added writeups exported from ctfnote

Short-Term-Fuel-Trim-misc.md

@@ -0,0 +1,67 @@
+# 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](https://en.wikipedia.org/wiki/Short-time_Fourier_transform).
+The data is actually the STFT of an audio signal.
+
+Using [scipy.signal.istft](https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.istft.html),
+we performed the inverse transform and reconstructed the audio signal
+```python
+
+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}`