import numpy as np

sample_rate = 16
frequency_hz = 3
samples = np.arange(sample_rate) / sample_rate
signal = np.sin(2 * np.pi * frequency_hz * samples)

spectrum = np.fft.rfft(signal)
frequencies = np.fft.rfftfreq(signal.size, d=1 / sample_rate)
magnitudes = np.abs(spectrum)

dominant_index = np.argmax(magnitudes[1:]) + 1
dominant_frequency = frequencies[dominant_index]

print("frequency bins:", frequencies)
print("magnitudes:", np.round(magnitudes, 3))
print("dominant frequency:", dominant_frequency)
print("matches expected:", np.isclose(dominant_frequency, frequency_hz))