Init commit with level 1 python source

source/level_1/level_1.py

@@ -0,0 +1,843 @@
+#! /usr/bin/env python
+
+from __future__ import annotations
+
+from pathlib import Path
+from typing import Dict, Tuple, List, Literal, TypedDict, Union
+
+import numpy as np
+import soundfile as sf
+from scipy.signal.windows import kaiser
+
+# --------------------------------
+# Public Type aliases (Level 1)
+# --------------------------------
+
+FrameType = Literal["OLS", "LSS", "ESH", "LPS"]
+"""
+Frame type codes:
+- "OLS": ONLY_LONG_SEQUENCE
+- "LSS": LONG_START_SEQUENCE
+- "ESH": EIGHT_SHORT_SEQUENCE
+- "LPS": LONG_STOP_SEQUENCE
+"""
+
+WinType = Literal["KBD", "SIN"]
+"""
+Window type codes:
+- "KBD": Kaiser-Bessel-Derived
+- "SIN": sinusoid
+"""
+
+FrameT = np.ndarray
+"""
+Time-domain frame.
+Expected shape: (2048, 2) for stereo (two channels).
+dtype: float (e.g., float32/float64).
+"""
+
+FrameChannelT = np.ndarray
+"""
+Time-domain single channel frame.
+Expected shape: (2048,).
+dtype: float (e.g., float32/float64).
+"""
+
+
+FrameF = np.ndarray
+"""
+Frequency-domain frame (MDCT coefficients).
+As per spec (Level 1):
+- If frame_type in {"OLS","LSS","LPS"}: shape (1024, 2)
+- If frame_type == "ESH": shape (128, 16) where 8 subframes x 2 channels
+  are placed in columns according to the subframe order (i.e., each subframe is (128,2)).
+"""
+
+ChannelKey = Literal["chl", "chr"]
+
+
+class AACChannelFrameF(TypedDict):
+    """Channel payload for aac_seq_1[i]["chl"] or ["chr"] (Level 1)."""
+    frame_F: np.ndarray
+    # frame_F for one channel:
+    # - ESH: shape (128, 8)
+    # - else: shape (1024, 1)
+
+
+class AACSeq1Frame(TypedDict):
+    """One frame dictionary of aac_seq_1 (Level 1)."""
+    frame_type: FrameType
+    win_type: WinType
+    chl: AACChannelFrameF
+    chr: AACChannelFrameF
+
+
+AACSeq1 = List[AACSeq1Frame]
+"""AAC sequence for Level 1:
+List of length K (K = number of frames).
+Each element is a dict with keys:
+- "frame_type", "win_type", "chl", "chr"
+"""
+
+# Global Options
+# -----------------------------------------------------------------------------
+
+# Window type
+# Options: "SIN", "KBD"
+WIN_TYPE: WinType = "SIN"
+
+
+# Private helpers for SSC
+# -----------------------------------------------------------------------------
+
+# See Table 1 in mm-2025-hw-v0.1.pdf
+STEREO_MERGE_TABLE: Dict[Tuple[FrameType, FrameType], FrameType] = {
+    ("OLS", "OLS"): "OLS",
+    ("OLS", "LSS"): "LSS",
+    ("OLS", "ESH"): "ESH",
+    ("OLS", "LPS"): "LPS",
+    ("LSS", "OLS"): "LSS",
+    ("LSS", "LSS"): "LSS",
+    ("LSS", "ESH"): "ESH",
+    ("LSS", "LPS"): "ESH",
+    ("ESH", "OLS"): "ESH",
+    ("ESH", "LSS"): "ESH",
+    ("ESH", "ESH"): "ESH",
+    ("ESH", "LPS"): "ESH",
+    ("LPS", "OLS"): "LPS",
+    ("LPS", "LSS"): "ESH",
+    ("LPS", "ESH"): "ESH",
+    ("LPS", "LPS"): "LPS",
+}
+
+def _detect_attack(next_frame_channel: FrameChannelT) -> bool:
+    """
+    Detect if next frame (single channel) implies ESH according to the spec's attack criterion.
+
+    Parameters
+    ----------
+    next_frame_channel : FrameChannelT
+        One channel of next_frame_T (shape: (2048,), dtype float).
+
+    Returns
+    -------
+    attack : bool
+        True if an attack is detected (=> next frame predicted ESH), else False.
+
+    Notes
+    -----
+    The spec describes:
+
+    - High-pass filter applied to next_frame_channel
+    - Split into 16 segments of length 128
+    - Compute segment energies s(l)
+    - Compute ds(l) = s(l) / s(l-1)
+    - Attack exists if there exists l in {1..7} such that:
+        s(l) > 1e-3 and ds(l) > 10
+    """
+    x = next_frame_channel # local alias, x assumed to be a 1-D array of length 2048
+
+    # High-pass filter H(z) = (1 - z^-1) / (1 - 0.5 z^-1)
+    # Implemented as: y[n] = x[n] - x[n-1] + 0.5*y[n-1]
+    y = np.zeros_like(x)
+    prev_x = 0.0
+    prev_y = 0.0
+    for n in range(x.shape[0]):
+        xn = float(x[n])
+        yn = (xn - prev_x) + 0.5 * prev_y
+        y[n] = yn
+        prev_x = xn
+        prev_y = yn
+
+    # Segment energies over 16 blocks of 128 samples.
+    s = np.empty(16, dtype=np.float64)
+    for l in range(16):
+        a = l * 128
+        b = (l + 1) * 128
+        seg = y[a:b]
+        s[l] = float(np.sum(seg * seg))
+
+    # ds(l) for l>=1. For l=0 not defined, keep 0.
+    ds = np.zeros(16, dtype=np.float64)
+    eps = 1e-12  # avoid division by zero without changing logic materially
+    for l in range(1, 16):
+        ds[l] = s[l] / max(s[l - 1], eps)
+
+    # Spec: check l in {1..7}
+    for l in range(1, 8):
+        if (s[l] > 1e-3) and (ds[l] > 10.0):
+            return True
+
+    return False
+
+
+def _decide_frame_type(prev_frame_type: FrameType, attack: bool) -> FrameType:
+    """
+    Decide current frame type for a single channel based on prev_frame_type and next-frame attack.
+
+    Parameters
+    ----------
+    prev_frame_type : FrameType
+        Previous frame type (one of "OLS","LSS","ESH","LPS").
+    attack : bool
+        Whether next frame is predicted ESH for this channel.
+
+    Returns
+    -------
+    frame_type : FrameType
+        The per-channel decision for the current frame.
+
+    Rules (spec)
+    ------------
+    - If prev is "LSS" => current is "ESH" (fixed)
+    - If prev is "LPS" => current is "OLS" (fixed)
+    - If prev is "OLS" => current is "LSS" if attack else "OLS"
+    - If prev is "ESH" => current is "ESH" if attack else "LPS"
+    """
+    if prev_frame_type == "LSS":
+        return "ESH"
+    if prev_frame_type == "LPS":
+        return "OLS"
+    if prev_frame_type == "OLS":
+        return "LSS" if attack else "OLS"
+    if prev_frame_type == "ESH":
+        return "ESH" if attack else "LPS"
+
+    raise ValueError(f"Invalid prev_frame_type: {prev_frame_type!r}")
+
+
+def _stereo_merge(ft_l: FrameType, ft_r: FrameType) -> FrameType:
+    """
+    Merge per-channel frame types into one common frame type using the spec table.
+
+    Parameters
+    ----------
+    ft_l : FrameType
+        Frame type decision for channel 0 (left).
+    ft_r : FrameType
+        Frame type decision for channel 1 (right).
+
+    Returns
+    -------
+    common : FrameType
+        The common final frame type.
+    """
+    try:
+        return STEREO_MERGE_TABLE[(ft_l, ft_r)]
+    except KeyError as e:
+        raise ValueError(f"Invalid stereo merge pair: {(ft_l, ft_r)}") from e
+
+
+
+# Private helpers for Filterbank
+# -----------------------------------------------------------------------------
+
+def _sin_window(N: int) -> np.ndarray:
+    """
+    Sine window (full length N).
+    w[n] = sin(pi/N * (n + 0.5)), 0 <= n < N
+    """
+    n = np.arange(N, dtype=np.float64)
+    return np.sin((np.pi / N) * (n + 0.5))
+
+
+def _kbd_window(N: int, alpha: float) -> np.ndarray:
+    """
+    Kaiser-Bessel-Derived (KBD) window (full length N).
+
+    This follows the standard KBD construction:
+    - Build Kaiser kernel of length N/2 + 1
+    - Use cumulative sum and sqrt normalization to form left and right halves
+    """
+    half = N // 2
+
+    # Kaiser kernel length: half + 1 samples (0 .. half)
+    # beta = pi * alpha per the usual correspondence with the ISO definition
+    kernel = kaiser(half + 1, beta=np.pi * alpha).astype(np.float64)
+
+    csum = np.cumsum(kernel)
+    denom = csum[-1]
+
+    w_left = np.sqrt(csum[:-1] / denom)  # length half, n = 0 .. half-1
+    w_right = w_left[::-1]               # mirror for second half
+
+    return np.concatenate([w_left, w_right])
+
+
+def _long_window(win_type: WinType) -> np.ndarray:
+    """
+    Long window (length 2048) for the selected win_type.
+    """
+    if win_type == "SIN":
+        return _sin_window(2048)
+    if win_type == "KBD":
+        # Assignment-specific alpha values
+        return _kbd_window(2048, alpha=6.0)
+    raise ValueError(f"Invalid win_type: {win_type!r}")
+
+
+def _short_window(win_type: WinType) -> np.ndarray:
+    """
+    Short window (length 256) for the selected win_type.
+    """
+    if win_type == "SIN":
+        return _sin_window(256)
+    if win_type == "KBD":
+        # Assignment-specific alpha values
+        return _kbd_window(256, alpha=4.0)
+    raise ValueError(f"Invalid win_type: {win_type!r}")
+
+
+def _window_sequence(frame_type: FrameType, win_type: WinType) -> np.ndarray:
+    """
+    Build the 2048-sample window sequence for OLS/LSS/LPS.
+
+    We follow the simplified assumption:
+    - The same window shape (KBD or SIN) is used globally (no mixed halves).
+    - Therefore, the left and right halves are drawn from the same family.
+    """
+    wL = _long_window(win_type)   # length 2048
+    wS = _short_window(win_type)  # length 256
+
+    if frame_type == "OLS":
+        return wL
+
+    if frame_type == "LSS":
+        # 0..1023: left half of long window
+        # 1024..1471: ones (448 samples)
+        # 1472..1599: right half of short window (128 samples)
+        # 1600..2047: zeros (448 samples)
+        out = np.zeros(2048, dtype=np.float64)
+        out[0:1024] = wL[0:1024]
+        out[1024:1472] = 1.0
+        out[1472:1600] = wS[128:256]
+        out[1600:2048] = 0.0
+        return out
+
+    if frame_type == "LPS":
+        # 0..447: zeros (448)
+        # 448..575: left half of short window (128)
+        # 576..1023: ones (448)
+        # 1024..2047: right half of long window (1024)
+        out = np.zeros(2048, dtype=np.float64)
+        out[0:448] = 0.0
+        out[448:576] = wS[0:128]
+        out[576:1024] = 1.0
+        out[1024:2048] = wL[1024:2048]
+        return out
+
+    raise ValueError(f"Invalid frame_type for long window sequence: {frame_type!r}")
+
+
+def _mdct(s: np.ndarray) -> np.ndarray:
+    """
+    MDCT (direct form) as given in the assignment.
+
+    Input:
+      s: windowed time samples of length N (N = 2048 or 256)
+
+    Output:
+      X: MDCT coefficients of length N/2
+
+    Definition:
+      X[k] = 2 * sum_{n=0 .. N-1} s[n] * cos(2*pi/N * (n + n0) * (k + 1/2))
+      where n0 = (N/2 + 1)/2
+    """
+    s = np.asarray(s, dtype=np.float64)
+    N = int(s.shape[0])
+    if N not in (2048, 256):
+        raise ValueError("MDCT input length must be 2048 or 256.")
+
+    n0 = (N / 2.0 + 1.0) / 2.0
+
+    n = np.arange(N, dtype=np.float64) + n0
+    k = np.arange(N // 2, dtype=np.float64) + 0.5
+
+    # Cosine matrix: shape (N, N/2)
+    C = np.cos((2.0 * np.pi / N) * np.outer(n, k))
+    X = 2.0 * (s @ C)
+
+    return X
+
+def _imdct(X: np.ndarray) -> np.ndarray:
+    """
+    IMDCT (direct form) as given in the assignment.
+
+    Input:
+      X: MDCT coefficients of length N/2 (N = 2048 or 256)
+
+    Output:
+      s: time samples of length N
+
+    Definition:
+      s[n] = (2/N) * sum_{k=0 .. N/2-1} X[k] * cos(2*pi/N * (n + n0) * (k + 1/2))
+      where n0 = (N/2 + 1)/2
+    """
+    X = np.asarray(X, dtype=np.float64).reshape(-1)
+    K = int(X.shape[0])
+    if K not in (1024, 128):
+        raise ValueError("IMDCT input length must be 1024 or 128.")
+
+    N = 2 * K
+    n0 = (N / 2.0 + 1.0) / 2.0
+
+    n = np.arange(N, dtype=np.float64) + n0
+    k = np.arange(K, dtype=np.float64) + 0.5
+
+    C = np.cos((2.0 * np.pi / N) * np.outer(n, k))  # (N, K)
+    s = (2.0 / N) * (C @ X)
+
+    return s
+
+
+def _filter_bank_esh_channel(x_ch: np.ndarray, win_type: WinType) -> np.ndarray:
+    """
+    ESH analysis for one channel.
+
+    Returns:
+      X_esh: shape (128, 8), where each column is the 128 MDCT coeffs of one short window.
+    """
+    wS = _short_window(win_type)
+    X_esh = np.empty((128, 8), dtype=np.float64)
+
+    # ESH subwindows are taken from the central region:
+    # start positions: 448 + 128*j, j = 0..7
+    for j in range(8):
+        start = 448 + 128 * j
+        seg = x_ch[start:start + 256] * wS
+        X_esh[:, j] = _mdct(seg)
+
+    return X_esh
+
+
+
+
+def _unpack_esh(frame_F: np.ndarray) -> tuple[np.ndarray, np.ndarray]:
+    """
+    Unpack ESH spectrum from shape (128, 16) into per-channel arrays (128, 8).
+
+    Mapping is the inverse of the packing used in filter_bank():
+      out[:, 2*j]   = left[:, j]
+      out[:, 2*j+1] = right[:, j]
+    """
+    if frame_F.shape != (128, 16):
+        raise ValueError("ESH frame_F must have shape (128, 16).")
+
+    left = np.empty((128, 8), dtype=np.float64)
+    right = np.empty((128, 8), dtype=np.float64)
+    for j in range(8):
+        left[:, j] = frame_F[:, 2 * j + 0]
+        right[:, j] = frame_F[:, 2 * j + 1]
+    return left, right
+
+
+def _i_filter_bank_esh_channel(X_esh: np.ndarray, win_type: WinType) -> np.ndarray:
+    """
+    ESH synthesis for one channel.
+
+    Input:
+      X_esh: (128, 8) MDCT coeffs for 8 short windows
+
+    Output:
+      x_ch: (2048, ) time-domain frame contribution (windowed),
+            ready for OLA at the caller level.
+    """
+    if X_esh.shape != (128, 8):
+        raise ValueError("X_esh must have shape (128, 8).")
+
+    wS = _short_window(win_type)
+    out = np.zeros(2048, dtype=np.float64)
+
+    # Each short IMDCT returns 256 samples. Place them at:
+    # start = 448 + 128*j, j=0..7 (50% overlap)
+    for j in range(8):
+        seg = _imdct(X_esh[:, j]) * wS  # (256,)
+        start = 448 + 128 * j
+        out[start:start + 256] += seg
+
+    return out
+
+# -----------------------------------------------------------------------------
+# Public Function prototypes (Level 1)
+# -----------------------------------------------------------------------------
+
+def SSC(frame_T: FrameT, next_frame_T: FrameT, prev_frame_type: FrameType) -> FrameType:
+    """
+    Sequence Segmentation Control (SSC).
+    Selects and returns the frame type for the current frame (i) based on input parameters.
+
+    Parameters
+    -------
+    frame_T: FrameT
+        current time-domain frame i, stereo, shape (2048, 2)
+    next_frame_T: FrameT
+        next time-domain frame (i+1), stereo, shape (2048, 2)
+        (used to decide transitions to/from ESH)
+    prev_frame_type: FrameType
+        frame type chosen for the previous frame (i-1)
+
+    Returns
+    -------
+    frame_type : FrameType
+        - "OLS" (ONLY_LONG_SEQUENCE)
+        - "LSS" (LONG_START_SEQUENCE)
+        - "ESH" (EIGHT_SHORT_SEQUENCE)
+        - "LPS" (LONG_STOP_SEQUENCE)
+    """
+    if frame_T.shape != (2048, 2):
+        raise ValueError("frame_T must have shape (2048, 2).")
+    if next_frame_T.shape != (2048, 2):
+        raise ValueError("next_frame_T must have shape (2048, 2).")
+
+    # Detect attack independently per channel on next frame.
+    attack_l = _detect_attack(next_frame_T[:, 0])
+    attack_r = _detect_attack(next_frame_T[:, 1])
+
+    # Decide per-channel type based on shared prev_frame_type.
+    ft_l = _decide_frame_type(prev_frame_type, attack_l)
+    ft_r = _decide_frame_type(prev_frame_type, attack_r)
+
+    # Stereo merge as per Table 1.
+    return _stereo_merge(ft_l, ft_r)
+
+
+def filter_bank(frame_T: FrameT, frame_type: FrameType, win_type: WinType) -> FrameF:
+    """
+    Filterbank stage (MDCT analysis).
+
+    Parameters
+    ----------
+    frame_T : FrameT
+        Time-domain frame, stereo, shape (2048, 2).
+    frame_type : FrameType
+        Type of the frame under encoding ("OLS"|"LSS"|"ESH"|"LPS").
+    win_type : WinType
+        Window type ("KBD" or "SIN") used for the current frame.
+
+    Returns
+    -------
+    frame_F : FrameF
+        Frequency-domain MDCT coefficients:
+        - If frame_type in {"OLS","LSS","LPS"}: array shape (1024, 2)
+          containing MDCT coefficients for both channels.
+        - If frame_type == "ESH": contains 8 subframes, each subframe has shape (128,2),
+          placed in columns according to subframe order, i.e. overall shape (128, 16).
+    """
+    if frame_T.shape != (2048, 2):
+        raise ValueError("frame_T must have shape (2048, 2).")
+
+    xL = frame_T[:, 0].astype(np.float64, copy=False)
+    xR = frame_T[:, 1].astype(np.float64, copy=False)
+
+    if frame_type in ("OLS", "LSS", "LPS"):
+        w = _window_sequence(frame_type, win_type)  # length 2048
+        XL = _mdct(xL * w)  # length 1024
+        XR = _mdct(xR * w)  # length 1024
+        out = np.empty((1024, 2), dtype=np.float64)
+        out[:, 0] = XL
+        out[:, 1] = XR
+        return out
+
+    if frame_type == "ESH":
+        Xl = _filter_bank_esh_channel(xL, win_type)  # (128, 8)
+        Xr = _filter_bank_esh_channel(xR, win_type)  # (128, 8)
+
+        # Pack into (128, 16): each subframe as (128,2) placed in columns
+        out = np.empty((128, 16), dtype=np.float64)
+        for j in range(8):
+            out[:, 2 * j + 0] = Xl[:, j]
+            out[:, 2 * j + 1] = Xr[:, j]
+        return out
+
+    raise ValueError(f"Invalid frame_type: {frame_type!r}")
+
+
+def i_filter_bank(frame_F: FrameF, frame_type: FrameType, win_type: WinType) -> FrameT:
+    """
+    Inverse filterbank (IMDCT synthesis).
+
+    Parameters
+    ----------
+    frame_F : FrameF
+        Frequency-domain MDCT coefficients as produced by filter_bank().
+    frame_type : FrameType
+        Frame type ("OLS"|"LSS"|"ESH"|"LPS").
+    win_type : WinType
+        Window type ("KBD" or "SIN").
+
+    Returns
+    -------
+    frame_T : FrameT
+        Reconstructed time-domain frame, stereo, shape (2048, 2).
+    """
+    if frame_type in ("OLS", "LSS", "LPS"):
+        if frame_F.shape != (1024, 2):
+            raise ValueError("For OLS/LSS/LPS, frame_F must have shape (1024, 2).")
+
+        w = _window_sequence(frame_type, win_type)
+
+        xL = _imdct(frame_F[:, 0]) * w
+        xR = _imdct(frame_F[:, 1]) * w
+
+        out = np.empty((2048, 2), dtype=np.float64)
+        out[:, 0] = xL
+        out[:, 1] = xR
+        return out
+
+    if frame_type == "ESH":
+        if frame_F.shape != (128, 16):
+            raise ValueError("For ESH, frame_F must have shape (128, 16).")
+
+        Xl, Xr = _unpack_esh(frame_F)
+        xL = _i_filter_bank_esh_channel(Xl, win_type)
+        xR = _i_filter_bank_esh_channel(Xr, win_type)
+
+        out = np.empty((2048, 2), dtype=np.float64)
+        out[:, 0] = xL
+        out[:, 1] = xR
+        return out
+
+    raise ValueError(f"Invalid frame_type: {frame_type!r}")
+
+
+def aac_coder_1(filename_in: Union[str, Path]) -> AACSeq1:
+    """
+    Level-1 AAC encoder.
+
+    Parameters
+    ----------
+    filename_in : str | Path
+        Input WAV filename.
+        Assumption: stereo audio, sampling rate 48 kHz.
+
+    Returns
+    -------
+    aac_seq_1 : AACSeq1
+        List of K encoded frames.
+        For each i:
+
+        - aac_seq_1[i]["frame_type"]: FrameType
+        - aac_seq_1[i]["win_type"]: WinType
+        - aac_seq_1[i]["chl"]["frame_F"]:
+            - ESH: shape (128, 8)
+            - else: shape (1024, 1)
+        - aac_seq_1[i]["chr"]["frame_F"]:
+            - ESH: shape (128, 8)
+            - else: shape (1024, 1)
+    """
+    filename_in = Path(filename_in)
+
+    x, fs = sf.read(str(filename_in), always_2d=True)
+    x = np.asarray(x, dtype=np.float64)
+
+    if x.shape[1] != 2:
+        raise ValueError("Input must be stereo (2 channels).")
+    if fs != 48000:
+        raise ValueError("Input sampling rate must be 48 kHz.")
+
+    hop = 1024
+    win = 2048
+
+    # Pad at the beginning to support the first overlap region.
+    # Tail padding is kept minimal; next-frame is padded on-the-fly when needed.
+    pad_pre = np.zeros((hop, 2), dtype=np.float64)
+    pad_post = np.zeros((hop, 2), dtype=np.float64)
+    x_pad = np.vstack([pad_pre, x, pad_post])
+
+    # Number of frames such that current frame fits; next frame will be padded if needed.
+    K = int((x_pad.shape[0] - win) // hop + 1)
+    if K <= 0:
+        raise ValueError("Input too short for framing.")
+
+    aac_seq: AACSeq1 = []
+    prev_frame_type: FrameType = "OLS"
+
+    for i in range(K):
+        start = i * hop
+
+        frame_t: FrameT = x_pad[start:start + win, :]
+        if frame_t.shape != (win, 2):
+            # This should not happen due to K definition, but we keep it explicit.
+            raise ValueError("Internal framing error: frame_t has wrong shape.")
+
+        next_t = x_pad[start + hop:start + hop + win, :]
+
+        # Ensure next_t is always (2048,2) by zero-padding at the tail.
+        if next_t.shape[0] < win:
+            tail = np.zeros((win - next_t.shape[0], 2), dtype=np.float64)
+            next_t = np.vstack([next_t, tail])
+
+        frame_type = SSC(frame_t, next_t, prev_frame_type)
+        frame_f = filter_bank(frame_t, frame_type, WIN_TYPE)
+
+        # Store per-channel as required by AACSeq1 schema
+        if frame_type == "ESH":
+            # frame_f: (128, 16) packed as [L0 R0 L1 R1 ... L7 R7]
+            chl_f = np.empty((128, 8), dtype=np.float64)
+            chr_f = np.empty((128, 8), dtype=np.float64)
+            for j in range(8):
+                chl_f[:, j] = frame_f[:, 2 * j + 0]
+                chr_f[:, j] = frame_f[:, 2 * j + 1]
+        else:
+            # frame_f: (1024, 2)
+            chl_f = frame_f[:, 0:1].astype(np.float64, copy=False)
+            chr_f = frame_f[:, 1:2].astype(np.float64, copy=False)
+
+        aac_seq.append({
+            "frame_type": frame_type,
+            "win_type": WIN_TYPE,
+            "chl": {"frame_F": chl_f},
+            "chr": {"frame_F": chr_f},
+        })
+        prev_frame_type = frame_type
+    return aac_seq
+
+
+def i_aac_coder_1(aac_seq_1: AACSeq1, filename_out: Union[str, Path]) -> np.ndarray:
+    """
+    Level-1 AAC decoder (inverse of aac_coder_1()).
+
+    Parameters
+    ----------
+    aac_seq_1 : AACSeq1
+        Encoded sequence as produced by aac_coder_1().
+    filename_out : str | Path
+        Output WAV filename.
+        Assumption: stereo audio, sampling rate 48 kHz.
+
+    Returns
+    -------
+    x : np.ndarray
+        Decoded audio samples (time-domain).
+        Expected shape: (N, 2) for stereo (N depends on input length).
+    """
+    filename_out = Path(filename_out)
+
+    hop = 1024
+    win = 2048
+    K = len(aac_seq_1)
+
+    # Output includes the encoder padding region, so we reconstruct
+    # full padded stream. For K frames: last frame starts at (K-1)*hop and spans win,
+    # so total length = (K-1)*hop + win
+    n_pad = (K - 1) * hop + win
+    y_pad = np.zeros((n_pad, 2), dtype=np.float64)
+
+    for i, fr in enumerate(aac_seq_1):
+        frame_type = fr["frame_type"]
+        win_type = fr["win_type"]
+
+        chl_f = np.asarray(fr["chl"]["frame_F"], dtype=np.float64)
+        chr_f = np.asarray(fr["chr"]["frame_F"], dtype=np.float64)
+
+        # Re-pack into the format expected by i_filter_bank()
+        if frame_type == "ESH":
+            if chl_f.shape != (128, 8) or chr_f.shape != (128, 8):
+                raise ValueError("ESH channel frame_F must have shape (128, 8).")
+
+            frame_f = np.empty((128, 16), dtype=np.float64)
+            for j in range(8):
+                frame_f[:, 2 * j + 0] = chl_f[:, j]
+                frame_f[:, 2 * j + 1] = chr_f[:, j]
+        else:
+            if chl_f.shape != (1024, 1) or chr_f.shape != (1024, 1):
+                raise ValueError("Non-ESH channel frame_F must have shape (1024, 1).")
+
+            frame_f = np.empty((1024, 2), dtype=np.float64)
+            frame_f[:, 0] = chl_f[:, 0]
+            frame_f[:, 1] = chr_f[:, 0]
+
+        frame_t_hat = i_filter_bank(frame_f, frame_type, win_type)  # (2048, 2)
+
+        start = i * hop
+        y_pad[start:start + win, :] += frame_t_hat
+
+    # Remove boundary padding that encoder adds: hop samples at start and hop at end.
+    if y_pad.shape[0] < 2 * hop:
+        raise ValueError("Decoded stream too short to unpad.")
+
+    y = y_pad[hop:-hop, :]
+
+    sf.write(str(filename_out), y, 48000)
+    return y
+
+
+def demo_aac_1(filename_in: Union[str, Path], filename_out: Union[str, Path]) -> float:
+    """
+    Demonstration for Level-1 codec.
+
+    Runs:
+    - aac_coder_1(filename_in)
+    - i_aac_coder_1(aac_seq_1, filename_out)
+    and computes total SNR between original and decoded audio.
+
+    Parameters
+    ----------
+    filename_in : str | Path
+        Input WAV filename (stereo, 48 kHz).
+    filename_out : str | Path
+        Output WAV filename (stereo, 48 kHz).
+
+    Returns
+    -------
+    SNR : float
+        Overall Signal-to-Noise Ratio in dB.
+    """
+    filename_in = Path(filename_in)
+    filename_out = Path(filename_out)
+
+    # Read original audio (reference)
+    x_ref, fs_ref = sf.read(str(filename_in), always_2d=True)
+    x_ref = np.asarray(x_ref, dtype=np.float64)
+
+    # Encode / decode
+    aac_seq_1 = aac_coder_1(filename_in)
+    x_hat = i_aac_coder_1(aac_seq_1, filename_out)
+    x_hat = np.asarray(x_hat, dtype=np.float64)
+
+    # Ensure 2D stereo shape (N, 2)
+    if x_hat.ndim == 1:
+        x_hat = x_hat.reshape(-1, 1)
+    if x_ref.ndim == 1:
+        x_ref = x_ref.reshape(-1, 1)
+
+    # Align lengths (use common overlap)
+    n = min(x_ref.shape[0], x_hat.shape[0])
+    x_ref = x_ref[:n, :]
+    x_hat = x_hat[:n, :]
+
+    # Match channel count conservatively (common channels)
+    c = min(x_ref.shape[1], x_hat.shape[1])
+    x_ref = x_ref[:, :c]
+    x_hat = x_hat[:, :c]
+
+    # Compute overall SNR over all samples and channels
+    err = x_ref - x_hat
+    p_signal = float(np.sum(x_ref * x_ref))
+    p_noise = float(np.sum(err * err))
+
+    if p_noise <= 0.0:
+        return float("inf")
+    if p_signal <= 0.0:
+        # Degenerate case: silent input
+        return -float("inf")
+    # else:
+    snr_db = 10.0 * np.log10(p_signal / p_noise)
+    return float(snr_db)
+
+
+if __name__ == "__main__":
+    # Example usage:
+    #   python -m level_1.level_1 input.wav output.wav
+    import sys
+
+    if len(sys.argv) != 3:
+        raise SystemExit("Usage: python -m level_1.level_1 <input.wav> <output.wav>")
+
+    in_wav = sys.argv[1]
+    out_wav = sys.argv[2]
+
+    print(f"Encoding/Decoding {in_wav} to {out_wav}")
+    snr = demo_aac_1(in_wav, out_wav)
+    print(f"SNR = {snr:.3f} dB")
+

source/level_1/tests/test_SSC.py

@@ -0,0 +1,199 @@
+import numpy as np
+import pytest
+
+# Adjust the import based on package/module layout.
+from level_1.level_1 import SSC
+
+# Helper "fixtures" for SSC
+# -----------------------------------------------------------------------------
+
+def _next_frame_no_attack() -> np.ndarray:
+    """
+    Build a next_frame_T that should NOT trigger ESH detection.
+
+    Uses exact zeros so all s2l are zero and the ESH condition (s2l > 1e-3) cannot hold.
+    """
+    return np.zeros((2048, 2), dtype=np.float64)
+
+
+def _next_frame_strong_attack(
+    *,
+    attack_left: bool,
+    attack_right: bool,
+    segment_l: int = 4,
+    baseline: float = 1e-6,
+    burst_amp: float = 1.0,
+) -> np.ndarray:
+    """
+    Build a next_frame_T (2048x2) that should trigger ESH detection on selected channels.
+
+    Spec: ESH if exists l in {1..7} with s2l > 1e-3 AND ds2l > 10.
+    We create:
+      - small baseline energy in all samples (avoids division by zero in ds2l),
+      - a strong burst inside one 128-sample segment l in 1..7.
+    """
+    assert 1 <= segment_l <= 7
+    x = np.full((2048, 2), baseline, dtype=np.float64)
+
+    a = segment_l * 128
+    b = (segment_l + 1) * 128
+
+    if attack_left:
+        x[a:b, 0] += burst_amp
+    if attack_right:
+        x[a:b, 1] += burst_amp
+
+    return x
+
+
+def _next_frame_below_s2l_threshold(
+    *,
+    left: bool,
+    right: bool,
+    segment_l: int = 4,
+    impulse_amp: float = 0.01,
+) -> np.ndarray:
+    """
+    Construct a next_frame_T where s2l is below 1e-3, so ESH must NOT be triggered,
+    even if ds2l could be large.
+
+    Put a single impulse of amplitude 'impulse_amp' inside a segment.
+    Energy in the 128-sample segment: s2l ~= impulse_amp^2.
+    With impulse_amp=0.01 => s2l ~= 1e-4 < 1e-3.
+    """
+    assert 1 <= segment_l <= 7
+    x = np.zeros((2048, 2), dtype=np.float64)
+
+    idx = segment_l * 128 + 10  # inside segment
+    if left:
+        x[idx, 0] = impulse_amp
+    if right:
+        x[idx, 1] = impulse_amp
+
+    return x
+
+
+# ---------------------------------------------------------------------
+# 1) Fixed/mandatory cases (prev frame type forces current type)
+# ---------------------------------------------------------------------
+
+def test_ssc_fixed_cases_prev_lss_and_lps() -> None:
+    """
+    Spec: if prev was:
+      - LSS => current MUST be ESH
+      - LPS => current MUST be OLS
+    independent of next frame check.
+    """
+    frame_t = np.zeros((2048, 2), dtype=np.float64)
+
+    # Even if next frame has a strong attack, LSS must force ESH.
+    next_attack = _next_frame_strong_attack(attack_left=True, attack_right=True)
+    out1 = SSC(frame_t, next_attack, "LSS")
+    assert out1 == "ESH"
+
+    # Even if next frame has a strong attack, LPS must force OLS.
+    out2 = SSC(frame_t, next_attack, "LPS")
+    assert out2 == "OLS"
+
+
+# ---------------------------------------------------------------------
+# 2) Cases requiring next-frame ESH prediction (energy/attack computation)
+# ---------------------------------------------------------------------
+
+def test_prev_ols_next_not_esh_returns_ols() -> None:
+    """
+    Spec: if prev=OLS, current is OLS or LSS.
+    Choose LSS iff (i+1) predicted ESH, else OLS.
+    """
+    frame_t = np.zeros((2048, 2), dtype=np.float64)
+    next_t = _next_frame_no_attack()
+
+    out = SSC(frame_t, next_t, "OLS")
+    assert out == "OLS"
+
+
+def test_prev_ols_next_esh_both_channels_returns_lss() -> None:
+    """
+    prev=OLS, next predicted ESH (both channels) => per-channel decisions are LSS and LSS
+    and merge table keeps LSS.
+    """
+    frame_t = np.zeros((2048, 2), dtype=np.float64)
+    next_t = _next_frame_strong_attack(attack_left=True, attack_right=True)
+
+    out = SSC(frame_t, next_t, "OLS")
+    assert out == "LSS"
+
+
+def test_prev_ols_next_esh_one_channel_returns_lss() -> None:
+    """
+    prev=OLS:
+      - one channel predicts ESH => LSS
+      - other channel predicts not ESH => OLS
+    Merge table: OLS + LSS => LSS.
+    """
+    frame_t = np.zeros((2048, 2), dtype=np.float64)
+
+    next1_t = _next_frame_strong_attack(attack_left=True, attack_right=False)
+    out1 = SSC(frame_t, next1_t, "OLS")
+    assert out1 == "LSS"
+
+    next2_t = _next_frame_strong_attack(attack_left=False, attack_right=True)
+    out2 = SSC(frame_t, next2_t, "OLS")
+    assert out2 == "LSS"
+
+
+def test_prev_esh_next_esh_both_channels_returns_esh() -> None:
+    """
+    prev=ESH:
+      - next predicted ESH => current ESH (per-channel)
+    Merge table: ESH + ESH => ESH.
+    """
+    frame_t = np.zeros((2048, 2), dtype=np.float64)
+    next_t = _next_frame_strong_attack(attack_left=True, attack_right=True)
+
+    out = SSC(frame_t, next_t, "ESH")
+    assert out == "ESH"
+
+
+def test_prev_esh_next_not_esh_both_channels_returns_lps() -> None:
+    """
+    prev=ESH:
+      - next not predicted ESH => current LPS (per-channel)
+    Merge table: LPS + LPS => LPS.
+    """
+    frame_t = np.zeros((2048, 2), dtype=np.float64)
+    next_t = _next_frame_no_attack()
+
+    out = SSC(frame_t, next_t, "ESH")
+    assert out == "LPS"
+
+
+def test_prev_esh_next_esh_one_channel_merged_is_esh() -> None:
+    """
+    prev=ESH:
+      - one channel predicts ESH => ESH
+      - other channel predicts not ESH => LPS
+    Merge table: ESH + LPS => ESH.
+    """
+    frame_t = np.zeros((2048, 2), dtype=np.float64)
+
+    next1_t = _next_frame_strong_attack(attack_left=True, attack_right=False)
+    out1 = SSC(frame_t, next1_t, "ESH")
+    assert out1 == "ESH"
+
+    next2_t = _next_frame_strong_attack(attack_left=True, attack_right=False)
+    out2 = SSC(frame_t, next2_t, "ESH")
+    assert out2 == "ESH"
+
+def test_threshold_s2l_must_exceed_1e_3() -> None:
+    """
+    Spec: next frame is ESH only if s2l > 1e-3 AND ds2l > 10 for some l in 1..7.
+    This test checks the necessity of the s2l threshold:
+      - Create a frame with s2l ~= 1e-4 < 1e-3 (single impulse with amp 0.01).
+      - Expect: not classified as ESH -> for prev=OLS return OLS.
+    """
+    frame_t = np.zeros((2048, 2), dtype=np.float64)
+    next_t = _next_frame_below_s2l_threshold(left=True, right=True, impulse_amp=0.01)
+
+    out = SSC(frame_t, next_t, "OLS")
+    assert out == "OLS"

source/level_1/tests/test_aac_level1.py

@@ -0,0 +1,123 @@
+from __future__ import annotations
+
+from pathlib import Path
+
+import numpy as np
+import pytest
+import soundfile as sf
+
+from level_1.level_1 import aac_coder_1, i_aac_coder_1
+
+# Helper "fixtures" for aac_coder_1 / i_aac_coder_1
+# -----------------------------------------------------------------------------
+
+def _snr_db(x_ref: np.ndarray, x_hat: np.ndarray) -> float:
+    """
+    Compute overall SNR (dB) over all samples and channels after aligning lengths.
+    """
+    x_ref = np.asarray(x_ref, dtype=np.float64)
+    x_hat = np.asarray(x_hat, dtype=np.float64)
+
+    if x_ref.ndim == 1:
+        x_ref = x_ref.reshape(-1, 1)
+    if x_hat.ndim == 1:
+        x_hat = x_hat.reshape(-1, 1)
+
+    n = min(x_ref.shape[0], x_hat.shape[0])
+    c = min(x_ref.shape[1], x_hat.shape[1])
+
+    x_ref = x_ref[:n, :c]
+    x_hat = x_hat[:n, :c]
+
+    err = x_ref - x_hat
+    ps = float(np.sum(x_ref * x_ref))
+    pn = float(np.sum(err * err))
+
+    if pn <= 0.0:
+        return float("inf")
+    if ps <= 0.0:
+        return -float("inf")
+
+    return float(10.0 * np.log10(ps / pn))
+
+
+@pytest.fixture()
+def tmp_stereo_wav(tmp_path: Path) -> Path:
+    """
+    Create a temporary 48 kHz stereo WAV with random samples.
+    """
+    rng = np.random.default_rng(123)
+    fs = 48000
+
+    # ~1 second of audio, keep small for test speed
+    n = fs
+    x = rng.normal(size=(n, 2)).astype(np.float64)
+
+    wav_path = tmp_path / "in.wav"
+    sf.write(str(wav_path), x, fs)
+    return wav_path
+
+
+def test_aac_coder_seq_schema_and_shapes(tmp_stereo_wav: Path) -> None:
+    """
+    Module-level contract test:
+    Ensure aac_seq_1 follows the expected schema and per-frame shapes.
+    """
+    aac_seq = aac_coder_1(tmp_stereo_wav)
+
+    assert isinstance(aac_seq, list)
+    assert len(aac_seq) > 0
+
+    for fr in aac_seq:
+        assert isinstance(fr, dict)
+
+        # Required keys
+        assert "frame_type" in fr
+        assert "win_type" in fr
+        assert "chl" in fr
+        assert "chr" in fr
+
+        frame_type = fr["frame_type"]
+        win_type = fr["win_type"]
+
+        assert frame_type in ("OLS", "LSS", "ESH", "LPS")
+        assert win_type in ("SIN", "KBD")
+
+        assert isinstance(fr["chl"], dict)
+        assert isinstance(fr["chr"], dict)
+        assert "frame_F" in fr["chl"]
+        assert "frame_F" in fr["chr"]
+
+        chl_f = np.asarray(fr["chl"]["frame_F"])
+        chr_f = np.asarray(fr["chr"]["frame_F"])
+
+        if frame_type == "ESH":
+            assert chl_f.shape == (128, 8)
+            assert chr_f.shape == (128, 8)
+        else:
+            assert chl_f.shape == (1024, 1)
+            assert chr_f.shape == (1024, 1)
+
+
+def test_end_to_end_aac_coder_decoder_high_snr(tmp_stereo_wav: Path, tmp_path: Path) -> None:
+    """
+    End-to-end module test:
+    Encode + decode and check SNR is very high (numerical-noise only).
+    Threshold is intentionally loose to avoid fragility.
+    """
+    x_ref, fs = sf.read(str(tmp_stereo_wav), always_2d=True)
+    assert fs == 48000
+
+    out_wav = tmp_path / "out.wav"
+
+    aac_seq = aac_coder_1(tmp_stereo_wav)
+    x_hat = i_aac_coder_1(aac_seq, out_wav)
+
+    # Basic sanity: output file exists and is readable
+    assert out_wav.exists()
+    x_hat_file, fs_hat = sf.read(str(out_wav), always_2d=True)
+    assert fs_hat == 48000
+
+    # SNR computed against the array returned by i_aac_coder_1 (should match file, but not required)
+    snr = _snr_db(x_ref, x_hat)
+    assert snr > 80.0

source/level_1/tests/test_filterbank.py

@@ -0,0 +1,235 @@
+import numpy as np
+import pytest
+
+from level_1.level_1 import FrameType, WinType, filter_bank, i_filter_bank
+
+# Helper "fixtures" for filterbank
+# -----------------------------------------------------------------------------
+
+def _ola_reconstruct(x: np.ndarray, frame_types: list[str], win_type: str) -> np.ndarray:
+    """
+    Analyze-synthesize each frame and overlap-add with hop=1024.
+    x: shape (N,2)
+    frame_types: length K, for frames starting at i*1024
+    """
+    hop = 1024
+    win = 2048
+    K = len(frame_types)
+
+    y = np.zeros_like(x, dtype=np.float64)
+
+    for i in range(K):
+        start = i * hop
+        frame_t = x[start:start + win, :]
+        frame_f = filter_bank(frame_t, frame_types[i], win_type)
+        frame_t_hat = i_filter_bank(frame_f, frame_types[i], win_type)
+        y[start:start + win, :] += frame_t_hat
+
+    return y
+
+
+def _snr_db(x: np.ndarray, y: np.ndarray) -> float:
+    err = x - y
+    ps = float(np.sum(x * x))
+    pn = float(np.sum(err * err))
+    if pn <= 0.0:
+        return float("inf")
+    return 10.0 * np.log10(ps / pn)
+
+# ---------------------------------------------------------------------
+# Forward filterbank tests
+# ---------------------------------------------------------------------
+
+@pytest.mark.parametrize("win_type", ["SIN", "KBD"])
+@pytest.mark.parametrize("frame_type", ["OLS", "LSS", "LPS"])
+def test_filterbank_shapes_long_sequences(frame_type: FrameType, win_type: WinType) -> None:
+    """
+    Contract test:
+    For OLS/LSS/LPS, filter_bank returns shape (1024, 2).
+    """
+    frame_t = np.zeros((2048, 2), dtype=np.float64)
+    frame_f = filter_bank(frame_t, frame_type, win_type)
+    assert frame_f.shape == (1024, 2)
+
+
+@pytest.mark.parametrize("win_type", ["SIN", "KBD"])
+def test_filterbank_shapes_esh(win_type: WinType) -> None:
+    """
+    Contract test:
+    For ESH, filter_bank returns shape (128, 16).
+    """
+    frame_t = np.zeros((2048, 2), dtype=np.float64)
+    frame_f = filter_bank(frame_t, "ESH", win_type)
+    assert frame_f.shape == (128, 16)
+
+
+@pytest.mark.parametrize("win_type", ["SIN", "KBD"])
+def test_filterbank_channel_isolation_long_sequences(win_type: WinType) -> None:
+    """
+    Module behavior test:
+    For OLS (representative long-sequence), channels are processed independently:
+    - If right channel is zero and left is random, right spectrum should be near zero.
+    """
+    rng = np.random.default_rng(0)
+    frame_t = np.zeros((2048, 2), dtype=np.float64)
+    frame_t[:, 0] = rng.normal(size=2048)
+
+    frame_f = filter_bank(frame_t, "OLS", win_type)
+
+    # Right channel output should be (close to) zero
+    assert np.max(np.abs(frame_f[:, 1])) < 1e-9
+
+
+@pytest.mark.parametrize("win_type", ["SIN", "KBD"])
+def test_filterbank_channel_isolation_esh(win_type: WinType) -> None:
+    """
+    Module behavior test:
+    For ESH, channels are processed independently:
+    - If right channel is zero and left is random, all odd columns (right) should be near zero.
+    """
+    rng = np.random.default_rng(1)
+    frame_t = np.zeros((2048, 2), dtype=np.float64)
+    frame_t[:, 0] = rng.normal(size=2048)
+
+    frame_f = filter_bank(frame_t, "ESH", win_type)
+
+    # Right channel appears in columns 1,3,5,...,15
+    right_cols = frame_f[:, 1::2]
+    assert np.max(np.abs(right_cols)) < 1e-9
+
+
+@pytest.mark.parametrize("win_type", ["SIN", "KBD"])
+def test_filterbank_esh_ignores_outer_regions(win_type: WinType) -> None:
+    """
+    Spec-driven behavior test:
+    ESH uses only the central 1152 samples (from 448 to 1599), split into 8 overlapping
+    windows of length 256 with 50% overlap.
+
+    Therefore, changing samples outside [448, 1600) must not affect the output.
+    """
+    rng = np.random.default_rng(2)
+
+    frame_a = np.zeros((2048, 2), dtype=np.float64)
+    frame_b = np.zeros((2048, 2), dtype=np.float64)
+
+    # Same central region for both frames
+    center = rng.normal(size=(1152, 2))
+    frame_a[448:1600, :] = center
+    frame_b[448:1600, :] = center
+
+    # Modify only the outer regions of frame_b
+    frame_b[0:448, :] = rng.normal(size=(448, 2))
+    frame_b[1600:2048, :] = rng.normal(size=(448, 2))
+
+    fa = filter_bank(frame_a, "ESH", win_type)
+    fb = filter_bank(frame_b, "ESH", win_type)
+
+    np.testing.assert_allclose(fa, fb, rtol=0.0, atol=0.0)
+
+
+@pytest.mark.parametrize("win_type", ["SIN", "KBD"])
+def test_filterbank_output_is_finite(win_type: WinType) -> None:
+    """
+    Sanity test:
+    Output must not contain NaN or inf for representative cases.
+    """
+    rng = np.random.default_rng(3)
+    frame_t = rng.normal(size=(2048, 2)).astype(np.float64)
+
+    for frame_type in ("OLS", "LSS", "ESH", "LPS"):
+        frame_f = filter_bank(frame_t, frame_type, win_type)
+        assert np.isfinite(frame_f).all()
+
+
+# ---------------------------------------------------------------------
+# Reverse i_filterbank tests
+# ---------------------------------------------------------------------
+
+
+@pytest.mark.parametrize("win_type", ["SIN", "KBD"])
+def test_ifilterbank_shapes_long_sequences(win_type: str) -> None:
+    frame_f = np.zeros((1024, 2), dtype=np.float64)
+    for frame_type in ("OLS", "LSS", "LPS"):
+        frame_t = i_filter_bank(frame_f, frame_type, win_type)
+        assert frame_t.shape == (2048, 2)
+
+
+@pytest.mark.parametrize("win_type", ["SIN", "KBD"])
+def test_ifilterbank_shapes_esh(win_type: str) -> None:
+    frame_f = np.zeros((128, 16), dtype=np.float64)
+    frame_t = i_filter_bank(frame_f, "ESH", win_type)
+    assert frame_t.shape == (2048, 2)
+
+
+@pytest.mark.parametrize("win_type", ["SIN", "KBD"])
+def test_roundtrip_per_frame_is_finite(win_type: str) -> None:
+    rng = np.random.default_rng(0)
+    frame_t = rng.normal(size=(2048, 2)).astype(np.float64)
+
+    for frame_type in ("OLS", "LSS", "ESH", "LPS"):
+        frame_f = filter_bank(frame_t, frame_type, win_type)
+        frame_t_hat = i_filter_bank(frame_f, frame_type, win_type)
+        assert np.isfinite(frame_t_hat).all()
+
+
+@pytest.mark.parametrize("win_type", ["SIN", "KBD"])
+def test_ola_reconstruction_ols_high_snr(win_type: str) -> None:
+    """
+    Core module-level test:
+    OLS analysis+synthesis with hop=1024 must reconstruct with high SNR
+    in the steady-state region.
+    """
+    rng = np.random.default_rng(1)
+
+    K = 6
+    N = 1024 * (K + 1)
+    x = rng.normal(size=(N, 2)).astype(np.float64)
+
+    y = _ola_reconstruct(x, ["OLS"] * K, win_type)
+
+    # Exclude edges (first and last hop) where full overlap is not available
+    a = 1024
+    b = N - 1024
+    snr = _snr_db(x[a:b, :], y[a:b, :])
+    assert snr > 50.0
+
+
+@pytest.mark.parametrize("win_type", ["SIN", "KBD"])
+def test_ola_reconstruction_esh_high_snr(win_type: str) -> None:
+    """
+    ESH analysis+synthesis with hop=1024 must reconstruct with high SNR
+    in the steady-state region.
+    """
+    rng = np.random.default_rng(2)
+
+    K = 6
+    N = 1024 * (K + 1)
+    x = rng.normal(size=(N, 2)).astype(np.float64)
+
+    y = _ola_reconstruct(x, ["ESH"] * K, win_type)
+
+    a = 1024
+    b = N - 1024
+    snr = _snr_db(x[a:b, :], y[a:b, :])
+    assert snr > 45.0
+
+
+@pytest.mark.parametrize("win_type", ["SIN", "KBD"])
+def test_ola_reconstruction_transition_sequence(win_type: str) -> None:
+    """
+    Transition sequence test matching the windowing logic:
+      OLS -> LSS -> ESH -> LPS -> OLS -> OLS
+    """
+    rng = np.random.default_rng(3)
+
+    frame_types = ["OLS", "LSS", "ESH", "LPS", "OLS", "OLS"]
+    K = len(frame_types)
+    N = 1024 * (K + 1)
+    x = rng.normal(size=(N, 2)).astype(np.float64)
+
+    y = _ola_reconstruct(x, frame_types, win_type)
+
+    a = 1024
+    b = N - 1024
+    snr = _snr_db(x[a:b, :], y[a:b, :])
+    assert snr > 40.0

source/level_1/tests/test_filterbank_internal.py

@@ -0,0 +1,102 @@
+import numpy as np
+import pytest
+
+from level_1.level_1 import _imdct, _mdct
+
+# Helper "fixtures" for filterbank internals (MDCT/IMDCT)
+# -----------------------------------------------------------------------------
+
+def _assert_allclose(a: np.ndarray, b: np.ndarray, *, rtol: float, atol: float) -> None:
+    # Helper for consistent tolerances across tests.
+    np.testing.assert_allclose(a, b, rtol=rtol, atol=atol)
+
+def _estimate_gain(y: np.ndarray, x: np.ndarray) -> float:
+    """
+    Estimate scalar gain g such that y ~= g*x in least-squares sense.
+    """
+    denom = float(np.dot(x, x))
+    if denom == 0.0:
+        return 0.0
+    return float(np.dot(y, x) / denom)
+
+
+tolerance = 1e-10
+
+@pytest.mark.parametrize("N", [256, 2048])
+def test_mdct_imdct_mdct_identity_up_to_gain(N: int) -> None:
+    """
+    Consistency test in coefficient domain:
+      mdct(imdct(X)) ~= g * X
+
+    For our chosen (non-orthonormal) scaling, g is expected to be close to 2.
+    """
+    rng = np.random.default_rng(0)
+    K = N // 2
+
+    X = rng.normal(size=K).astype(np.float64)
+    x = _imdct(X)
+    X_hat = _mdct(x)
+
+    g = _estimate_gain(X_hat, X)
+    _assert_allclose(X_hat, g * X, rtol=tolerance, atol=tolerance)
+    _assert_allclose(np.array([g]), np.array([2.0]), rtol=tolerance, atol=tolerance)
+
+
+@pytest.mark.parametrize("N", [256, 2048])
+def test_mdct_linearity(N: int) -> None:
+    """
+    Linearity test:
+      mdct(a*x + b*y) == a*mdct(x) + b*mdct(y)
+
+    This should hold up to numerical error.
+    """
+    rng = np.random.default_rng(1)
+    x = rng.normal(size=N).astype(np.float64)
+    y = rng.normal(size=N).astype(np.float64)
+
+    a = 0.37
+    b = -1.12
+
+    left = _mdct(a * x + b * y)
+    right = a * _mdct(x) + b * _mdct(y)
+
+    _assert_allclose(left, right, rtol=tolerance, atol=tolerance)
+
+
+@pytest.mark.parametrize("N", [256, 2048])
+def test_imdct_linearity(N: int) -> None:
+    """
+    Linearity test for IMDCT:
+      imdct(a*X + b*Y) == a*imdct(X) + b*imdct(Y)
+    """
+    rng = np.random.default_rng(2)
+    K = N // 2
+
+    X = rng.normal(size=K).astype(np.float64)
+    Y = rng.normal(size=K).astype(np.float64)
+
+    a = -0.5
+    b = 2.0
+
+    left = _imdct(a * X + b * Y)
+    right = a * _imdct(X) + b * _imdct(Y)
+
+    _assert_allclose(left, right, rtol=tolerance, atol=tolerance)
+
+
+@pytest.mark.parametrize("N", [256, 2048])
+def test_mdct_imdct_outputs_are_finite(N: int) -> None:
+    """
+    Sanity test: no NaN/inf on random inputs.
+    """
+    rng = np.random.default_rng(3)
+    K = N // 2
+
+    x = rng.normal(size=N).astype(np.float64)
+    X = rng.normal(size=K).astype(np.float64)
+
+    X1 = _mdct(x)
+    x1 = _imdct(X)
+
+    assert np.isfinite(X1).all()
+    assert np.isfinite(x1).all()