【源码】Timbre Modeler：基于小波的时频信号分解与重构

函数调用形式

For function call

[yo,afz,t,G,tg] = waveletmodel(yi,Fs,fh,ff,fd,ffl)

Define input:

yi - 采样的音乐信号sampled musical sound, row vector

Fs - yi的采样率sample rate of yi (samples/sec)

fh - 小波形状的Hermite基系数Hermite basis coefficients for wavelet shape, row vector (if unsure set fh=1).

ff - 音乐声音的基频fundamental frequency of musical sound (cycles/sec)

fd - 频域滤波器带宽frequency domain filter bandwidth

ffl - 小波滤波器谐振频率集set of wavelet filter resonant frequencies, ff normalized row vector

Define output:

yo - 滤波后输出的声音filtered output sound, row vector

afz - 堆叠振幅轮廓模型stacked amplitude contour model

t - 时间向量time vector for yo and afz

G - 高斯小波滤波器Gaussian wavelet filter

tg - time vector for G

示例：使用30个带宽为330Hz的谐波过滤一个A3（220Hz）钢琴音符。用标准高斯小波重构平滑后的输出信号。接下来，通过先将输入信号按平滑输出分解，然后重复滤波过程来重构瞬态输出信号。这里只需使用第一Hermite小波。

Example: Filter an A3 (220Hz) piano note using 30 harmonics with bandwidths of 330Hz. Reconstruct a smoothed output signal with a standard Gaussian wavelet. Next reconstruct a transient output signal by first decomposing the input by the smoothed output then repeating a filtering process. This time, simply use the 1st Hermite wavelet.

示例代码：

%% get sampled musical audio

yi = audioread(‘a3-piano.wav’)’; Fs=44100;

%% specify hermite filter structure, fundamental frequency,

%% frequency set and bandwidth

fh=[1]; ff = 220; ffl = (1:30); fd = 1.5*ff;

%% generate model for standard gaussian wavelet

[yo1,afz1,t,G1,tg] = waveletmodel(yi,Fs,fh,ff,fd,ffl);

%% plot smooth model in first figure and play sound

figure(1)

sound(yo1,Fs)

waveletplottool(yi,yo1,afz1,t,G1,tg)

%% specify wavelet shape as the 1st hermite wavelet

fh = [0 1];

%% subtract output from input then refilter with 1st order wavelet

[yo2,afz2,_,G2,] = waveletmodel(yi-yo1,Fs,fh,ff,fd,ffl);

%% plot 1st order transience model in next figure and play sound

figure(2)

sound(yo2,Fs)

waveletplottool(yi-yo1,yo2,afz2,t,G2,tg)

参考文献：

[1] Hermite Transform and wavelets - https://qr.ae/pNrYxL

[2] more on wavelets https://qr.ae/pNrJJ9

[3] wavelet filter algorithm https://qr.ae/TxQMDl

[4] modeled timbre gallery - https://qr.ae/pNrPEd

[5] Gaussian Fourier transform and bandwidth interpretations https://qr.ae/pXR35y

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