$2\mathrm{.}1$ Task $1$: Quantization

First, you should build a function that reads the sound file helloWorld.wav

and saves it along with its sampling frequency. Play the sound file to listen to the quality of the signal before its transmission. Using a uniform quantizer as done in a previous homework, quantize the signal using L$=2^($n$)$ levels, where n is the number of bits per sample. Your

code should be generic enough to allow any general n to be used. The output of this should be a stream of bits representing the quantized signal. Note that you should be able to transform the bits back to the quantized levels, which you will need in Task $3.$ Play the quantized sound file for n$=2$ and note the difference compared to the original one.

$2\mathrm{.}2$ Task $2$: Pulse Shaping

Before sending the stream of bits on the channel, each bit needs to be pulse$-$ shaped. In this task, we will be using the raised cosine pulse, denoted p$\_($rc$)($t$),$ discussed in class. Transform the stream of bits from Task $1$ into binary polar signaling, and then shape each symbol with p$\_($rc$)($t$)$ via convolution. Note that you need to upsample the stream of bits before convolving it with p$\_($rc$)($t$).$ Make sure the energy of p$\_($rc$)($t$)$ is normalized.

Plot the first T$=400$ shaped samples. Make sure the time vector accurately

describes the true time.

$2\mathrm{.}3$ Task $3$: AWGN Channel

For a specific SNR value $($in dB$),$ send the shaped symbols into an AWGN

channel by simply adding Gaussian noise. Plot the T noisy shaped samples and compare to the figure from Task $2.$ Pass the output of the channel through a matched filter to maximize the received SNR$.$ Acquire samples from the matched filter output every T$\_($b$).$ Note that you need to start sampling after some specific delay. Compare the samples to the optimum threshold to detect the binary data. Compute the empirical BER P$\_($b$),$ and compare to the analytical BER derived in class. Convert the detected bits back to their corresponding quantized levels. Play the received signal and compare to the quantized one before transmission as well as the original one.

Finally, redo Task $3$ for different SNR values $($from $-5$ dB to $10$ dB $),$ and

plot the BER vs$.$ SNR using the semilogy command. On the same curve, plot the analytical BER vs$.$ SNR and compare.