SimpleDSP
SimpleDSP is a basic DSP library which is for arduino and most of the microcontrollers which can be programmed in C/C++
Performance:
Here is some examples for its performance. Actually it is not optimized for performance. Its main focuses are portability and education.
Arduino Nano
- FFT 16 points: 2 ms
- FFT 32 points: 6 ms
- FFT 64 points: 16 ms
- fir filter 10 coeficients: 190 us
- fir filter 23 coeficients: 453 us
- fir filter 46 coeficients: 900 us
10 coeficients FIR filter can be run at 5khz max frequency on an Arduino Nano.
Arduino Due
- FFT 64 points: 2 ms
- FFT 128 points: 6 ms
- FFT 256 points: 10 ms
Fast Fourier Transform (FFT) and Inverse Fast Fourier Transform (IFFT)
Arduino Example
FFT and IFFT functions require 2 arguments.
data
data lenght
Do not forget to add #include "simpleDSP_FFT.h"
Full example for FFT and IFFT please refer here
FFT(data,DATA_LEN);
IFFT(data,DATA_LEN);
calcTime = millis()-startTime;
Serial.print("Total calculation time: ");
Serial.println(calcTime);
FIR Filter
Theory
Arduino Example
FIR is filter structure which keep delays and coeficients of filter. There are 2 public functions. firInit
initiliazes the structure according to parameters and makes required memory allocations. Coeficients and its lenght are given as parameter to this function
Do not forget to add #include "simpleDSP_fir.h"
void firInit(FIR *fir, int coefBLen, float *coefsB);
float firFilt(FIR *fir, int input);
Serial.begin(9600);
firInit(&fir1, 46, coef);
Serial.println("FIR filter initiliaze finished");
float a;
startTime = micros();
for (int i = 0; i < 255; i++)
{
a = firFilt(&fir1, input[i]);
}
calcTime = micros() - startTime;
Serial.print("Total calculation time: ");
Serial.println(calcTime);
IIR Filter
Theory
Arduino Example
IIR is filter structure which keep delays and coeficient of filter. There are 2 functions to implement IIR filter using SimpleDSP library. initIIR function is the constructor function for the filter. Filter coeficients for a and b should be given as arguments to this function. After init, filtIIR must be used as filtering function. This function requires 2 arguments. Object instance and data. It returns the filtered output.
void iirInit(IIR *iir, int coefBLen, float *coefsB, int coefALen, float *coefsA);
float iirFilt(IIR *iir, int input);
Do not forget to add #include "simpleDSP_iir.h"
to your code.
Serial.begin(9600);
iirInit(&iir1, 4, coefB, 4, coefA);
Serial.println("IIR filter initiliaze finished");
float a;
startTime = micros();
for (int i = 0; i < 255; i++)
{
a = iirFilt(&iir1, input[i]);
}
calcTime = micros() - startTime;
Serial.print("Total calculation time: ");
Serial.println(calcTime);
Octave Test Code
This code create sample data and plot the signal and its FFT. The octave code only needed for testing of function. Create sample signal which is at 10 kHz sample rate and it is the combination of 3.2 kHz and 800 Hz sine waves.
N=255;
f1=800;
f2=3200;
fo=10000;
for i=1:1:N
x(i)=1000*cos(2*pi*f1*i/fo)+1000*cos(2*pi*f2*i/fo);
printf("%d\n",x(i));
end
Calculate and plot x and FFT of x. For fft x axis values are calculated using kor=(1:N)*fo/N;
plot(x);
X=abs(FFT(x));
figure;
kor=(1:N)*fo/N;
plot(kor,X);
Output from octave
Graph of Raw Signal
Graph of FFT Signal
Filter Design Using Octave
output of fir functions can be used as filter coeficients
Examples:
freqz (fir1 (40, 0.3));
freqz (fir1 (15, [0.2, 0.5], "stop")); # note the zero-crossing at 0.1
freqz (fir1 (15, [0.2, 0.5], "stop", "noscale"));
figure
b= fir1 (20, 0.3, "low");
y = filter(b,1,x);
plot(y)
filter frequency response
figure
[b, a] = butter(3, 0.3, "low");
y = filter(b,a,x);
plot(y)
octave:> b
b =
0.049533 0.1486 0.1486 0.049533
octave:> a
a =
1.00000 -1.16192 0.69594 -0.13776
Outputs after filtering
Time Domain Signal
FFT of Output Signal