I used fft function in numpy which resulted in a complex array. How to get the exact frequency values?
15.1k 21 21 gold badges 78 78 silver badges 136 136 bronze badges asked Sep 12, 2010 at 12:59 575 1 1 gold badge 5 5 silver badges 6 6 bronze badgesnp.fft.fftfreq tells you the frequencies associated with the coefficients:
import numpy as np x = np.array([1,2,1,0,1,2,1,0]) w = np.fft.fft(x) freqs = np.fft.fftfreq(len(x)) for coef,freq in zip(w,freqs): if coef: print('6> * exp(2 pi i t * )'.format(c=coef,f=freq)) # (8+0j) * exp(2 pi i t * 0.0) # -4j * exp(2 pi i t * 0.25) # 4j * exp(2 pi i t * -0.25) The OP asks how to find the frequency in Hertz. I believe the formula is frequency (Hz) = abs(fft_freq * frame_rate) .
Here is some code that demonstrates that.
First, we make a wave file at 440 Hz:
import math import wave import struct if __name__ == '__main__': # http://stackoverflow.com/questions/3637350/how-to-write-stereo-wav-files-in-python # http://www.sonicspot.com/guide/wavefiles.html freq = 440.0 data_size = 40000 fname = "test.wav" frate = 11025.0 amp = 64000.0 nchannels = 1 sampwidth = 2 framerate = int(frate) nframes = data_size comptype = "NONE" compname = "not compressed" data = [math.sin(2 * math.pi * freq * (x / frate)) for x in range(data_size)] wav_file = wave.open(fname, 'w') wav_file.setparams( (nchannels, sampwidth, framerate, nframes, comptype, compname)) for v in data: wav_file.writeframes(struct.pack('h', int(v * amp / 2))) wav_file.close() This creates the file test.wav . Now we read in the data, FFT it, find the coefficient with maximum power, and find the corresponding fft frequency, and then convert to Hertz:
import wave import struct import numpy as np if __name__ == '__main__': data_size = 40000 fname = "test.wav" frate = 11025.0 wav_file = wave.open(fname, 'r') data = wav_file.readframes(data_size) wav_file.close() data = struct.unpack('h'.format(n=data_size), data) data = np.array(data) w = np.fft.fft(data) freqs = np.fft.fftfreq(len(w)) print(freqs.min(), freqs.max()) # (-0.5, 0.499975) # Find the peak in the coefficients idx = np.argmax(np.abs(w)) freq = freqs[idx] freq_in_hertz = abs(freq * frate) print(freq_in_hertz) # 439.8975