Perceptual Audio Coding Hw1

MUS 422/EE 367C Winter 2006/07 Assignment 1 Due January 19, 2007 1) Data rates and the need for compression: There has been recent discussion in the audio market about the need to move to higher bit precision and greater sample rates. In particular, sampling rates of 96 kHz and 192 kHz using 24 bits per sample have been adopted in the DVD-Audio format. Let’s look at some implications for using such a format for passing 5-channel audio. a) How much storage is needed for 2 hours of these types of audio signals? b) If the CD format throughput for audio is equal to 1.411 Mb/s (million bits per second), what compression ratio is needed to pass these types of audio signals through a CD system? c) If the DVD-Video format throughput for audio is equal to 6.144 Mb/s (million bits per second), what compression ratio is needed to pass these types of audio signals through a DVD-Video system? d) If the DVD-Audio format throughput for audio is equal to 9.6 Mb/s, what compression ratio is needed to pass these types of audio signals through a DVD-Audio system? 2) Signal Representation and Summary Properties: Consider the following signal:

⎧sin( 4000πt ) sin( 2π t ) x(t ) = ⎨ ⎩0 elsewhere

for 0 ≤ t ≤

1 2

which represents a 2 kHz sine wave windowed with a sine window to a duration of 1/2 second. Do the following: a) Graph the signal b) Compute the signal summary properties (i.e., bias, average power, energy and standard deviation) from the time domain description of the signal. c) Compute and graph the Fourier Transform of this signal. d) Compute the signal summary properties from the frequency domain description of the signal. e) Sample this signal at an 16 kHz sampling rate. f) Use the sinc function interpolation to estimate the original signal from its samples, and compare with the original signal. How well does it do? (See also the Appendix of Chapter 3, page 68, of the textbook). 3) A first audio coder: In this exercise you will build a simple audio coder that codes the audio signal with 8 bits per sample. This exercise puts in place the basic routines for reading and writing audio files that will be useful in later exercises.

a)

Find a 16-bit PCM audio file format that 1) is well documented, 2) you can play on your computer, and 3) has sound samples you can find. (For example, information about the WAV file format is readily available on the internet. The Sound Recorder utility can be used to record and play PCM wave files.) Describe the file format. Get yourself a few good quality sound samples for testing codecs (see for example the sound assessment material at http://www.tnt.uni-hannover.de/project/mpeg/audio/sqam/). Make sure you can play your samples.

b)

Write an audio encoder that reads in 16-bit PCM audio files, “re-quantizes” the samples using only the 8 MSB (most significant bits), packs the quantized samples into arrays of BYTES, writes the results into a coded file format you define

c)

Write an audio decoder that reads in your coded file, converts your data back into 16-bit PCM codes, and writes out your decoded audio data into an audio file you can play. Verify that your encoder/decoder is bug-free.

d)

Test your codec on some sound samples. Describe the quantization noise you hear.

What compression ratios do you get?

4) Reading Assignment: Chapter 2 - Quantization from the textbook, M. Bosi and R. E. Goldberg, “Introduction to Digital Audio Coding and Standards”, KAP Springer 2003.