Find out the Fourier transform of x(t), X(f), sketch them; 2. Find out the Nyquist sampling frequency
Question:
Find out the Fourier transform of x(t), X(f), sketch them;
2. Find out the Nyquist sampling frequency of x(t).
3. Given sampling rate fs, write down the expression of the Fourier transform of xs(t) ! Xs(f) in terms of X(f).
4. Let sampling frequency fs = 1 Hz, sketch the sampled signal xs(t) = x(kTs) and the Fourier transform of xs(t).
5. Let sampling frequency fs = 2Hz, repeat 4.
6. Let sampling frequency fs = 0:5Hz, repeat 4.
7. Let sampling frequency fs = 1:5Hz, repeat 4.
8. Let sampling frequency fs = 2=3Hz, repeat 4.
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:
Xs(f) = X
k
x(kTs) exp(¡j 2¼f kTs)
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);
2. Quantize the data vector y, using N = 3 bits (8 levels) uniform quantizer. Output PCM code number (0 to 2N ¡ 1).
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 le, compare the original wave le to see if there is any distortion.
Expert Answer:
