Digital Audio. Lecture-6

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Hubert Boyd
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1 Digital Audio Lecture-6

2 Topics today Digitization of sound PCM Lossless predictive coding 2

3 Sound Sound is a pressure wave, taking continuous values Increase / decrease in pressure can be measured in amplitude, which can be digitized Measure the amplitude at equally spaced time intervals (sampling) and represent it with one of finite digital values (quantization) Sampling frequency refers the rate at which h the sampling is performed 3

4 Digitizing Sound Start with the following questions Sampling Rate/Frequency?? Degree of quantization?? Uniform quantization or Nonuniform Quantization?? File Format??? 4

5 Nyquist Theorem Named after Harry Nyquist, mathematician i at Bell Labs For lossless digitization, the sampling rate should be at least twice the maximum frequency responses. Indeed many times more the better. The frequency equal to half the Nyquist rate is called Nyquist Frequency. If signal is band limited (minimum frequency=f 1, minimum frequency=f 2 ), then the required sampling rate is at least 2(f 2 - f 1 ) 5

6 Signal-to-Noise Ratio (SNR) Random fluctuation leads to noise in analog systems Ratio of the power of the correct signal to the power of the noise is called the Signalto-Noise Ratio (SNR), measured in decibel (db). V SNR = 10 log10 = 20 log10 V 2 signal 2 noise V V signal noise SNR is the measure of quality of signal 6

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8 Signal-to-Quantization-Noise Ratio (SQNR) Digital signals stores only quantized values Number of bits / sample dictates the precision Dividing voltage in a fixed range like 0 to 1 into 256 levels leads a round off error. The difference between the value of the analog signal, for a particular sampling time, and the nearest quantization interval value gives the quantization error or quantization noise. Quality of quantization is characterized by SQNR 8

9 Signal-to-Quantization-Noise Ratio (SQNR)[2] N bits/sample can represent the digital signal in the range 2 N-1 to 2 N-1-1 corresponding the the analog signal in the range V max to +V max. Each quantization level represent the voltage of 2V max / 2 N Vsignal SQNR= 20log = 20log10 V N db quan_ noise = 20 xnx log2 = 6.02 N ( db ) Mapping Vsignal to 2^N-1 and Vquan_noice to ½ Since the quantization error is statistically independent & uniformly distributed from 0 to ½, instead of the studied worst case, we have SQNR=6.02N+1.76 (db) 9

10 Non Linear Quantization Better quantization with limited bits Use of Weber s Law response α stimulus/stimulus Can be written as dr = k(1/s)ds Integrating, r=k ln s + C Stated otherwise, r=k ln (s/s 0 ) s 0 is the lowest stimulus that causes the response Non-linear quantization takes advantage of this logarithmic relation Find the stimulus for every unit response from the stimulus-response plot 10

11 Non Linear Quantization [2] This leads more concentrated quantization near the low end of stimulus & more compressed quantization towards the higher end of the stimulus 11

12 Audio Filtering Filter the audio signal before sampling (A to D) to remove unwanted frequencies For speech signal, retain 50Hz to 10Khz For Music signal, retain 20Hz to 20KHz Filter after D to A conversion Use low pass filter 12

13 Audio Quality vs. Data Rate The uncompressed data rate increases as more bits are used for quantization. Stereo: double the bandwidth to transmit a digital audio signal. Data rate and bandwidth in sample audio applications 13

14 Quantization and Transmission of Audio Coding of Audio: Quantization and transformation of data are collectively known as coding of the data. a) For audio, the µ-law technique for companding audio signals is usually combined with an algorithm that exploits the temporal redundancy present in audio signals. b) Differences in signals between the present and a past time can reduce the size of signal values and also concentrate the histogram of pixel values (differences, now) into a much smaller range. 14

15 Quantization and Transmission of Audio[2] c) The result of reducing the variance of values is that lossless compression methods produce a bitstream with shorter bit lengths for more likely values In general, producing quantized sampled output for audio is called PCM (Pulse Code Modulation). The differences version is called DPCM (and a crude but efficient variant is called DM). The adaptive version is called ADPCM. 15

16 Coding of Audio using PCM PCM Pulse Code Modulation Produces sampled, quantized output of the audio signal Standard telephony assumes the highest frequency of speech to reproduce is 4kHz, the sampling frequency is 8kHz. Now 8 bit sample size leads the bit rate 64kbps Before the digitizationiti process to begin, the signal is filtered to have sounds only up to 4kHz 16

17 Coding of Audio using PCM [2] 17

18 Coding of Audio using PCM [3] 18

19 Lossless Predictive Coding Transmits differences, difference between the prediction about the next sample to the current sample Predicts the next sample being equal to the current one, and code the difference A better linear predictor would be 19

20 Lossless Predictive Coding [2] 20

21 Lossless Predictive Coding [3] Predictive coding is lossless, since decoder produces the same signal as the original Let f1,f2,f3,f4,f5=21,22,27,25,22 Add an additional data at the beginning f0=f1. Transmit the first value uncoded d and transmit the rest of error values 21

22 Lossless Predictive Coding [4] 22

23 Lossless Predictive Coding [5] So, the encoded sequence would be ,1,6,1,-4 Decode it to get the signals again???? 23

24 Reference: Chapter 6 24

ECE 556 BASICS OF DIGITAL SPEECH PROCESSING. Assıst.Prof.Dr. Selma ÖZAYDIN Spring Term-2017 Lecture 2

ECE 556 BASICS OF DIGITAL SPEECH PROCESSING Assıst.Prof.Dr. Selma ÖZAYDIN Spring Term-2017 Lecture 2 Analog Sound to Digital Sound Characteristics of Sound Amplitude Wavelength (w) Frequency ( ) Timbre