The Fast Fourier Transform (FFT) is a powerful tool for analyzing and processing digital signals, but it can also be tricky to implement correctly and efficiently in C. In this article, you will learn some common pitfalls and best practices for writing FFT code in C, such as:
There are many libraries available for performing FFT in C, such as FFTW, Kiss FFT, or Intel MKL. However, not all libraries are equally suited for your needs and constraints. You should consider factors such as performance, accuracy, portability, licensing, and documentation when choosing a library. You should also benchmark and test your code with different libraries and compare the results.
C does not have a native complex data type, so you need to use either a struct, an array, or a library-defined type to represent complex numbers. You also need to perform complex arithmetic operations, such as addition, multiplication, and conjugation, using either macros, functions, or operators. You should be careful about the syntax and semantics of these operations, and avoid unnecessary conversions and copies.
True in reality all the numbers we handle are real. We need to address complex numbers as an ordered pair by defining a structure or class. As a consequence we need to define through callable functions addition .. multiplication .. division .. probably to create your own math library
The FFT algorithm works best when the input data size is a power of two, or a product of small prime factors. If your data size does not meet this condition, you may need to align and pad your data with zeros or other values to improve the performance and accuracy of the FFT. You should also avoid using dynamic memory allocation and pointer arithmetic, as they may introduce overhead and errors.
The FFT transforms data from the time domain to the frequency domain, or vice versa. However, the output data may have a different scale and magnitude than the input data, depending on the library and the direction of the transform. You may need to scale and normalize your data before or after the FFT, using factors such as the data size, the sampling frequency, or the window function. You should also be aware of the units and dimensions of your data, such as volts, hertz, or decibels.
Last but not least, one needs to take into account the accuracy and the range of floating-point numbers (single- or double-precision). From my personal experience single-precision floating-point numbers can lead to significant accumulated errors, e.g. breaking the stability of potentially stable digital IIR filters. The topic is getting even more tricky when one tries to optimize the computiations or does not have access to a hardware FPU unit and introduces the fixed-point arithmetics.
Window functions are used to reduce the spectral leakage and improve the resolution of the FFT. They are applied to the input data before the FFT, and they modify the shape and amplitude of the data. There are many types of window functions, such as rectangular, Hamming, Hann, Blackman, or Kaiser. You should choose a window function that matches your application and your signal characteristics, such as the signal-to-noise ratio, the frequency range, or the transient behavior.
The output of the FFT is a complex array that contains the amplitude and phase information of the frequency components of the input signal. You may need to process and manipulate this array to extract useful information, such as the power spectrum, the magnitude spectrum, the phase spectrum, or the spectrogram. You may also need to plot and display this information using tools such as MATLAB, Python, or Excel. You should understand how to interpret and visualize the results of the FFT, and avoid common mistakes such as aliasing, noise, or artifacts.
In my experience it's best to critically evaluate whether the FFT algorithm is really what your application needs. Remember that the FFT is a specific implementation of the DFT, and on a variety of platforms it's less efficient at doing what you might want than other classes of DFT algorithms. For example, implemented as a GPU fragment shader, a direct implementation of the DFT can be more efficient than the FFT in terms of processing latency.