From Analog to Digital: Signal Simulation

Simon chauveau — Tue, 09 Sep 2025 09:07:08 +0000

Ever wondered how sound—like your voice or music—is transformed into digital data that can be stored on a computer or phone? In this post, we’ll explore how it works using a simple MATLAB simulation.

Simple simulation

Step 1 : Creation of Analog Signal
First, we create a sine wave (like a pure tone) at 100 Hz:

t = 0:0.0001:0.01;       % very fine step (continuous-like time)
f = 100;                 % frequency = 100 Hz
x_analog = sin(2*pi*f*t);

Let’s visualize it:

figure;
plot(t, x_analog, 'LineWidth', 1.5);
title('Analog Signal (Sine Wave)');
xlabel('Time (s)'); ylabel('Amplitude');

This waveform represents our original sound.

Step 2 : Sampling the Signal
Sampling is like taking snapshots of the signal at regular intervals. The higher the sampling frequency, the better the quality.

I tested three sampling frequencies:

150 Hz : Too slow
200 Hz : Just enough (Nyquist rate)
1000 Hz : Good

For this example, we use 1000 Hz:

Fs = 1000;               % Sampling frequency = 1 kHz
Ts = 1/Fs;               % Sampling period
n = 0:Ts:0.01;           % Discrete sample points
x_sampled = sin(2*pi*f*n);

Visualizing the sampled signal:

figure;
stem(n, x_sampled, 'filled');
title('Sampled Signal');
xlabel('Time (s)'); ylabel('Amplitude');

Step 3 : Quantization
Quantization rounds each sample to the nearest level. More levels = better detail.

I tested:

3 bits : 8 levels
4 bits : 16 levels
6 bits : 64 levels

Here’s the 4-bit version:

bits = 4;                           % Number of bits
levels = 2^bits;                    % Quantization levels
x_min = min(x_sampled);
x_max = max(x_sampled);
q_step = (x_max - x_min)/levels;    % Step size

x_index = round((x_sampled - x_min)/q_step); % Map samples to indices
x_quantized = x_index*q_step + x_min;        % Map back to amplitude

Visualizing the quantized signal:

figure;
stem(n, x_quantized, 'filled');
title(['Quantized Signal (' num2str(bits) '-bit)']);
xlabel('Time (s)'); ylabel('Amplitude');

Step 4 : Encoding (Binary)
Now we convert each quantized value into binary:

binary_codes = dec2bin(x_index, bits); % Convert indices to binary words

To display the first 10 samples:

disp('--- First 10 encoded samples ---');
disp(binary_codes(1:10));

Step 5 : Digital Stream
Finally, we combine all binary codes into one bitstream:

bitstream = reshape(binary_codes.',1,[]); % Concatenate into one string

Display the first 40 bits:

disp('--- First 40 bits of the stream ---');
disp(bitstream(1:40));

This bitstream is what computers and phones use to store and process sound.

GitHub

You can find the full MATLAB code and result images on my GitHub repository:

CSimon-278 / MathAlgo-Assinment1

🎧 Analog to Digital Signal Simulation in MATLAB

This project demonstrates how an analog signal (like sound) is transformed into a digital signal that can be stored and processed by computers and phones. Using MATLAB, we simulate each step of the process: signal creation, sampling, quantization, binary encoding, and bitstream generation.

📌 What You'll Learn

How analog signals are represented in MATLAB
The importance of sampling frequency (Nyquist theorem)
How quantization affects signal quality
How binary encoding creates a digital bitstream
Visual comparisons of signal fidelity at different settings

🧪 Simulation Steps

Analog Signal Creation
Generate a 100 Hz sine wave to represent a pure tone.
Sampling
Sample the signal at different frequencies (150 Hz, 200 Hz, 1000 Hz) to observe aliasing and clarity.
Quantization
Apply different bit depths (3, 4, 6 bits) to see how resolution affects signal accuracy.
Binary Encoding
Convert quantized values…

View on GitHub