writeups2026tamu/Short-Term-Fuel-Trim-misc.md

Short Term Fuel Trim - misc

The data is a list of 129*1380 complex numbers

# STFT shape: complex64 (129, 1380)
 (0.000000000000000000e+00+0.000000000000000000e+00j)
 (0.000000000000000000e+00+0.000000000000000000e+00j)
 (-1.484999775886535645e+00+0.000000000000000000e+00j)
 (2.873720169067382812e+00+0.000000000000000000e+00j)
 (9.447572708129882812e+00+0.000000000000000000e+00j)
 (8.104647827148437500e+01+0.000000000000000000e+00j)
 (1.316259765625000000e+01+0.000000000000000000e+00j)
 (-3.101673889160156250e+02+0.000000000000000000e+00j)
 (-4.186026916503906250e+02+0.000000000000000000e+00j)
 (-5.818300781250000000e+02+0.000000000000000000e+00j)
 (2.119775390625000000e+02+0.000000000000000000e+00j)
 (-1.738154602050781250e+02+0.000000000000000000e+00j)
 (-2.650747985839843750e+02+0.000000000000000000e+00j)
 (-3.873171691894531250e+02+0.000000000000000000e+00j)
 (-4.193124389648437500e+02+0.000000000000000000e+00j)
 (-1.984837646484375000e+02+0.000000000000000000e+00j)
 (-1.092494659423828125e+02+0.000000000000000000e+00j)
 

STFT stands for short time Fourier transform. The data is actually the STFT of an audio signal.

Using scipy.signal.istft, we performed the inverse transform and reconstructed the audio signal

with open("numbers.txt", "r") as f:
    lines = f.readlines()

shape =  (129, 1380)

nums = np.array([complex(l.strip()) for l in lines[1:]])
arr = nums.reshape(*shape)


sampling_rate_hz = 44100

t, z = istft(arr, fs=sampling_rate_hz)

from scipy.io import wavfile

def time_series_to_wav(arr, sample_rate=44100):
    #sample_rate = 44100  # Hz — set correctly
    #samples = samples.astype(np.float32)

    arr_mean = arr.mean()
    arr_ptp = arr.max() - arr.min()

    samples = (arr - arr_mean)*2/arr_ptp
    
    # Normalize if float in [-1,1], convert to 16-bit:
    scaled = (samples * 32767).astype(np.int16)

    wavfile.write("out.wav", sample_rate, scaled)

time_series_to_wav(z, sample_rate=44100)

The flag is spoken text, and can be transcribed from the wav file.

The flag is gigem{fft_is_50_0p}