Filter: Alter Notch filter formula to remove /0 and allow perfect notch.

This formulation of the notch equations lets the user specify the depth of the Notch. The presence of a diveide by A prevents the gain going to zero and therefore achieving a perfect notch. It also provides the risk that a user may attempt to do this and cause a divide by zero error. This change adds the ability to achive a perfect notch and removes the possibility of a divide by zero.

Add Notch Filter parameter checking

libraries/Filter/NotchFilter.cpp

@@ -20,9 +20,13 @@
  */
 template <class T>
 void NotchFilter<T>::calculate_A_and_Q(float center_freq_hz, float bandwidth_hz, float attenuation_dB, float& A, float& Q) {
-    const float octaves = log2f(center_freq_hz / (center_freq_hz - bandwidth_hz / 2.0f)) * 2.0f;
     A = powf(10, -attenuation_dB / 40.0f);
+    if (center_freq_hz > 0.5 * bandwidth_hz) {
+        const float octaves = log2f(center_freq_hz / (center_freq_hz - bandwidth_hz / 2.0f)) * 2.0f;
         Q = sqrtf(powf(2, octaves)) / (powf(2, octaves) - 1.0f);
+    } else {
+        Q = 0.0;
+    }
 }
 
 /*
@@ -31,26 +35,32 @@ void NotchFilter<T>::calculate_A_and_Q(float center_freq_hz, float bandwidth_hz,
 template <class T>
 void NotchFilter<T>::init(float sample_freq_hz, float center_freq_hz, float bandwidth_hz, float attenuation_dB)
 {
-    // adjust the center frequency to be in the allowable range
-    center_freq_hz = constrain_float(center_freq_hz, bandwidth_hz * 0.52f, sample_freq_hz * 0.48f);
-
+    // check center frequency is in the allowable range
+    if ((center_freq_hz > 0.5 * bandwidth_hz) && (center_freq_hz < 0.5 * sample_freq_hz)) {
         float A, Q;
         calculate_A_and_Q(center_freq_hz, bandwidth_hz, attenuation_dB, A, Q);
         init_with_A_and_Q(sample_freq_hz, center_freq_hz, A, Q);
+    } else {
+        initialised = false;
+    }
 }
 
 template <class T>
 void NotchFilter<T>::init_with_A_and_Q(float sample_freq_hz, float center_freq_hz, float A, float Q)
 {
+    if ((center_freq_hz > 0.0) && (center_freq_hz < 0.5 * sample_freq_hz) && (Q > 0.0)) {
         float omega = 2.0 * M_PI * center_freq_hz / sample_freq_hz;
-    float alpha = sinf(omega) / (2 * Q/A);
-    b0 =  1.0 + alpha*A;
+        float alpha = sinf(omega) / (2 * Q);
+        b0 =  1.0 + alpha*sq(A);
         b1 = -2.0 * cosf(omega);
-    b2 =  1.0 - alpha*A;
-    a0_inv =  1.0/(1.0 + alpha/A);
-    a1 = -2.0 * cosf(omega);
-    a2 =  1.0 - alpha/A;
+        b2 =  1.0 - alpha*sq(A);
+        a0_inv =  1.0/(1.0 + alpha);
+        a1 = b1;
+        a2 =  1.0 - alpha;
         initialised = true;
+    } else {
+        initialised = false;
+    }
 }
 
 /*
@@ -61,7 +71,12 @@ T NotchFilter<T>::apply(const T &sample)
 {
     if (!initialised) {
         // if we have not been initialised when return the input
-        // sample as output
+        // sample as output and update delayed samples
+        ntchsig2 = ntchsig1;
+        ntchsig1 = ntchsig;
+        ntchsig = sample;
+        signal2 = signal1;
+        signal1 = sample;
         return sample;
     }
     ntchsig2 = ntchsig1;