/**
 * Phase 6 Task 4 — inverse DWT, multilevel wavedec/waverec (perfect
 * reconstruction), and the continuous wavelet transform (CWT).
 *
 * `idwt` inverts `dwt` (`../typed/signal.ts`) via the shared periodization
 * filter bank in `./wavelet-filters.ts`, which supports the full family list
 * (`SUPPORTED_WAVELETS`: haar, db1-4, sym2-4, coif1-2) and matches
 * `pywt.idwt(..., mode='periodization')` bit-for-bit. For Haar/db1 this is
 * verified equivalent to the earlier hardcoded closed-form 2-tap inverse
 * (`x[2i] = s*(approx[i]+detail[i])`, `x[2i+1] = s*(approx[i]-detail[i])`,
 * `s = 1/sqrt(2)`) — no behavior change for existing callers.
 *
 * @packageDocumentation
 */
/**
 * Inverse single-level discrete wavelet transform (periodization boundary).
 * Exactly inverts `dwt` for every wavelet in `SUPPORTED_WAVELETS`
 * (`./wavelet-filters.ts`): haar, db1-4, sym2-4, coif1-2.
 *
 * @param approx - Approximation (low-pass) coefficients
 * @param detail - Detail (high-pass) coefficients, same length as `approx`
 * @param wavelet - Wavelet name (default 'haar'); see `SUPPORTED_WAVELETS`
 * @returns Reconstructed signal, length `2 * approx.length`
 */
export declare function idwt(approx: number[], detail: number[], wavelet?: string): number[];
/**
 * Multilevel discrete wavelet decomposition: repeatedly applies `dwt` to the
 * approximation coefficients.
 *
 * @param x - Input signal
 * @param wavelet - Wavelet name (passed through to `dwt`); see
 *   `SUPPORTED_WAVELETS` in `./wavelet-filters.ts`
 * @param level - Number of decomposition levels (>= 1)
 * @returns `[cA_level, cD_level, cD_{level-1}, ..., cD_1]` (pywt order)
 */
export declare function wavedec(x: number[], wavelet?: string, level?: number): number[][];
/**
 * Inverse of `wavedec`: repeatedly applies `idwt` from the coarsest level
 * (`coeffs[0]` = cA_level) up to the finest detail (`coeffs[coeffs.length-1]`
 * = cD_1), reconstructing the original signal.
 *
 * @param coeffs - Coefficient arrays as returned by `wavedec`
 * @param wavelet - Wavelet name (passed through to `idwt`)
 * @returns Reconstructed signal
 */
export declare function waverec(coeffs: number[][], wavelet?: string): number[];
/**
 * Continuous wavelet transform: convolves `x` with a discretized, normalized
 * wavelet at each requested scale.
 *
 * @param x - Input signal
 * @param scales - Wavelet scales to evaluate (each > 0)
 * @param wavelet - 'ricker' (Mexican-hat, default) or 'morlet'
 * @returns `scales.length` x `x.length` matrix, row `i` = CWT at `scales[i]`
 */
export declare function cwt(x: number[], scales: number[], wavelet?: string): number[][];
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