diff --git a/shazam/filter.go b/shazam/filter.go
index 32419eb..d8b3db5 100644
--- a/shazam/filter.go
+++ b/shazam/filter.go
@@ -4,34 +4,33 @@ import (
 	"math"
 )
 
-// LowPassFilter implements a simple first-order low-pass filter
+// LowPassFilter is a first-order low-pass filter using H(p) = 1 / (1 + pRC)
 type LowPassFilter struct {
 	alpha float64 // Filter coefficient
 	yPrev float64 // Previous output value
 }
 
-// NewLowPassFilter creates a new LowPassFilter with the specified cutoff frequency and sample rate
+// NewLowPassFilter creates a new low-pass filter
 func NewLowPassFilter(cutoffFrequency, sampleRate float64) *LowPassFilter {
-	// Calculate filter coefficient (alpha) based on cutoff frequency and sample rate
-	alpha := 1.0 - math.Exp(-2.0*math.Pi*cutoffFrequency/sampleRate)
-
+	rc := 1.0 / (2 * math.Pi * cutoffFrequency)
+	dt := 1.0 / sampleRate
+	alpha := dt / (rc + dt)
 	return &LowPassFilter{
 		alpha: alpha,
 		yPrev: 0,
 	}
 }
 
-// Filter filters the input signal using the low-pass filter and returns the filtered output
+// Filter processes the input signal through the low-pass filter
 func (lpf *LowPassFilter) Filter(input []float64) []float64 {
 	filtered := make([]float64, len(input))
-
 	for i, x := range input {
-		// Update filter output using the single-pole low-pass filter equation
-		output := lpf.alpha*x + (1-lpf.alpha)*lpf.yPrev
-		lpf.yPrev = output
-
-		filtered[i] = output
+		if i == 0 {
+			filtered[i] = x * lpf.alpha
+		} else {
+			filtered[i] = lpf.alpha*x + (1-lpf.alpha)*lpf.yPrev
+		}
+		lpf.yPrev = filtered[i]
 	}
-
 	return filtered
 }