Update README snippet to 48kHz and Cheby2 comparison (#27)

* feat: update README and graphs to 48kHz and Butterworth vs Chebyshev II comparison

* fix: update generate_graphs.py to use 48kHz for signal decomposition plot

Author: jmrplens

.github/images/signal_decomposition.png

@@ -287,23 +287,23 @@ import numpy as np
 from pyoctaveband import octavefilter
 
 # 1. Generate a signal (Sum of 250Hz and 1000Hz)
-fs = 8000
-t = np.linspace(0, 0.5, fs // 2, endpoint=False)
+fs = 48000
+t = np.linspace(0, 0.5, int(fs * 0.5), endpoint=False)
 y = np.sin(2 * np.pi * 250 * t) + np.sin(2 * np.pi * 1000 * t)
 
-# 2. Compare architectures (Butterworth vs Chebyshev I)
+# 2. Compare architectures (Butterworth vs Chebyshev II)
 # Filter with Butterworth (default)
 spl_b, freq, xb_butter = octavefilter(y, fs=fs, fraction=1, sigbands=True, filter_type='butter')
 
-# Filter with Chebyshev I (ripples in passband, steeper roll-off)
-spl_c, _, xb_cheby = octavefilter(y, fs=fs, fraction=1, sigbands=True, filter_type='cheby1')
+# Filter with Chebyshev II (flat passband, ripples in stopband)
+spl_c2, _, xb_cheby2 = octavefilter(y, fs=fs, fraction=1, sigbands=True, filter_type='cheby2')
 
-# 'xb_butter' and 'xb_cheby' contain the time-domain signals per band
+# 'xb_butter' and 'xb_cheby2' contain the time-domain signals per band
 ```
 
 <img src="https://raw.githubusercontent.com/jmrplens/PyOctaveBand/main/.github/images/signal_decomposition.png" width="80%"></img>
 
-*The plot compares the **Butterworth** (solid blue) and **Chebyshev I** (dashed red) responses. The bottom plot shows the **Impulse Response**, highlighting the differences in stability and decay.*
+*The plot compares the **Butterworth** (solid blue) and **Chebyshev II** (dashed red) responses. The bottom plot shows the **Impulse Response**, highlighting the differences in stability and transient decay.*
 
 ---
 

README.md

@@ -241,8 +241,8 @@ def generate_multichannel_response(output_dir: str) -> None:
 
 def generate_decomposition_plot(output_dir: str) -> None:
     """Generate time-domain decomposition plot comparing two filter types (Butterworth vs Chebyshev II)."""
-    print("Generating signal_decomposition.png with comparison (Butter vs Cheby2)...")
-    fs = 8000
+    print("Generating signal_decomposition.png with comparison (Butter vs Cheby2) @ 48kHz...")
+    fs = 48000
     duration = 0.5
     t = np.linspace(0, duration, int(fs * duration), endpoint=False)
 
@@ -265,7 +265,7 @@ def generate_decomposition_plot(output_dir: str) -> None:
 
     # 1. Original Signal
     axes[0].plot(t, y, color="black", linewidth=1.5)
-    axes[0].set_title("Original Signal (250 Hz + 1000 Hz Sum)", fontweight="bold")
+    axes[0].set_title("Original Signal (250 Hz + 1000 Hz Sum) @ 48 kHz", fontweight="bold")
     axes[0].set_ylim(y_lim)
     axes[0].set_xlim(0, 0.04)