MPEG, the MP3 Standard, and Audio Compression

Transcription

1 MPEG, the MP3 Standard, and Audio Compression Mark ilgore and Jamie Wu Mathematics of the Information Age September 16, 23 Audio Compression Basic Audio Coding. Why beneficial to compress? Lossless versus Lossy Compression. How are MP3s Compressed? What makes MP3 Compression Different? What other formats lie in our future? 1

2 PCM Why Compress?? Eliminate redundancy Most basic encoder/decoder is PCM Lots of redundancy b/c PCM representation is a basic sine wave If representing the sine wave based on frequency rather than time, only need to store information regarding frequency, amplitude, and phase in order to represent the information Can reduce data without information loss Extends playing time, Allows for miniaturization and greater equipment tolerance, Reduces cost 2

3 Lossless vs. Lossy (Perceptive) Lossless coding allows perfect reconstruction of a signal (theoretically) Lossy Coding creates a more highly compressed signal, but some unnecessary frequencies are eliminated Perceptually, however, lossy coding results in no difference in how it SOUNDS to a person MP3s are lossy, but perceptually lossless MPEG Moving Picture Experts Group Aim to create standards relating to synchronized audio and video compression MPEG-1 MPEG-2 3

4 MPEG-1 Block Diagrams Topics Discussed in Detail After Diagrams Layers I and II Filter Bank (32 Sub-Bands) 31 Uniform Midtread Quanitzer Bitstream Formatting Coded Audio Data DFT 512/124 Hann Window Psychoacoustic Model Coding of Side Information 4

5 Layer III Filter Bank (32 Sub-Bands) 31 MDCT 511 Non-Uniform Midtread Quantizer Rate/Distortion Loop DFT 2 * 124 Hann Window Psychoacoustic Model Huffman Coding Coding of Side Information Bitstream Formatting Coded Audio Data Time to Frequency Mapping Filters parse signal to bands Quantized to a limited number of bits Noise put in bands barely audible Sent to decoder where sound is restored Input H y y G Output x x H y y G Encoder Decoder 5

6 Z Transform Assists in splitting frequencies Discrete Time generalization of the Fourier transform Important Properties Linearity Convolution Theorem Delay Theorem Can model all kinds of filter banks through it Representation of frequency content Layer III Filter Bank (32 Sub-Bands) 31 MDCT 511 Non-Uniform Midtread Quantizer Rate/Distortion Loop DFT 2 * 124 Hann Window Psychoacoustic Model Huffman Coding Coding of Side Information Bitstream Formatting Coded Audio Data 6

7 Time to Frequency Mapping Filters parse signal to bands Quantized to a limited number of bits Noise put in bands barely audible Sent to decoder where sound is restored Input H y y G Output x x H y y G Encoder Decoder MPEG Time to Frequency Mapping Analysis Filter: Synthesis Filter: 1 2 π 32 h k [ n] = h[ n] cos k + ( n + 16) 1 π [ n] = 32 h[ n] cos k + ( n + 16) k =,1,,31; n =,1,,511 Uses a filter of 32 bands, signal represented by 512 samples The above equations allow for taking apart the signal (the h part of the time to frequency mapping diagram) and putting it back together (the g part of the time to frequency mapping diagram) g k

8 Layer III Filter Bank (32 Sub-Bands) 31 MDCT 511 Non-Uniform Midtread Quantizer Rate/Distortion Loop DFT 2 * 124 Hann Window Psychoacoustic Model Huffman Coding Coding of Side Information Bitstream Formatting Coded Audio Data PQMF & MDCT Both are methods of time to frequency mapping Pseudo-Quadrature Mirror Function Multiple Discrete Cosine Transformation Mathematically, they are equivalent PQMF involves using Z transforms to represent the amplitudes of the frequency MDCT involves performing a block transform using a window to represent amplitudes These amplitudes are then quantized 8

9 Layer III Filter Bank (32 Sub-Bands) 31 MDCT 511 Non-Uniform Midtread Quantizer Rate/Distortion Loop DFT 2 * 124 Hann Window Psychoacoustic Model Huffman Coding Coding of Side Information Bitstream Formatting Coded Audio Data Pyschoacoustic Model determines masking threshold for each sub band Uses human auditory property of Auditory Masking 9

10 Non-uniform Quantizer Analog to digital Quantizer: Maps amplitude values into finite number of bits Non-uniform : changes sample size according to amplitude values parts of signal with lesser amplitude coded with greater accuracy increases signal to noise ratio (SNR) Layer III Filter Bank (32 Sub-Bands) 31 MDCT 511 Non-Uniform Midtread Quantizer Rate/Distortion Loop DFT 2 * 124 Hann Window Psychoacoustic Model Huffman Coding Coding of Side Information Bitstream Formatting Coded Audio Data 1

11 Huffman coding For better data compression, variable-length Huffman codes are used to encode the quantized samples. quantized MDCT coefficients (for long blocks) arranged in order from lowest to highest frequency whole range divided into 3 sections, each coded with a different set of Huffman tables Bitstream Formatting formats encoded quantized samples into an encoded bitstream final form in which the compressed signal is transmitted. 11

12 MPEG-4 and The Future? Incorporates speech and music compression More of an extension of MPEG-2 compression techniques with independent techniques geared specifically at coding for speech content (some coding for meaning) Hasn t really taken off yet, only time will tell MPEG-2 AAC (Advanced Audio Coding) is the audio format that is used if you download from the apple itunes store 12