0.12 Lab 8 - number representation and quantization  (Page 4/5)

Down load the audio files speech.au and music.au . Use your Uquant function to quantize each of these signals to 7, 4, 2 and 1 bits/sample.Listen to the original and quantized signals and answer the following questions:

• For each signal, describe the change in quality as the number of b/sample is reduced?
• For each signal, is there a point at which the signal quality deteriorates drastically?At what point (if any) does it become incomprehensible?
• Which signal's quality deteriorates faster as the number of levels decreases?
• Do you think 4 b/sample is acceptable for telephone systems? ... 2 b/sample?

Use subplot to plot in the same figure, the four quantized speech signals over theindex range 7201:7400. Generate a similar figure for the music signal, using the same indices.Make sure to use orient tall before printing these out.

Error analysis

As we have clearly observed, quantization produces errors in a signal. The most effective methods for analysis of the error turn outto be probabilistic. In order to apply these methods, however, one needs to have a clear understanding of the error signal'sstatistical properties. For example, can we assume that the error signal is white noise? Can we assume that it is uncorrelatedwith the quantized signal? As you will see in this exercise, both of these are good assumptions if the quantization intervalsare small compared with sample-to-sample variations in the signal.

If the original signal is $X$ , and the quantized signal is $Y$ , the error signal is defined by the following:

Compute the error signal for the quantized speech for 7, 4, 2 and 1 b/sample.

When the spacing, $\Delta$ , between quantization levels is sufficiently small,a common statistical model for the error is a uniform distribution from $\frac{-\Delta }{2}$ to $\frac{\Delta }{2}$ . Use the command hist(E,20) to generate 20-bin histograms for each of the four error signals.Use subplot to place the four histograms in the same figure.

Inlab report

1. Hand in the histogram figure.
2. How does the number of quantization levels seem to affect the shape of the distribution?
3. Explain why the error histograms you obtain might not be uniform?

Next we will examine correlation properties of the error signal. First compute and plot an estimate of the autocorrelation functionfor each of the four error signals using the following commands:

[r,lags] = xcorr(E,200,'unbiased');

plot(lags,r)

Now compute and plot an estimate of the cross-correlation function between the quantized speech Y and each error signal E using

[c,lags] = xcorr(E,Y,200,'unbiased');

plot(lags,c)

Inlab report

1. Hand in the autocorrelation and cross-correlation estimates.
2. Is the autocorrelation influenced by the number of quantization levels? Do samples in the error signal appear to be correlated with each other?
3. Does the number of quantization levels influence the cross-correlation?

Signal to noise ratio

One way to measure the quality of a quantized signal is by the Power Signal-to-Noise Ratio (PSNR).This is defined by the ratio of the power in the quantized speech to power in the noise.