SIMS-201 Audio Digitization

2  Overview Chapter 12 Digital Audio Digitization of Audio Samples Quantization Reconstruction Quantization error

3  Digitization of Audio Samples Audio signals are continuous in time and amplitude Audio signal must be digitized in both time and amplitude to be represented in binary form. Discrete in time by sampling – Nyquist Discrete in amplitude by quantization Once samples have been captured, they must be made discrete in amplitude. The two step digitization process Step 1: Sampling (in previous lecture) Step 2: Quantization

4  Quantization Quantization Converts actual amplitude sample values (usually voltage measurements) into an integer approximation Process of rounding off a continuous value so that it can be represented by a fixed number of binary digits Tradeoff between number of bits required and error Human perception limitations affect allowable error Specific application affects allowable error Two approaches to quantization Rounding the sample to the closest integer. (e.g. round 3.14 to 3) Create a Quantizer table that generates a staircase pattern of values based on a step size.

5 Consider an audio signal with a voltage range between -10 and +10 Assume the audio waveform has already been time sampled, as shown How can the amplitude also be converted into discrete values?

6 For this example, let’s choose to represent each sample by 4 bits There are an infinite number of voltages between -10 and 10. We will have to assign a range of voltages to each 4-bit codeword. There will be 16 steps. Why? How large will each step be?

7 A CD Player Example Please read the full example on Page 176 (Chapter 12) in the book Sampling Music at recording studios follow audio industry standard for highest frequency (bandwidth) = 20kHz Thus minimum (Nyquist) sampling rate is 40kHz (or samples per second). Audio industry oversamples a little – using to be on safe side. Quantization CD’s use 16 bits to represent each sample – total of 2 16 = possible samples (unique combinations/codes) on one CD. Each channel is converted into bits at rate of: samples/sec * 16 bits/sample = bits/sec 60 minutes * 60 secs/min * bits/sec * 2 channels (stereo) = bits = MB (about the size of on CD) Exercise Please right click on any.MP3 file and go to Properties | Summary and review the Bit Rate and Audio sample rate.

8  Reconstruction Analog-to-Digital Converter (ADC) provides the sampled and quantized binary code. Digital-to-Analog Converter (DAC) converts the quantized binary code back into an approximation of the analog signal (reverses the quantization process) by clocking the code to the same sample rate as the ADC conversion. Quantization and Reconstruction example on next two slides:

9 QUANTIZATION

10 RECONSTRUCTION

11  Quantization Error After quantization, some information is lost Errors (noise) introduced The difference between the original sample value and the rounded value is called the quantization error A signal to noise ratio (SNR) is the ratio of the relative sizes of the signal values and the errors. The higher the SNR, the smaller the average error is with respect to the signal value, and the better the fidelity. Quantization is only an approximation.

12 Other Applications In addition to digital audio for entertainment purposes, there are many applications of discredited audio signals: Most telephone calls digitized, and reconstructed during transmission Because digitized signals are more efficient in terms of system bandwidth, they are the choice for any application involving expensive communication resources such as satellite links Because info in digital form is much more amendable to encryption and encoding, digital audio is used for military and other secure applications.

13 Chapters Read So Far Everyone should have read the following chapters thus far: Chapter 1: What is the Information in the Information Revolution? Chapter 3: Representing Information in Bits Chapter 4: The Need and Basis for Data Protocols Chapter 5: From the Real World to Images and Video Chapter 7: Compressing Information Chapter 8: Image Compression (please read) Chapter 9: Digital Video (please read) Chapter 10: Audio as Information Chapter 11: Sampling of Audio Signals Chapter 12: Digital Audio Information Technology Inside and Outside