more accurate state initialization

reverse_goertzel.py

@@ -7,22 +7,25 @@ def goertzel_sinusoid(freq, duration, sample_rate, amplitude):
     omega = (2.0 * math.pi * freq) / sample_rate
     coeff = 2.0 * math.cos(omega)
     
-    # Initialize state variables
-    q1 = 1.0 # previous sample in sinusoid (1.0 for sample 1)
-    q2 = 1.0 # previous previous sample (approximately 1.0 for sample 1)
-    result = []
+    # Initialize state variables for cos wave
+    # You can use 1.0 for q1 and q2 for a cos wave with slightly larger amplitude and a phase shift of 1/2 a sample
+    # q1 previous sample in sinusoid
+    q1 = math.cos(omega * (n - 1)) # use math.sin(omega * (n-1)) for sin wave
+    # q2 previous previous sample
+    q2 = math.cos(omega * (n - 2)) # use math.sin(omega * (n-2)) for sin wave
+    result = np.zeros(n)
     
     for i in range(n):
         sample = coeff * q1 - q2
         q2 = q1
         q1 = sample
-        result.append(sample * amplitude)
+        result[i] = sample * amplitude
     
     return result
 
-def sinusoid(n, cycles=1):
+def sinusoid(n, cycles=1, phase=0):
     result = []
-    for i in range(1, n+1):
+    for i in range(phase, n+phase):
         sample = math.cos(2.0 * cycles * math.pi * (i/n))
         result.append(sample)
     return result
@@ -34,12 +37,13 @@ def main():
     signal = goertzel_sinusoid(1, cycles, samp_per_cycle, 1)
     reference = np.array(sinusoid(len, cycles))
     error = reference - signal
+    print("max amplitude:", signal.max())
     print("max error:", error.max())
     x = np.array(range(0, len))
     plt.plot(x, signal)
     plt.plot(x, reference)
     plt.plot(x, error)
-    #plt.plot(x, error*100)
+    #plt.plot(x, error*100000000000)
     plt.show()
 
 if __name__ == "__main__":