42 rrc pulse fixes (#50)

* better handling of the discontinuity in the rrc_taps() pulse shaping design function

* pulse shaping filter length now includes approximation based on roll-off factor alpha and a sidelobe attenuation level of 72 dB (12 bit dynamic range)

---------

Co-authored-by: MattCarrickPL <120057274+MattCarrickPL@users.noreply.github.com>

torchsig/datasets/synthetic.py

@@ -280,7 +280,12 @@ def _generate_samples(self, item: Tuple) -> np.ndarray:
         symbols = const[symbol_nums]
         zero_padded = np.zeros((self.iq_samples_per_symbol * len(symbols),), dtype=np.complex64)
         zero_padded[::self.iq_samples_per_symbol] = symbols
-        self.pulse_shape_filter = self._rrc_taps(11, signal_description.excess_bandwidth)
+
+        # estimate total filter length for pulse shape
+        AdB = 72 # sidelobe attenuation level, 72 dB -> 12 bit dynamic range
+        pulse_shape_filter_length = estimate_filter_length(AdB,1,signal_description.excess_bandwidth)
+        pulse_shape_filter_span = int((pulse_shape_filter_length-1)/2) # convert filter length into the span
+        self.pulse_shape_filter = self._rrc_taps(pulse_shape_filter_span, signal_description.excess_bandwidth)
         xp = cp if self.use_gpu else np
         filtered = xp.convolve(xp.array(zero_padded), xp.array(self.pulse_shape_filter), "same")
 
@@ -296,7 +301,8 @@ def _rrc_taps(self, size_in_symbols: int, alpha: float = .35) -> np.ndarray:
         n = np.arange(-M * Ns, M * Ns + 1)
         taps = np.zeros(int(2 * M * Ns + 1))
         for i in range(int(2 * M * Ns + 1)):
-            if abs(1 - 16 * alpha ** 2 * (n[i] / Ns) ** 2) <= np.finfo(np.float64).eps / 2:
+            # handle the discontinuity at t=+-Ns/(4*alpha)
+            if (n[i]*4*alpha == Ns or n[i]*4*alpha == -Ns):
                 taps[i] = 1 / 2. * ((1 + alpha) * np.sin((1 + alpha) * np.pi / (4. * alpha)) - (1 - alpha) * np.cos(
                     (1 - alpha) * np.pi / (4. * alpha)) + (4 * alpha) / np.pi * np.sin(
                     (1 - alpha) * np.pi / (4. * alpha)))
@@ -925,3 +931,23 @@ def _generate_samples(self, item: Tuple) -> np.ndarray:
             np.random.set_state(orig_state)  # return numpy back to its previous state
 
         return modulated[-self.num_iq_samples:]
+
+
+def estimate_filter_length ( AdB, fs, transitionBandwidth ):
+    # estimate the length of an FIR filter using harris' approximaion,
+	# N ~= (sampling rate/transition bandwidth)*(sidelobe attenuation in dB / 22)
+    # fred harris, Multirate Signal Processing for Communication Systems,
+    # Second Edition, p.59
+    filter_length = int(np.round((fs/transitionBandwidth)*(AdB/22)))
+
+    # odd-length filters are desirable because they do not introduce a half-sample delay
+    if (np.mod(filter_length,2) == 0):
+        filter_length += 1
+
+    return filter_length
+
+
+
+
+
+