# 2.4 Audio Compression

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1 2.4 Audio Compression Pulse Code Modulation Audio signals are analog waves. The acoustic perception is determined by the frequency (pitch) and the amplitude (loudness). For storage, processing and transmission in the computer audio signals must converted into a digital representation. The classical way to do that is called pulse code modulation (PCM). It consists of three steps: sampling, quantization and coding Sampling The analog signal is sampled periodically. At each sampling interval the analog value of the signal (e.g., the voltage level) is recorded as a real number. After sampling the signal is no longer continuous but discrete in the temporal dimension

2 Sampling Theorem of Nyquist In order to reconstruct the original analog signal without loss we obviously need a minimum sampling frequency. The minimum sampling frequency f A is given by the sampling theorem of Nyquist (1924): For noise-free channels the sampling frequency f A must be twice as high as the highest frequency occurring in the signal: f A = 2 f S Example: Sampling a Signal at Different Rates input waveform clock sampled output (a) Sampling rate is much higher than signal frequency input waveform clock (b) Sampling rate is lower than signal frequency sampled output input waveform clock (c) Sampling rate is at the Nyquist limit sampled output 2.4-4

3 Quantization The range of values occurring in the analog signal is subdivided into a fixed number of discrete intervals. Since all analog values contained in an interval will be mapped to the same interval number we introduce a quantization error. If the size of the quantization interval is a then the maximum quantization error is a/2. a/2 a/2 a Binary Coding We now have to determine a unique binary representation for each quantization interval. In principle any binary code does the job. The simplest code (which is in fact often used in practice) is to encode each interval with a fixed-size binary number

4 PCM: The Complete Process Sampling interval The combination of the steps sampling, quantization and binary coding is called Pulse Code Modulation (PCM) CODECs The devices performing A/D conversion and D/A conversion are called CODECs (Coders/Decoders). PCM-Signale Analogsignale Analogsignale CODEC CODEC Note: A modem is used to transmit digital signals over analog links, a codec is used to transmit analog signals over digital links

5 PCM Telephone Channel Sampling Rate Starting point: an analog CCITT telephone channel Frequency range: Hz, i.e., audio bandwidth: 3100 Hz (sufficient for speech) Sampling frequency: Sampling period: f A = 8 khz T A = 1/ f A = 1/8000 Hz = 125 s The sampling frequency chosen by CCITT is higher than the Nyquist limit: for a maximum frequency of 3400 Hz in the signal a sampling frequency of 6800 Hz would be sufficient. This has technical reasons (noise, influence of filters, channel separation, etc) Quantization of the Amplitude The minimum number of quantization intervals is determined by the understandability of speech at the receiver. Based on experimental experience CCITT has chosen 256 quantization intervals. With standard binary coding we thus need 8 bits per sample

6 Bit Rate of the PCM Channel We conclude that the bit rate of a standard PCM channel is 8 bits * 8000/s = 64 kbit/s Non-Linear Quantization With linear quantization all intervals have the same size, they do not depend on the amplitude of the signal. However it would be desirable to have a smaller amount of quantization noise at small amplitude levels because quantization noise is more disturbing in quiet times. This goal can be reached with non-linear quantization. We simply chose larger quantization intervals at higher amplitude values. Technically this can be done by a signal compressor which preceeds the coding step. At the receiver side an expander is used to reconstruct the original dynamics. Many compressors use a logarithmic mapping. In digital electronics this is often approximated by a piecewise-linear curve. The 13-segment compressor curve is a typical example

7 13-Segment Compressor Curve number of the quantisation interval /2 1_ ¼ 1/8 1/16 1/32 ½ normalised amplitude of the signal Delta Modulation Instead of coding the absolute values of the amplitude, the difference to the value in the previous interval is coded in one bit. Only steps of +1 or 1 are possible Signal changes too fast, coding error Quantization Intervals Coding: 1 = increasing signal 0 = decreasing signal time Sampling interval

8 Differential PCM (DPCM) In differential PCM we encode the actual difference between the signal values in two adjacent intervals with a small number of bits. This leads to a bit rate and precision between that of encoding the absolute values and delta modulation. Adaptive DPCM (ADPCM) The dynamics in real audio signals are often such that we have quiet periods and loud periods. In quiet periods (i.e., periods with low variance of the amplitude) we can encode the signal with fewer bits than in loud periods. This is called Adaptive Pulse Code Modulation (ADPCM). For example, ADPCM allows us to compress a HiFi stereo audio signal from 1.4 Mbit/s to 0.2 Mbit/s without loss of quality. Well-known ADPCM algorithms are -law and A-law Typical Sampling and Quantization Parameters Sampling Rate 8 khz telephony, -law encoding, SUN Audio 32 khz Digital Radio Broadcast 44,1 khz Audio-CD 48 khz Digital Audio Tape (DAT) Quantization 8 bits 256 amplitude levels: speech 16 bits amplitude levels: HiFi music

9 2.4.2 Audio Compression with Psycho-Acoustic Models Compression based on semantic irrelevance We remove those parts of the signal at the source that the receiver will not be able to hear anyway. Example: The Masking Effect A high-amplitude signal masks out a low-amplitude signal at an adjacent frequency Psycho-Acoustic Models Audio Level 200 Hz Masker 500 Hz Masker 2 khz Masker 5 khz Masker Masking Threshold khz

10 Example: MPEG Audio Characteristics Compression to 32, 64, 96, 128 or 192 kbit/s Audio channels Mono or Two independent channels or "Joint Stereo" Techniques Sampling rates: 32 khz, 44,1 khz or 48 khz 16 bits per sample Maximum encoding and decoding delay: 80 ms at 128 kbit/s A psycho-acoustic model controls the quantization Two Techniques in MPEG-1 Audio MUSICAM ASPEC Masking Pattern Universal Sub-band Integrated Coding and Multiplexing Advanced Spectral Entropy Coding Institut für Rundfunktechnik, München FhG Erlangen Sub-band Coding Overlapping dynamic frequency bands, entropy coding (Huffman) Simple and easy to implement Very good quality at very low bit rates

11 MPEG Audio Encoder and Decoder Encoder Digital Audio Signal (PCM) Time/ Frequency Mapping Quantizer and Coding ISO/MPEG/AUDIO Bitstream Frame Packing Psychoacoustic Model Decoder ISO/MPEG/AUDIO Bitstream Frame Unpacking Reconstruction Frequency/ Time Mapping Digital Audio Signal (PCM) Three Layers in MPEG Audio 1. Sub-band coding with 32 bands with the MUSICAM technique High data rate mono, stereo, 48 khz, 44.1 khz, 32 khz 2. Sub-band coding with MUSICAM, more complex psycho-acoustic model Intermediate Better sound quality at low bit rates 3. Transformation-based compression with the ASPEC technique Lowest data rate Stereo Audio in CD quality at less than 128 kbit/s! Mono Audio in telephone quality at 8 kbit/s MPEG audio layer three, encoded with ASPEC, is also called MP3 (!)

12 MP3 History (1) As early as 1987 the Fraunhofer Institut für Integrierte Schaltkreise (Institute of Integrated Circuits) in Erlangen (Germany) began with the development of audio compression techniques that took the specific properties of the human perceptual system into account. Their technique was included into the MPEG Audio standard of ISO (IS and IS ) as MPEG Audio Layer 3 (MP3). This is currently the strongest audio compression standard in use. The original goal was a reduction of the data rate by a factor of 12 compared to an audio CD, without an audible difference MP3 History (2) As usual, ISO only standardizes the technical parameters and the decoder. The inner workings of the encoder remain unspecified. This gives developers significant freedom to develop specific encoding techniques, and even get patents for their encoding algorithms. As a consequence we know very little about the exact implementation of the MP3 encoder written by the Fraunhofer Institute. Exact details on their psycho-acoustic model are not published. The Fraunhofer Institute also holds a patent on its optimized encoding mechanism for MP

13 MPEG Audio Layers (1) MP3 subdivides the data stream into frames. Each frame corresponds to the audio signal in a certain time period. It contains 384 samples. The samples represent values out of 32 frequency sub-bands. There are 12 values from each sub-band MPEG Audio Layers (2) Layer 1 Frequency masking: Usage of a DCT-based filter. At any given time the algorithm only considers one frame. The frequences occurring in this frame are subdivided into the frequency bands and then filtered. Layer 2 Temporal masking: At any given time the algorithm looks at three adjacent frames, the current, the previous and the next frame. This allows to take advantage of temporal masking effects as perceived by the human ear. Layer 3 Non-linear masking: The frequencies are subdivided into bands of different widths. Also, stereo channels are encoded differentially, i.e., the difference between the two channels rather than the absolute values are encoded. The last step is a Huffman coding of the coefficients

14 Layer 1: Psycho-Acoustic Effect 1. Sensitivity of the human ear 2. The frequency masking effect Experiment: Play a tone of 1 khz (the masking tone) at a certain amplitude (e.g., 60 db). Then add a test tone (e.g., of 1.1 khz) and increase its amplitude until the the test tone is heard. This will happen at a much higher amplitude than in the quiet Layer 1: Compression Apply a sub-band filter to subdivide the signal into 32 bands ( critical bands ). For each band, define a masking curve that indicates at which level the signal will be masked by adjacent bands. Algorithm: Compute the energy in each band. If the energy in a band is smaller than the masking threshold of a neighboring band, do not encode the band. Otherwise encode the band. Quantize the coefficients with a quantization factor. Choose the factor so that the quantization error is smaller than the masking factor (1 bit in the quantization corresponds to a noise of 6 db)

15 Layer 1: Example The table shows the levels of the first 16 out of the 32 bands Band Level The level of band 8 is 60 db. We assume that is has a masking threshold of 12 db for band 7 and of 15 db for band 9. The level of band 7 is 10 db (< 12 db), thus we ignore it. The level of band 9 is 35 db (> 15 db), thus encode it. Choose the quantization factor so that the quantization error will be less than 2 bits (12 db) Layer 2: Psycho-Acoustic Effect Temporal masking: When we hear a loud sound that suddenly stops, it takes a while until we can hear soft sounds again. Experiment: Play a masking tone of 1 khz at 60 db and a 1.1 khz test tone at 40 db (the test tone is not heard, it is masked). Stop the masking tone and after a short delay also the test tone. Vary the delay to find the time threshold at which the test tone can just be heard

16 Layer 2: Compression Repeat the experiment with other test tones: In a way similar to layer 1, we take advantage of this temporal phenomenon to mask out sub-bands, this time those of adjacent frames. For simplification we assume that a sub-band can mask out its neighbors only in one preceeding and one succeeding frame Layer 3: Psycho-Acoustic Effect The contrast resolution of the human ear decreases with the frequency of the signal. In layers 1 and 2 the frequency spectrum is subdivided into 32 critical bands of identical size. In layer 3, the frequencies are distributed in a non-linear fashion, in a way so that all bands contribute equally to the perception by the ear. The Bark We introduce a new unit: the Bark (named after Barkhausen) 1 Bark = width of a critical band. For frequencies < 500 Hz: 1 Bark = f/100. For frequencies > 500 Hz: 1 Bark = 9+4 log(f/1000)

17 Layer 3: Compression Masking Thresholds on critical band scale: Layer 3 comes closer to human perception by choosing a more appropriate definition of the sub-bands, based on the Bark. In addition to frequency masking and temporal masking, as in layers 1 and 2, layer 3 also introduces the differential coding of stereo signals, as well as an entropy encoding of the coefficients based on the Huffman code Performance of MP3 Layer Target bitrate Ratio Quality at 64 kbit/s Quality at 128 kbit/s Theor. min delay Layer kbit/s 4: ms Layer kbit/s 6: ms Layer 3 64 kbit/s 12: ms Quality measure: 5 = perfect, 4 = just noticeable, 3 = slightly annoying, 2 = annoying, 1 = very annoying Real delay is about three times the theoretical delay

18 2.4.3 Speech Coding Special codecs optimized for the human voice can reach a very high speech quality at very low data rates.they operate at the normal range of the voice, i.e. at Hz. Such special codecs are most often based on Linear Predictive Coding (LPC) Linear Predictive Coding (1) LPC models the anatomy of the human voice organs as a system of connected tubes of different diameters. refl[0] refl[1] tube 1 tube 2... tube p

19 Linear Predictive Coding (2) Acoustic waves are produced by the vocal cords, flow through a system of tubes, are partially reflected at the transitions and interfere with the following waves. The reflection rate at each transition is modeled by the reflection coefficient refl[0],..., refl[p-1]. We can thus characterize the (speaker-dependent) production of the voice signal with a very small number of parameters LPC Encoder The LPC Algorithm The audio signal is decomposed into small frames of fixed length (20 30 ms). For each frame s[i] we compute p weights lpc[0],.., lpc[p-1] so that s[i] is approximated by lpc[0] * s[i-1] + lpc[1] * s[i-2] lpc[p-1] * s[i-p] Popular values for p are 8 or 14. A synthetically generated source signal is used as input to the model. The generated source can be switched between two modes: voiced (for vowels) and noise (voiceless, for consonants). The differences between the synthetically generated signal and the real voice signal during the frame are detected and used to re-calculate the prediction coefficients lpc[i]. For each frame the mode of excitation (voiced or voiceless) and the current values of the parameters are encoded and transmitted

20 LPC Variations CELP (Code Excited Linear Prediction): We not only distinguish voiced and voiceless but many more types of excitation. These are pre-defined by the developers and stored in the form of a codebook. For each frame we transmit the index into the codebook and the lpc parameters. ACELP: like CELP, but with an adaptive codebook LPC Examples G Adaptive CELP Encoder (Code Excited Linear Predictor). Bit rate for G.723.1: 5,3 kbit/s kbit/s GSM Regular Pulse Excitation Long Term Prediction (RPE-LTP) LPC encoding The synthetically generated signal is based on earlier signal values. Bit rate for GSM 06.10: 13.2 kbit/s

21 Specialized Speech Coding vs. PCM Coding ITU-T Standards for Speech Coding A selection from the G.7xx-Standards: G.711: 64 kbit/s (GSTN telephony, H.323 and H.320 Videoconferencing) G.728 LD-CELP: 16 kbit/s (GSM telephony, H.320 Videoconferencing) G.729 ACELP: 8 kbit/s (GSM telephony, H.324 Vi-deo-telephony) G MPE/ACELP 5.3 kbit/s bis 6.3 kbit/s (GSTN Video-telephony, H.323 telephony)

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