(a) Use MATLAB to create a 1-s sinusoidal signal using the sampling rate of fs=1000 Hz x(t)=1.8

(a) To create a 1u002Dsecond sinusoidal signal with a sampling rate of 1000 Hz, we need to generate

Question

(a) Use MATLAB to create a $1-\mathrm{s}$ sinusoidal signal using the sampling rate of $f_s=1000 \mathrm{~Hz}$ $$ x(t)=1.8 \cos (2 \pi \times 100 t)+1.0 \sin (2 \pi \times 150 t+\pi / 4), $$ where each sample $x(t)$ can be round off using 3-bit signed integer (directly round off the calculated $x(t))$ and evaluate the SQNR. (b) Use MATLAB to design an oversampling system including the anti-aliasing filter with a selectable integer factor $L$ using the same equation for the input $x(t)$. (c) Recover the signal using the quantized 3-bit signal and measure the SQNRs for the following integer factors: $L=2, L=4, L=8, L=16$, and $L=32$. From the results, explain which one offers better quality for the recovered signals.

   (a) Use MATLAB to create a $1-\mathrm{s}$ sinusoidal signal using the sampling rate of $f_s=1000 \mathrm{~Hz}$
$$
x(t)=1.8 \cos (2 \pi \times 100 t)+1.0 \sin (2 \pi \times 150 t+\pi / 4),
$$
where each sample $x(t)$ can be round off using 3-bit signed integer (directly round off the calculated $x(t))$ and evaluate the SQNR.
(b) Use MATLAB to design an oversampling system including the anti-aliasing filter with a selectable integer factor $L$ using the same equation for the input $x(t)$.
(c) Recover the signal using the quantized 3-bit signal and measure the SQNRs for the following integer factors: $L=2, L=4, L=8, L=16$, and $L=32$. From the results, explain which one offers better quality for the recovered signals.

Digital Signal Processing: Fundamentals and Applications

Lizhe Tan, Jean… 3rd Edition

Chapter 11, Problem 29

Instant Answer

Step 1

We can do this using the following MATLAB code: ```matlab fs = 1000; % Sampling rate in Hz t = 0:1/fs:1-1/fs; % Time vector from 0 to 1 second x = 1.8*cos(2*pi*100*t) + 1.0*sin(2*pi*150*t + pi/4); % Signal equation x_quantized = round(x*(2^2-1))/(2^2-1); % Show more…

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(a) Use MATLAB to create a $1-\mathrm{s}$ sinusoidal signal using the sampling rate of $f_s=1000 \mathrm{~Hz}$ $$ x(t)=1.8 \cos (2 \pi \times 100 t)+1.0 \sin (2 \pi \times 150 t+\pi / 4), $$ where each sample $x(t)$ can be round off using 3-bit signed integer (directly round off the calculated $x(t))$ and evaluate the SQNR. (b) Use MATLAB to design an oversampling system including the anti-aliasing filter with a selectable integer factor $L$ using the same equation for the input $x(t)$. (c) Recover the signal using the quantized 3-bit signal and measure the SQNRs for the following integer factors: $L=2, L=4, L=8, L=16$, and $L=32$. From the results, explain which one offers better quality for the recovered signals.

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