Two Bit Analog to Digital Converter – MATLAB Let x (t) = 0.8 cos(2*pi*t) + 0.15,

Question

Two Bit Analog to Digital Converter – MATLAB
Let x (t) = 0.8 cos(2*pi*t) + 0.15, 0 t 1, and zero otherwise, be the input to a two bit ADC converter.
a.) For a sampling period Ts = 0.025 sec; determine and plot using MATLAB the sampled signal:
x (nTs) = x(t)It = nTs

b.) The four level quantizer, (see Figure 1.2), corresponding to the 2 bit ADC is defined as:
x(nTs)<(+1)x (nTs)= = -2,-1,0,1
Where x(nTs), found above, is the input and x (nTs) is the output of the quantizer. Let the quantization step be = 0.5. Plot the input-output characterization of the quantizer, and find the quantized output for each of the sample values of the sampled signal x(nTs).

c.) To transform the quantized values into unique binary 2 bit values, consider the following code:
x (nTs) = -2 10
x (nTs) = - 11
x (nTs) = 0 00
x (nTs) = 01
Obtain the digital signal corresponding to x(t).

Explanation / Answer

a. fairly straightforward for generating a signal. simply set t = [0:0.025:1]; and x=(function above). Plot this to confirm the data. b. and c. Unless otherwise stated, you'll need to write an M-files for both of these. b. can be written with a switch or if...elseif...else conditions. c. is more problematic on my version (I use a 2007 student version). It is possible to utilize only two bits, however, if you have too much trouble with the bit manipulation, you can always use an N X 2 array to encode the data.

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