STFT Spectrogram of Swept-Frequency Ultrasonic Sensor Output for Echo Tracking

Project info

• Field of studyInstrumentation and Sensors
• LevelMaster's thesis (S2)
• Method typeSignal Processing
• Estimated build time± 5 working days
• Toolsspectrogram, chirp (Signal Processing Toolbox)
• PriceUS$28 - US$169

Research goal

Analyse echo amplitude using Spectrogram (STFT) to identify the effect of sweep frequency and suppress background acoustic noise.

Variables

Example result

• 128Window length (ms)
• 75Overlap (%)
• 7.813Frequency resolution (Hz)
• 230.5True sweep rate (Hz/s)
• 230.477Estimated sweep rate (Hz/s)
• 79.401Dynamic range (dB)

The spectrogram of Echo amplitude with a 128 ms window tracks a frequency sweep of 230 Hz/s (true value 230 Hz/s) at 7.8 Hz resolution, making the time-varying frequency content clear.

Computed from illustrative synthetic data, not from a real study.

About Spectrogram (STFT)

A spectrogram (STFT) shows how a signal's frequency content changes over time by computing FFTs on a sliding window. It suits non-stationary signals such as speech, machine vibration, radar, and biological signals.

Steps

1. 1Define the sampling frequency and signal
2. 2Choose window length, overlap, and FFT points
3. 3Compute the spectrogram
4. 4Convert to dB and plot as a heat map
5. 5Track the dominant frequency over time
6. 6Adjust the window to trade time against frequency resolution

Assumptions to check

• The signal changes slowly relative to window length
• Short windows give good time but poor frequency resolution, and vice versa
• The sampling frequency satisfies Nyquist

Reading and reporting the results

Present the spectrogram with clear axes and units, then interpret the frequency pattern over time. State the window length, overlap, and window type used.

Example MATLAB code

A short starting script with this project's variable names. The delivered version is adapted to your data and fully commented.

rng(4);
fs = 2000;
sweep_frequency = (0:1/fs:4-1/fs)';
echo_amplitude = chirp(sweep_frequency, 50, 4, 500, 'linear') + 0.2*randn(size(sweep_frequency));   % 50 to 500 Hz sweep

win = hamming(256);
noverlap = 224;
nfft = 512;
[S, f, t] = spectrogram(echo_amplitude, win, noverlap, nfft, fs);
P = 10*log10(abs(S).^2 + eps);

[~, imax] = max(abs(S), [], 1);                    % dominant frequency per frame
fdom = f(imax);
pfit = polyfit(t(:), fdom(:), 1);
fprintf('Estimated sweep rate: %.1f Hz/s (true 112.5)\n', pfit(1));

figure;
imagesc(t, f, P); axis xy; colorbar;
xlabel('Time (s)'); ylabel('Frequency (Hz)'); title('Spectrogram (dB)');
hold on; plot(t, fdom, 'w--'); hold off;

Packages and prices

Choose how much help you need. Each higher package includes everything in the lower ones. Prices exclude 11% VAT.

• Payment: 50% down payment before work starts, balance after the deliverables are handed over
• Tax: Prices exclude 11% VAT
• Data and academic integrity: Results are computed from your own research data; you write and stand behind your manuscript, we help with the analysis and your understanding of it
• Revisions: Up to 2 revisions are included in the price (Package 3: 3 rounds)

Frequently asked questions