07. Analysis of the Recorded Signal in MATLAB

Purpose of the section

To learn how to load a recorded IQ file into MATLAB, build time-domain and spectral representations of the signal, and estimate the main parameters of the test tone.

1. Why MATLAB analysis is needed

After observing the signal in HDSDR, it is important to move to offline analysis. This allows the student to:

• work with the same recording many times;
• repeat calculations;
• compare analysis methods;
• estimate frequency and level;
• prepare for later modeling in Simulink.

MATLAB is especially convenient for the first analysis because it allows quick:

• reading of data;
• plotting;
• FFT computation;
• automation of simple measurements.

2. What should be known about the recorded file

Before starting the analysis, the following must be documented:

• file name;
• sample format;
• sampling rate;
• receiver tuning frequency;
• data type;
• order of I and Q samples.

A common format is:

• interleaved I/Q;
• int8, int16, or float;
• a sequence of the form
  I0, Q0, I1, Q1, I2, Q2, ...

The sample type depends on the program that wrote the file, and reading it with the wrong type gives a meaningless spectrum:

Source	Format	How to read it
rtl_sdr command-line tool (.bin, .cu8)	unsigned 8-bit, offset 127.5	fread(fid, 'uint8') - 127.5
HDSDR / SDR# / SDR++ baseband recording (.wav)	signed 16-bit inside a WAV file	audioread(filename, 'native'): I is column 1, Q column 2
course and AD9363 captures (.ci16)	signed 16-bit, interleaved	fread(fid, 'int16')

A WAV file starts with a header; fread from the start of the file would read the header as samples.

3. Main analysis tasks

Within the first block it is necessary to:

1. Load the IQ file.
2. Convert it into a complex signal.
3. Plot a fragment of the time-domain waveform.
4. Plot the spectrum.
5. Find the frequency of the main peak.
6. Estimate the tone level.
7. Save the results for the report.

4. General work sequence

Step 1. Load the data

Read the raw file into an array.

Step 2. Form the complex signal

Combine I and Q into a complex vector:

• I: real part;
• Q: imaginary part.

Step 3. Normalize if needed

Bring the values to a convenient range.

Step 4. Time-domain analysis

Plot the real part, imaginary part, or magnitude of the signal.

Step 5. Spectral analysis

Compute FFT and obtain the spectral picture.

Step 6. Peak estimation

Find the maximum index and convert it into frequency.

5. Example structure of a MATLAB script

filename = 'tone_capture_iq.bin';
fs = 2.4e6;

fid = fopen(filename, 'rb');
raw = fread(fid, 'int16');
fclose(fid);

i_data = raw(1:2:end);
q_data = raw(2:2:end);

x = double(i_data) + 1j * double(q_data);
% rtl_sdr .bin/.cu8 instead: raw = fread(fid, 'uint8') - 127.5;
% HDSDR .wav instead:        y = audioread(filename, 'native'); x = double(y(:,1)) + 1j*double(y(:,2));

Nview = min(length(x), 2000);
t = (0:Nview-1)/fs;

figure;
plot(t, real(x(1:Nview)));
xlabel('Time, s');
ylabel('Amplitude');
title('Real part of IQ signal');
grid on;

Nfft = 4096;
X = fftshift(fft(x(1:Nfft), Nfft));
f = (-Nfft/2:Nfft/2-1)*(fs/Nfft);

figure;
plot(f, 20*log10(abs(X)+1e-12));
xlabel('Frequency, Hz');
ylabel('Magnitude, dB');
title('Spectrum of recorded tone');
grid on;

[~, idx] = max(abs(X));
f_peak = f(idx);

disp(['Peak frequency = ', num2str(f_peak), ' Hz']);

f_peak is the offset from the receiver's tuning frequency, not the radio frequency: the tone is at f_tune + f_peak. The same script is in blocks/block_01_intro_sdr/matlab/iq_analysis_example.m, and its Python twin in python/iq_analysis_example.py.

6. What should be seen on the plots

In the time domain

The student should see:

• regular oscillation;
• a stable signal shape;
• no obvious spikes or strong distortion.

In the spectrum

The student should see:

• a pronounced narrow peak;
• peak location corresponding to the tone;
• noise floor;
• possibly weak parasitic components.

7. Useful parameters to estimate

Within the first analysis it is useful to determine:

• frequency of the maximum spectral peak;
• relative peak level;
• peak width;
• noise-floor level;
• possible mirror components;
• possible DC component near zero frequency.

8. What to pay attention to

1. Data format

If the type or I/Q order is wrong, the spectrum will be incorrect.

2. Frequency scale

Sampling frequency and center frequency must be interpreted correctly.

3. Analysis window

Too short a fragment may degrade frequency resolution.

4. Overload

If the receiver was overloaded, this may appear as:

• extra peaks;
• a wide “dirty” spectrum;
• time-domain distortion.

9. What to include in the report

It is recommended to add:

• a short description of the file used;
• recording parameters;
• time-domain plot;
• spectrum plot;
• estimated peak frequency;
• a short comment on signal quality.

10. Conclusions

After this stage the student should:

• be able to load an IQ file into MATLAB;
• build a time-domain waveform and a spectrum;
• determine the frequency of the main tone;
• understand how offline analysis confirms the observation made in HDSDR.