feature/high-low-pass-filter (#2)

Co-authored-by: Bastian Bührig <bastian.buehrig@2bconsult.eu>
Reviewed-on: #2

pkg/convolve/convolve.go

@@ -341,3 +341,115 @@ func FadeOutLinear(data []float64, fadeSamples int) []float64 {
 	}
 	return out
 }
+
+// ApplyLowpassButterworth applies a 2nd-order Butterworth low-pass filter to the data.
+// cutoffHz: cutoff frequency in Hz, sampleRate: sample rate in Hz.
+func ApplyLowpassButterworth(data []float64, sampleRate int, cutoffHz float64) []float64 {
+	if cutoffHz <= 0 || cutoffHz >= float64(sampleRate)/2 {
+		return data
+	}
+	// Biquad coefficients
+	w0 := 2 * math.Pi * cutoffHz / float64(sampleRate)
+	cosw0 := math.Cos(w0)
+	sinw0 := math.Sin(w0)
+	Q := 1.0 / math.Sqrt(2) // Butterworth Q
+	alpha := sinw0 / (2 * Q)
+
+	b0 := (1 - cosw0) / 2
+	b1 := 1 - cosw0
+	b2 := (1 - cosw0) / 2
+	a0 := 1 + alpha
+	a1 := -2 * cosw0
+	a2 := 1 - alpha
+
+	// Normalize
+	b0 /= a0
+	b1 /= a0
+	b2 /= a0
+	a1 /= a0
+	a2 /= a0
+
+	// Apply filter (Direct Form I)
+	out := make([]float64, len(data))
+	var x1, x2, y1, y2 float64
+	for i := 0; i < len(data); i++ {
+		x0 := data[i]
+		y0 := b0*x0 + b1*x1 + b2*x2 - a1*y1 - a2*y2
+		out[i] = y0
+		x2 = x1
+		x1 = x0
+		y2 = y1
+		y1 = y0
+	}
+	return out
+}
+
+// ApplyHighpassButterworth applies a 2nd-order Butterworth high-pass filter to the data.
+// cutoffHz: cutoff frequency in Hz, sampleRate: sample rate in Hz.
+func ApplyHighpassButterworth(data []float64, sampleRate int, cutoffHz float64) []float64 {
+	if cutoffHz <= 0 || cutoffHz >= float64(sampleRate)/2 {
+		return data
+	}
+	// Biquad coefficients
+	w0 := 2 * math.Pi * cutoffHz / float64(sampleRate)
+	cosw0 := math.Cos(w0)
+	sinw0 := math.Sin(w0)
+	Q := 1.0 / math.Sqrt(2) // Butterworth Q
+	alpha := sinw0 / (2 * Q)
+
+	b0 := (1 + cosw0) / 2
+	b1 := -(1 + cosw0)
+	b2 := (1 + cosw0) / 2
+	a0 := 1 + alpha
+	a1 := -2 * cosw0
+	a2 := 1 - alpha
+
+	// Normalize
+	b0 /= a0
+	b1 /= a0
+	b2 /= a0
+	a1 /= a0
+	a2 /= a0
+
+	// Apply filter (Direct Form I)
+	out := make([]float64, len(data))
+	var x1, x2, y1, y2 float64
+	for i := 0; i < len(data); i++ {
+		x0 := data[i]
+		y0 := b0*x0 + b1*x1 + b2*x2 - a1*y1 - a2*y2
+		out[i] = y0
+		x2 = x1
+		x1 = x0
+		y2 = y1
+		y1 = y0
+	}
+	return out
+}
+
+// CascadeLowcut applies the low-cut (high-pass) filter multiple times for steeper slopes.
+// slopeDb: 12, 24, 36, ... (dB/octave)
+func CascadeLowcut(data []float64, sampleRate int, cutoffHz float64, slopeDb int) []float64 {
+	if slopeDb < 12 {
+		slopeDb = 12
+	}
+	n := slopeDb / 12
+	out := data
+	for i := 0; i < n; i++ {
+		out = ApplyHighpassButterworth(out, sampleRate, cutoffHz)
+	}
+	return out
+}
+
+// CascadeHighcut applies the high-cut (low-pass) filter multiple times for steeper slopes.
+// slopeDb: 12, 24, 36, ... (dB/octave)
+func CascadeHighcut(data []float64, sampleRate int, cutoffHz float64, slopeDb int) []float64 {
+	if slopeDb < 12 {
+		slopeDb = 12
+	}
+	n := slopeDb / 12
+	out := data
+	for i := 0; i < n; i++ {
+		out = ApplyLowpassButterworth(out, sampleRate, cutoffHz)
+	}
+	return out
+}