instructables
QuickFFT: High Speed FFT for Arduino
by abhilash_patel
In one of my instructable, I prepared a code for FFT
that can be found over here: EasyFFT
//www.yout ube.com/embed/e-7WoZ6lzmA
This code was able to perform FFT of up to 128
samples on Arduino nano. A higher sample number
than this is not possible due to the limited memory of
Arduino. I have modi ed the function a little bit to
Typical Arduino has limited RAM and processing
improve speed and reduce memory consumption. This
power, and FFT is a computationally-intensive process.
modi cation allows Arduino to perform FFT ve times
For many real-time applications, the only requirement
faster and consumes almost half memory. This
is to get frequency with maximum amplitude or
Instructable does not cover Working of FFT,
required to detect frequency peaks.
references for it can be found at EasyFFT.
https://www.instructables.com/ORIG/F05/ZMIL/KB6ICK9B/F05ZMILKB6ICK9B.ino
…
Download
Step 1: Working
The typical FFT function is modi ed to improve the speed with lesser accuracy. As shown in the image a test signal
needs to be multiplied by sine or cosine waveforms. These values can be between 0 to 1, so making oating
multiplication is a must. in Arduino, Floating multiplication is slow compared to integer operations.
In this function, the sine/cosine wave is replaced by a square wave. As we have to multiply a test signal with a
QuickFFT: High Speed FFT for Arduino: Page 1
square wave which may have value 0,1 or -1. Due to that, we can replace oating multiplication to simply integer
addition or subtraction. For Arduino integer addition or subtraction is around 5 times faster. This makes solving
around 5 times faster.
Due to this modi cation now frequency bin values can be stored as an integer (which was previously oat) and we
get another advantage of lower memory consumption. In Arduino Nano, int consumes 2 bytes of memory while
oat consumes 4 bytes of memory. Due to this advantage in the new code, we are able to perform FFT for almost
256 samples (previously 128 samples).
In Normal FFT we needed to store the sine value to make a solution faster. In new function, as we no more required
sine/cosine values we can eliminate it and save some memory.
Im ple m e nt a t io n:
Implementing this function is straight forward. We can simply copy the function at the ens of code. This function
can be executed using the below command:
float f= Q_FFT(data,256,100);In function Q_FFT,
data: this term is an array having signal values, the recommended sample size are 2, 4, 8, 32, 64, 128, 256, 512, ...
onwards. if the sample size does not belong to these values it will be clipped to the nearest lower side of values. for
example, if the sample size is 75 than FFT will be carried out for 64 numbers of samples. Max number of sample size
is limited by available RAM on Arduino.
The second term speci es the number of samples in an array and the last term is sampling frequency in Hz.
QuickFFT: High Speed FFT for Arduino: Page 2
Step 2: Code
This section explains the modi cation made in EasyFFT code that needs to be kept in mind while making
modi cation in the code,
1. As explained before, here integers are used to do FFT. Int in Arduino is a 16-bit number and can contain values
from -32768 to 32768. whenever the value of this int exceeds this range it causes the problem. to eliminate this
problem after ever level calculation. if any of the value exceeds 15000 complete arrays will be divided by 100. this
will prevent the int to over ow.
2. Amplitude calculation: To calculate amplitude, the real and imaginary part needs to be squared and the square
root of the sum is required. squaring and the square root of the function is time taking. to make the process faster,
this code will simply do some of the magnitudes of real and imaginary parts. This is surely less accurate and may
lead to the wrong conclusion in some cases. you may choose to return to the Normal method for magnitude
calculation but it will take more time and you also need to do some arrangement to store these numbers.
3. This code does not have a module for multiple peak detection. It will simply choose the value with max amplitude
(excluding the rst number which is DC o set). If you need multiple peaks you can refer EasyFFT code and do
required modi cation over here. In that case, some array/variable also needs to be declared as a global variable.
4. The function contains the following line:
unsigned int Pow2[13]={1,2,4,8,16,32,64,128,256,512,1024,2048};
declaring the above variables as a global variable (pasting it at the start of code) will save somewhere 1
milliseconds time at every execution.
5. Unlike the EasyFFT function, where the top 5 peaks were stored in the prede ned array. This function will return a
oat value. this value represents the frequency with maximum amplitude in Hz. So the representation of code will
look something like this.
float f= Q_FFT(data,256,100);
6. Peak Detection: Once frequency with max amplitude is found this function uses an amplitude of frequency just
before and after it to calculate the accurate results. Amplitude used in this calculation is also the sum of modulus
(not the square root of the sum of squares)
if Fn is the frequency with max amplitude then the frequency can be calculated from below formula.
Actual F= (An-1 *Fn-1 + An-1 *Fn-1 + An-1 *Fn-1 ) / (An-1+An+An+1)
where An is amplitude of n the frequency and Fn-1 is frequency value.
https://www.instructables.com/ORIG/FJ3/PHNR/KB6ICK8T/FJ3PHNRKB6ICK8T.ino
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Step 3: Results:
QuickFFT: High Speed FFT for Arduino: Page 3
Download
Solving time is shown in the above image comparison
with EasyFFT. Speed of it shown with the comparison.
For sample data having 3 sinusoidal waves with
di erent frequencies is shown. The result from
QuickFFT is compared with Scilab output. As we can
see in the image 3 peaks with max amplitude is
matching with Scilab output. However, the output
consists of lots of noise, which may be misleading for
some applications. So it is advised to check code
properly before applying to your application.
I hope you found this code useful for your project. In
case of any query or suggestion please do comment.
QuickFFT: High Speed FFT for Arduino: Page 4