sdr.to_real_pb(x_c: NDArray[complex_]) → NDArray[float_]

Converts the complex baseband signal \(x_c[n]\) centered at \(0\) with sample rate \(f_{s,c}\) to a real passband signal \(x_r[n]\) centered at \(f_{s,r}/4\) with sample rate \(f_{s,r} = 2f_{s,c}\).

Parameters:
x_c: NDArray[complex_]

The complex baseband signal \(x_c[n]\) centered at \(0\) with sample rate \(f_{s,c}\).

Returns:

The real passband signal \(x_r[n]\) centered at \(f_{s,r}/4\) with sample rate \(f_{s,r} = 2f_{s,c}\).

Examples

Create a complex baseband signal with frequency components at -150, 0, and 50 Hz, at a sample rate of 500 sps. Notice the spectrum is asymmetric.

In [1]: sample_rate = 500; \
   ...: x_c = ( \
   ...:     0.1 * np.exp(1j * 2 * np.pi * -150 / sample_rate * np.arange(1000)) \
   ...:     + 1.0 * np.exp(1j * 2 * np.pi * 0 / sample_rate * np.arange(1000)) \
   ...:     + 0.5 * np.exp(1j * 2 * np.pi * 50 / sample_rate * np.arange(1000)) \
   ...: ); \
   ...: x_c = sdr.awgn(x_c, snr=30)
   ...: 

In [2]: plt.figure(figsize=(8, 4)); \
   ...: sdr.plot.time_domain(x_c[0:50], sample_rate=sample_rate); \
   ...: plt.title("Time-domain signal $x_c[n]$"); \
   ...: plt.tight_layout();
   ...: 

In [3]: plt.figure(figsize=(8, 4)); \
   ...: sdr.plot.periodogram(x_c, fft=2048, sample_rate=sample_rate); \
   ...: plt.title("Periodogram of $x_c[n]$"); \
   ...: plt.tight_layout();
   ...:
../../_images/sdr_to_real_pb_1.png ../../_images/sdr_to_real_pb_2.png

Convert the complex baseband signal to a real passband signal with sample rate 1 ksps and center of 250 Hz. Notice the spectrum is now complex-conjugate symmetric. The complex exponentials are now real sinusoids at 100, 250, and 300 Hz.

In [4]: x_r = sdr.to_real_pb(x_c); \
   ...: sample_rate *= 2
   ...: 

In [5]: plt.figure(figsize=(8, 4)); \
   ...: sdr.plot.time_domain(x_r[0:100], sample_rate=sample_rate); \
   ...: plt.title("Time-domain signal $x_r[n]$"); \
   ...: plt.tight_layout();
   ...: 

In [6]: plt.figure(figsize=(8, 4)); \
   ...: sdr.plot.periodogram(x_r, fft=2048, sample_rate=sample_rate); \
   ...: plt.title("Periodogram of $x_r[n]$"); \
   ...: plt.tight_layout();
   ...:
../../_images/sdr_to_real_pb_3.png ../../_images/sdr_to_real_pb_4.png