Inconsistency in the two-sided bandwidth with the Nyquist sampling theorem criterion

[tapyu]

Version

2.1.1 (Default)

System Information

not applied

Description

Based on the docstring of the signal builders

torchsig/torchsig/signals/builders/fm.py

Lines 16 to 30 in 9b1949e

	def fm_modulator(
	bandwidth: float,
	sample_rate: float,
	num_samples: int,
	rng: np.random.Generator | None = None,
	) -> np.ndarray:
	"""Frequency Modulator (FM) signal generator.
	Generates FM signals using Carson's Rule for bandwidth calculation.
	Args:
	bandwidth: Desired 3 dB bandwidth of the signal (Hz).
	sample_rate: Sampling rate for the IQ signal (Hz).
	num_samples: Number of IQ samples to produce.
	rng: Random number generator for reproducibility. If None, creates a new default generator.

It defines as the 3-dB bandwidth, but does not say whether it is two-sided or one-sided. When not specified, one may understand that the author makes the bandwidth cover the full frequency span. In this case, for a baseband signal, the bandwidth would be within [-B/2, B/2] Hz. In this case, the Nyquist sampling theorem criterion for no aliasing would be

$$ f_s \geq B $$

where $f_s$ is the sampling rate in Hz. However, in the same code you check

torchsig/torchsig/signals/builders/fm.py

Lines 51 to 52 in 9b1949e

	if bandwidth > sample_rate / 2:
	raise ValueError("bandwidth must be less than sample_rate/2")

This is only consistent for one-side 3-dB bandwidth definition!

If you mean bandwidth B as the frequency for the range [-B, B] Hz, please, say that is a two-sided 3-dB bandwidth. Otherwise, your definition makes the bandwidth vague.

How to Reproduce the Bug

not applied