data, perceptual coding: it transforms the raw data to a domain that more accurately reflects the information content.

While data reduction ( compression, be it lossy or lossless ) is a main goal of transform coding, it also allows other goals: one may represent data more accurately for the original amount of space – for example, in principle, if one starts with an analog or high-resolution digital master, an MP3 file of a given size should provide a better representation than a raw uncompressed audio in WAV or AIFF file of the same size.

The DCT, and in particular the DCT-II, is often used in signal and image processing, especially for lossy data compression, because it has a strong " energy compaction " property ( Ahmed, Natarajan and Rao, 1974 ; Rao and Yip, 1990 ): most of the signal information tends to be concentrated in a few low-frequency components of the DCT, approaching the Karhunen-Loève transform ( which is optimal in the decorrelation sense ) for signals based on certain limits of Markov processes.

Motion JPEG uses a lossy form of intraframe compression based on the discrete cosine transform ( DCT ).

If the image were partitioned directly and the wavelet transform separately applied to each segment, under lossy compression the boundaries between segments would tend to be noticeable in the reconstructed image even when no

Avoiding pre-echo is a substantial design difficulty in transform domain lossy audio codecs such as MP3, MPEG-4 AAC, and Vorbis.

Wave files can also contain data encoded with a variety of ( lossy ) codecs to reduce the file size ( for example the GSM or MP3 formats ).

* Lossy codecs: Many of the more popular codecs in the software world are lossy, meaning that they reduce quality by some amount in order to achieve compression.

This is especially true if the data is to undergo further processing ( for example editing ) in which case the repeated application of processing ( encoding and decoding ) on lossy codecs will degrade the quality of the resulting data such that it is no longer identifiable ( visually, audibly or both ).

The decreasing cost of storage capacity and network bandwidth has a tendency to reduce the need for lossy codecs for some media.

* In lossy predictive codecs, previous and / or subsequent decoded data is used to predict the current sound sample or image frame.

The compression ratio ( that is, the size of the compressed file compared to that of the uncompressed file ) of lossy video codecs is nearly always far superior to that of the audio and still-image equivalents.

Another technique involves simply transcoding from one lossy video format to another, which exploits the difference in the how the separate video codecs process motion and color information.

The two video codecs are the lossless " FFV1 ", and the lossless and lossy Snow codec, the development of which has stalled, while its bitstream format hasn't been finalized yet, making it experimental for now ( February 2011 ), and the multimedia container is " NUT " which is also not being actively developed anymore, but is still maintained.

However, Apple Lossless is not a variant of AAC ( which is a lossy format ), but rather a distinct lossless format that uses linear prediction similar to other lossless codecs.

( Previously only recording to ATRAC lossy codecs was possible.

This allows the use of lossy and lossless codecs together.

The PSNR is most commonly used as a measure of quality of reconstruction of lossy compression codecs ( e. g., for image compression ).

Rockbox on software decoding platforms ( non-Archos ) supports playback of twelve lossy codecs ( depending on how one counts ), five lossless, two uncompressed and twelve miscellaneous formats.

# Texture is encoded by lossy compression in a way similar to minimum description length ( MDL ) principle, but here the length of the data given the model is approximated by the number of samples times the entropy of the model.

This makes lossy compression unsuitable for storing the intermediate results in professional audio engineering applications, such as sound editing and multitrack recording.

* Spatial Audio Coding ( MPEG Surround ), a lossy compression format for surround sound

The Layer III ( MP3 ) component uses a lossy compression algorithm that was designed to greatly reduce the amount of data required to represent an audio recording and sound like a decent reproduction of the original uncompressed audio for most listeners.

** The CD audio still bears the artifacts of compression, so converting it back into a lossy format such as MP3 may aggravate the sound artifacts of encoding ( see transcoding ).

Transcoding files between lossy formats always results in lower quality sound.

It is better to retain a copy in a lossless format ( such as TTA, FLAC or WavPack for sound ), and then encode directly from the lossless source file to the lossy formats required.

Most audio formats use lossy compression, to produce as small as possible a file compatible with the desired sound quality.

Generally, lossy data compression schemes are guided by research on how people perceive the data in question.

In lossy audio compression, methods of psychoacoustics are used to remove non-audible ( or less audible ) components of the signal.

The fact that the lossy spectrograms are different from the uncompressed one indicates that they are in fact lossy, but nothing can be assumed about the effect of the changes on perceived quality.

Most lossy compression reduces perceptual redundancy by first identifying sounds which are considered perceptually irrelevant, that is, sounds that are very hard to hear.

Other types of lossy compressors, such as the linear predictive coding ( LPC ) used with speech, are source-based coders.

Some of these methods are inherently lossy while others may preserve all relevant information from the original, uncompressed video.

In contrast, lossy compression ( for example JPEG, or MP3 ) can achieve much higher compression ratios at the cost of a decrease in quality, as visual or audio compression artifacts from loss of important information are introduced.

Information-theoretical foundations for lossy data compression are provided by rate-distortion theory.

There are two basic lossy compression schemes:

This is because these types of data are intended for human interpretation where the mind can easily " fill in the blanks " or see past very minor errors or inconsistencies – ideally lossy compression is transparent ( imperceptible ), which can be verified via an ABX test.

Flaws caused by lossy compression that are noticeable to the human eye or ear are known as compression artifacts.

Many media transforms, such as Gaussian blur, are, like lossy compression, irreversible: the original signal cannot be reconstructed from the transformed signal.

Lossless audio formats are most often used for archiving or production purposes, with smaller lossy audio files being typically used on portable players and in other cases where storage space is limited and / or exact replication of the audio is unnecessary.

Parametric and lossy ' instantaneous ' ( i. e. electronic ) nonlinear optical phenomena, in which the optical fields are not too large, can be described by a Taylor series expansion of the dielectric Polarization density ( dipole moment per unit volume ) P ( t ) at time t in terms of the electrical field E ( t ):

More frequently, the smaller file sizes of compressed but lossy formats such as MP3 are used to store and transfer audio.

The latest versions of Sony's ATRAC are ATRAC3 and ATRAC3plus, both of which are true lossy compression schemes and both require decompression on replay.

DCTs are important to numerous applications in science and engineering, from lossy compression of audio ( e. g. MP3 ) and images ( e. g. JPEG ) ( where small high-frequency components can be discarded ), to spectral methods for the numerical solution of partial differential equations.