Digital Signal Processing and Fourier Transform

Lab 1: Sampling Theory, Quantization and PCM
In this lab, you will familiar with Sampling theorem, quantization and PCM generation. Pre-lab Assignment

: Given signal

x(t) = sinc(t), x(t).

1. Find out the Fourier transform of

x(t), X(f ), sketch them;

2. Find out the Nyquist sampling frequency of 3. Given sampling rate terms of

fs , write down the expression of the Fourier transform of xs (t) → Xs (f ) in fs = 1
Hz, sketch the sampled signal

X(f ). xs (t) = x(kTs ) and the Fourier

4. Let sampling frequency transform of

xs (t). fs = 2Hz , repeat 4. fs = 0.5Hz , repeat 4. fs = 1.5Hz , repeat 4. fs = 2/3Hz , repeat 4.

5. Let sampling frequency 6. Let sampling frequency 7. Let sampling frequency 8. Let sampling frequency

Lab Assignment 1: Sampling Theorem 1. Design matlab programs to illustrate items 3-8 in pre-lab assignment. You need to plot all the graphs. Using the Fourier transform of

xs (t) as: x(kTs ) exp(−j 2πf kTs ) k Xs (f ) =

2. Compare your results with your sketches in your pre-lab assignment and explain them.

Lab Assignment 2: Quantization of Voice 1. Read pcm.wav le into vector

y (you can truncate the original data to the desired length); N = 3 bits (8 levels) uniform quantizer. Output PCM code

2. Quantize the data vector N number (0 to 2 − 1).

y,

using

3. Generate binary (0 and 1) bit stream from PCM code number (this bit stream will be used in the later labs). 4. Recover the quantized sample values and replay the wave see if there is any distortion. 5. Repeat the above procedure, changing the number of quantization bits ered voice quality using different le, compare the original wave le to

N.

Summarize the recov-

N.
1

Transmitter y Read pcm.wav quantization yq ~ (0,2^L−1) bit stream yb ~ (0, 1)

Receiver yb’ Recover quan. levels yq’ play back

Figure 1: Procedure diagram.

2