The plots at the bottom of the question are not mirrored. If you plot those using lines instead of dots you’ll see the numeric results have very high frequencies. The absolute component matches, but the phase doesn’t. When this happens, it’s almost certainly a case of a shift in the time domain. And indeed, you … Read more
Indeed, if the frame lasts T seconds, the frequencies of the DFT are k/T Hz, where k is an integer. As a consequence, oversampling does not improve the accuracy of the estimated frequency, as long as these frequencies are identifed as maxima of the magnitude of the DFT. On the contrary, considering longer frames lasting … Read more
I suggest you step away from your code and first master ability to perform a fft call and make sense of the result returned from that call … either read in a sin curve of known freq or just write a function to populate an array with a floating point sin curve ( this is … Read more
Actually, you don’t have to swap the different quadrants, it’s needed only if you’re a human and want a more natural looking visualization of the FFT result (i.e. with the 0 frequency in the middle, negative frequencies left/bottom and positive frequencies up/right). To invert the FFT, you need to pass the result of the forward … Read more
What you’re doing in your code is actually not correlation at all. You are using the template and performing convolution with the input image. If you recall from the Fourier Transform, the multiplication of the spectra of two signals is equivalent to the convolution of the two signals in time/spatial domain. Basically, what you are … Read more
In the end, the most simple thing (calculating the coefficient with a riemann sum) was the most portable/efficient/robust way to solve my problem: import numpy as np def cn(n): c = y*np.exp(-1j*2*n*np.pi*time/period) return c.sum()/c.size def f(x, Nh): f = np.array([2*cn(i)*np.exp(1j*2*i*np.pi*x/period) for i in range(1,Nh+1)]) return f.sum() y2 = np.array([f(t,50).real for t in time]) plot(time, y) … Read more
You could certainly wrap whatever FFT implementation that you wanted to test using Cython or other like-minded tools that allow you to access external libraries. GPU-based If you’re going to test FFT implementations, you might also take a look at GPU-based codes (if you have access to the proper hardware). There are several: reikna.fft, scikits.cuda. … Read more
You can use this class, which is fast enough for real time audio analysis public class FFT { int n, m; // Lookup tables. Only need to recompute when size of FFT changes. double[] cos; double[] sin; public FFT(int n) { this.n = n; this.m = (int) (Math.log(n) / Math.log(2)); // Make sure n is … Read more
The Discrete Fourier transform (DFT) and, by extension, the FFT (which computes the DFT) have the origin in the first element (for an image, the top-left pixel) for both the input and the output. This is the reason we often use the fftshift function on the output, so as to shift the origin to a … Read more
There are quite a few similar/related questions on SO already which are well worth reading as the answers contain a lot of useful information and advice, but in essence you need to do this: Convert the audio data to the format required by FFT (e.g. int -> float, with separate L/R channels); Apply suitable window … Read more