Demodulates the pulse-shaped complex samples \(\tilde{x}[n]\) into decimal symbol decisions \(\hat{s}[k]\) using matched filtering and maximum-likelihood estimation.

Parameters:¶

x_tilde: ArrayLike¶

The received pulse-shaped complex samples \(\tilde{x}[n]\) to demodulate, with sps samples per symbol and length sps * s_hat.size + pulse_shape.size - 1.

Returns:¶

• The decimal symbol decisions \(\hat{s}[k]\), \(0\) to \(M-1\).

• The matched filter outputs \(\tilde{a}[k]\).

• The complex symbol decisions \(\hat{a}[k]\).