The objective of the project is to study PCM and its variations as a waveform coding technique. In particular, we will c

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The Objective Of The Project Is To Study Pcm And Its Variations As A Waveform Coding Technique In Particular We Will C 1 (110.83 KiB) Viewed 37 times

The Objective Of The Project Is To Study Pcm And Its Variations As A Waveform Coding Technique In Particular We Will C 2 (35.37 KiB) Viewed 37 times

The objective of the project is to study PCM and its variations as a waveform coding technique. In particular, we will consider uniform PCM, non-uniform PCM, differential PCM, delta modulation and adaptive delta modulation. First, record a piece of speech into Matlab with a certain sampling frequency (greater than the Nyquist rate), and form a vector with the resulting samples. Make sure to take a sufficiently long speech signal for statistical analysis. Normalize the vector so that the samples are in the interval (-1,1) Work to do: 1. Plot the histogram of the source samples by removing the silence periods so that there is no (incorrect) “spike" at x = 0. Generate a third or fourth order polynomial fit to the histogram. Then, normalize this function to estimate the probability density function (PDF) of the source signal. Comment on the nature of these samples. 2. Assuming that uniform PCM is used, estimate the resulting SQNR based on your estimate of the source sample PDF in the first part. Leave this as a function of the number of quantization bits (v). Plot a (v, SQNR) graph for a range of different quantization bit levels, e.g., for X-axis v € {4, 6, 8, 10, 12). 3. Consider your original vector you have recorded, and apply uniform PCM to come up with a digital representation. Provide samples of (zoomed in versions) of the encoded version along with the original vector. Estimate the mean square error as well as the signal power (directly from the vector - by averaging across time), and the resulting SONR. Do this for three different values of the number of quantization bits, e.g., v = 4,6,8 bits. Compare your answer with your answer in the previous part. 4. Use an A-law or u-law compander (no need for both) to perform non-uniform PCM (with v = 8 bits), and study the resulting signal quality. Vary the parameter of the compander to optimize the quality of representation. What is your optimized value? How much improvement do you observe by varying the parameter of the compander? How much improvement do you observe in the resulting SQNR over uniform PCM? 5. Consider the first (direct) implementation of differential PCM with 4-bit quantization and encode the speech vector you have recorded. Decide on the exact quantizer to use (recall that the new dynamic range for the difference between the consecutive samples is small), and report on the quality of the resulting encoding (in terms of SQNR).

6. Repeat the previous part with the alternate implementation of differential PCM, which does not result in error accumulation. 7. Use delta modulation to encode the speech signal. Try different step sizes, and report on the best one (providing the smallest mean square error). Do this for two or three different sampling rates. Comment on your results. 8. Lastly, use adaptive delta modulation to encode the speech signal. Assume that the step size is increased according to aA, and reduced according to A/a; and optimize the value of a (by estimating the mean square error for your example). For all the relevant) parts, play the encoded speech vectors as well, and comment on the quality of the resulting representations based on your perception (along with the mean square error and SQNR results). Also, for all the relevant parts (to help with your discussion and comments) provide sample plots of the original and encoded files (with proper zoom).