如何用低成本MCU实现音乐频谱显示

周四, 8 九月 2022 - 10:26

最近在做一个有趣的小项目，其中有一小部分的内容的是使用FFT做音乐频谱显示。于是就有了下面这个音乐频谱显示的低成本方案，话不多说，看看低成本MCU如何实现FFT音乐频谱显示吧。

♦音频采集硬件电路

音频采集的硬件电路比较简单，主要的器件就是麦克风和LM358运放。

图中电路R5可调电阻的作用是来调节运放的增益。R4的作用的是给运放一个VDD*R4/(R3+R4) 的直流偏置，这里加直流偏置是由于ADC只能采集正电压值，为了不丢失负电压的音频信号，给信号整体加了一个直流偏置。

但是这个图还有一个小问题，运放的输出端加了一个电容C2，C2会把直流偏置给隔掉。在设计时，这个电容可以去掉。

下图是按照上图搭建的音频采集电路的输出信号，图中波动信号是施加的外部音频，是我们需要做音乐频谱显示需要的信号。该信号有一个2.3v的直流偏置，在后续处理时需要减去这个偏置。

♦CTimer+ADC+DMA 音频信号采集

为了呼应标题，我们选择的MCU是LPC845，这是NXP的一款低成本的MCU。考虑到我们平常听的音乐频率大都低于5kHz，在软件设计时设置ADC采样频率为10kHz。不要问为什么，问就是采样定理。

LPC845的ADC有8个触发源，我们使用CTiimer match3来触发ADC，将寄存器SEQA_CTRL的bit 14:12设置为0x5。CTimer match 3的输出频率为10kHz。

为了确保我们采集数据的实时性，DMA建议配置成双buffer模式，以防止采样的数据被覆盖掉。

♦FFT音频信号处理

在DMA搬运ADC采样值时，使用了双buffer来搬，ADC采样值需要减去一个2.3V的直流偏置。

Samples[]数组用于FFT计算。

<pre style="overflow-x:auto; background-color:#e9e9e9;"> //Calculate the FFT input buffer
if(g_DmaTransferDoneFlag_A == true)
{
for (i=0; i<128; i++)
{
Samples[i] =(int16_t)(((g_AdcConvResult_A[i] & 0xfff0) >> 4) - 2979);//substract the 2.3v offset in the Amplifier output
}
g_DmaTransferDoneFlag_A = false;

}
else if(g_DmaTransferDoneFlag_B == true)
{
for (i=0; i<128; i++)
{
Samples[i] =(int16_t)(((g_AdcConvResult_B[i] & 0xfff0) >> 4) - 2979);//substract the 2.3v offset in the Amplifier output
}
g_DmaTransferDoneFlag_B = false;
}</pre>

根据FFT算法的原理，在进行FFT计算之前，还需要将ADC的采样值Samples[]乘上一个窗函数，这里我们使用的汉宁窗函数，由于篇幅限制，具体原理可以去查看FFT算法相关的资料。

<pre style="overflow-x:auto; background-color:#e9e9e9;"> //If 'Window' isn't rectangular, apply window
if(Window == Triangular){
//Apply a triangular window to the data.
for(Cnt = 0; Cnt<Len; Cnt++){
if(Cnt<(Len/2)) Samples[Cnt] = ((int32_t)Samples[Cnt]*Cnt)>>L2Len;
else Samples[Cnt] = ((int32_t)Samples[Cnt]*((Len/2)-Cnt))>>L2Len;
}
}
else if(Window == Hann){
//Use the cosine window wavetable to apply a Hann windowing function to the samples
for(Cnt = 0; Cnt<Len; Cnt++){
Index = (Cnt*CWLen)>>L2Len;
Samples[Cnt] = ((int32_t)Samples[Cnt]*(int32_t)CosWindow[Index])>>(CWBD);
}
}</pre>

前面说了这么多，FFT算法才是实现音乐频谱显示的关键部分（其实上边每一步都缺一不可）。

我在网上找了好多FFT算法的资料，大家在做频谱显示时，用到最多的就是CMSIS DSP的算法库。于是乎，采用CMSIS DSP的库貌似是首选。

但是不用不知道，一用才发现，由于CMSIS DSP的库使用的是查表的方式，我的64K Flash的LPC845轻轻松松就被撑爆了。没办法，只能改用其他方案。经过不懈的查阅资料，在GitHub找到一份FFT算法的代码，这个代码写的非常简洁，而且用起来很好用，感谢发布者pyrohaz，下面是FFT代码的一部分。

<pre style="overflow-x:auto; background-color:#e9e9e9;">/*
FIX_MPY() - fixed-point multiplication & scaling.
Substitute inline assembly for hardware-specific
optimization suited to a particluar DSP processor.
Scaling ensures that result remains 16-bit.
*/
inline short FIX_MPY(short a, short b)
{
/* shift right one less bit (i.e. 15-1) */
int c = ((int)a * (int)b) >> 14;
/* last bit shifted out = rounding-bit */
b = c & 0x01;
/* last shift + rounding bit */
a = (c >> 1) + b;
return a;
}
fix_fft(short fr[], short fi[], short m, short inverse)函数，FFT计算函数

int fix_fft(short fr[], short fi[], short m, short inverse)
{
int mr, nn, i, j, l, k, istep, n, scale, shift;
short qr, qi, tr, ti, wr, wi;

n = 1 << m;

/* max FFT size = N_WAVE */
if (n > N_WAVE)
return -1;

mr = 0;
nn = n - 1;
scale = 0;

/* decimation in time - re-order data */
for (m=1; m<=nn; ++m) {
l = n;
do {
l >>= 1;
} while (mr+l > nn);
mr = (mr & (l-1)) + l;

if (mr <= m)
continue;
tr = fr[m];
fr[m] = fr[mr];
fr[mr] = tr;
ti = fi[m];
fi[m] = fi[mr];
fi[mr] = ti;
} </pre>

接 fix_fft(short fr[], short fi[], short m, short inverse)函数

<pre style="overflow-x:auto; background-color:#e9e9e9;"> l = 1;
k = LOG2_N_WAVE-1;
while (l < n) {
if (inverse) {
/* variable scaling, depending upon data */
shift = 0;
for (i=0; i<n; ++i) {
j = fr[i];
if (j < 0)
j = -j;
m = fi[i];
if (m < 0)
m = -m;
if (j > 16383 || m > 16383) {
shift = 1;
break;
}
}
if (shift)
++scale;
} else {
/*
fixed scaling, for proper normalization --
there will be log2(n) passes, so this results
in an overall factor of 1/n, distributed to
maximize arithmetic accuracy.
*/
shift = 1;
}</pre>
接fix_fftr(short f[], int m, int inverse)函数

<pre style="overflow-x:auto; background-color:#e9e9e9;"> /*
it may not be obvious, but the shift will be
performed on each data point exactly once,
during this pass.
*/
istep = l << 1;
for (m=0; m<l; ++m) {
j = m << k;
/* 0 <= j < N_WAVE/2 */
wr = Sinewave[j+N_WAVE/4];
wi = -Sinewave[j];
if (inverse)
wi = -wi;
if (shift) {
wr >>= 1;
wi >>= 1;
}
for (i=m; i<n; i+=istep) {
j = i + l;
tr = FIX_MPY(wr,fr[j]) - FIX_MPY(wi,fi[j]);
ti = FIX_MPY(wr,fi[j]) + FIX_MPY(wi,fr[j]);
qr = fr[i];
qi = fi[i];
if (shift) {
qr >>= 1;
qi >>= 1;
}
fr[j] = qr - tr;
fi[j] = qi - ti;
fr[i] = qr + tr;
fi[i] = qi + ti;
}
}
--k;
l = istep;
}
return scale;
}

/*
fix_fftr() - forward/inverse FFT on array of real numbers.
Real FFT/iFFT using half-size complex FFT by distributing
even/odd samples into real/imaginary arrays respectively.
In order to save data space (i.e. to avoid two arrays, one
for real, one for imaginary samples), we proceed in the
following two steps: a) samples are rearranged in the real
array so that all even samples are in places 0-(N/2-1) and
all imaginary samples in places (N/2)-(N-1), and b) fix_fft
is called with fr and fi pointing to index 0 and index N/2
respectively in the original array. The above guarantees
that fix_fft "sees" consecutive real samples as alternating
real and imaginary samples in the complex array.
*/
int fix_fftr(short f[], int m, int inverse)
{
int i, N = 1<<(m-1), scale = 0;
short tt, *fr=f, *fi=&f[N];

if (inverse)
scale = fix_fft(fi, fr, m-1, inverse);
for (i=1; i<N; i+=2) {
tt = f[N+i-1];
f[N+i-1] = f[i];
f[i] = tt;
}
if (! inverse)
scale = fix_fft(fi, fr, m-1, inverse);
return scale;
}</pre>

int fix_fft(short fr[], short fi[], short m, short inverse) 是FFT算法的计算函数，fr[]是ADC采集到信号值的实部，fi[]是ADC采集到信号值的虚部。经过fix_fft函数处理之后，fr[]是FFT计算所得实部，fi[]是计算所得的虚部。

我们最终要显示的音乐频谱其实是FFT频域中音频的幅值，幅值的计算是实部的平方+虚部的平方开根号。下面是具体的幅值计算部分的代码，每一个幅值点对应OLED的一列像素点。

<pre style="overflow-x:auto; background-color:#e9e9e9;">//Calculate the magnitude
for(Cnt = 0; Cnt<Len; Cnt++){
//Square the real components
R = (int32_t)Samples[Cnt]*(int32_t)Samples[Cnt];

//Square the imaginary components
I = (int32_t)Imag[Cnt]*(int32_t)Imag[Cnt];

//Calculate the magnitude and sum into BufSum. As there
//are more samples than columns, sum the magnitude of
//the bins. E.g. for 128 samples and 64 pixels on the LCD,
//each column should be the sum of 2 bins (128/64). If there
//are 512 samples and 64 pixels on the LCD, each column should
//be the sum of 8 bins (512/64)
BufSum += isqrt(R + I);

//Calculate the index for the column
Index = Cnt;

//Reset BufSum once the index has changed
if(Index != IndO){
//Write buffer sum to the column. Scale BufSum dependent on
//input amplitude range. If 'ColumnFilter' is more than 0,
//low pass filter the value to smooth out erratic changes.
if(Decibels){
Col[Index] += (int32_t)(20.0f*log10f(BufSum)-Col[Index])>>ColumnFilter; //calculate the DB
}
else{
Col[Index] += (BufSum-Col[Index])>>ColumnFilter; //calculate the amplitude
}

//Limit maximum column value
if(Col[Index] >= YPix-9) Col[Index] = YPix-10;

IndO = Index;
BufSum = 0;
}
}</pre>

♦效果展示

下面是实际频谱显示的测试效果。

来源：<a href="https://mp.weixin.qq.com/s/VTCxVwUX0wSNJ4v4eMhW5A">恩智浦MCU加油站</a>
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如何用低成本MCU实现音乐频谱显示

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