mingus.extra.fft

Find the frequencies in raw audio data by using fast Fourier transformations (supplied by numpy).

This module can also convert the found frequencies to Note objects.

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mingus.extra.fft.x

Attribute of type: int 128

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mingus.extra.fft._fft(a, n=None, axis=-1)

Compute the one-dimensional discrete Fourier Transform.

This function computes the one-dimensional n-point discrete Fourier Transform (DFT) with the efficient Fast Fourier Transform (FFT) algorithm [CT].

a : array_like

Input array, can be complex.

n : int, optional

Length of the transformed axis of the output. If n is smaller than the length of the input, the input is cropped. If it is larger, the input is padded with zeros. If n is not given, the length of the input along the axis specified by axis is used.

axis : int, optional

Axis over which to compute the FFT. If not given, the last axis is used.

out : complex ndarray

The truncated or zero-padded input, transformed along the axis indicated by axis, or the last one if axis is not specified.

IndexError

if axes is larger than the last axis of a.

numpy.fft : for definition of the DFT and conventions used. ifft : The inverse of fft. fft2 : The two-dimensional FFT. fftn : The n-dimensional FFT. rfftn : The n-dimensional FFT of real input. fftfreq : Frequency bins for given FFT parameters.

FFT (Fast Fourier Transform) refers to a way the discrete Fourier Transform (DFT) can be calculated efficiently, by using symmetries in the calculated terms. The symmetry is highest when n is a power of 2, and the transform is therefore most efficient for these sizes.

The DFT is defined, with the conventions used in this implementation, in the documentation for the numpy.fft module.

[CT]	Cooley, James W., and John W. Tukey, 1965, “An algorithm for the machine calculation of complex Fourier series,” Math. Comput. 19: 297-301.

>>> np.fft.fft(np.exp(2j * np.pi * np.arange(8) / 8))
array([ -3.44505240e-16 +1.14383329e-17j,
         8.00000000e+00 -5.71092652e-15j,
         2.33482938e-16 +1.22460635e-16j,
         1.64863782e-15 +1.77635684e-15j,
         9.95839695e-17 +2.33482938e-16j,
         0.00000000e+00 +1.66837030e-15j,
         1.14383329e-17 +1.22460635e-16j,
         -1.64863782e-15 +1.77635684e-15j])

>>> import matplotlib.pyplot as plt
>>> t = np.arange(256)
>>> sp = np.fft.fft(np.sin(t))
>>> freq = np.fft.fftfreq(t.shape[-1])
>>> plt.plot(freq, sp.real, freq, sp.imag)
[<matplotlib.lines.Line2D object at 0x...>, <matplotlib.lines.Line2D object at 0x...>]
>>> plt.show()

In this example, real input has an FFT which is Hermitian, i.e., symmetric in the real part and anti-symmetric in the imaginary part, as described in the numpy.fft documentation.

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mingus.extra.fft._find_log_index(f)

Look up the index of the frequency f in the frequency table.

Return the nearest index.

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mingus.extra.fft.analyze_chunks(data, freq, bits, chunksize=512)

Cut the one channel data in chunks and analyzes them separately.

Making the chunksize a power of two works fastest.

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mingus.extra.fft.data_from_file(file)

Return (first channel data, sample frequency, sample width) from a .wav file.

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mingus.extra.fft.find_Note(data, freq, bits)

Get the frequencies, feed them to find_notes and the return the Note with the highest amplitude.

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mingus.extra.fft.find_frequencies(data, freq=44100, bits=16)

Convert audio data into a frequency-amplitude table using fast fourier transformation.

Return a list of tuples (frequency, amplitude).

Data should only contain one channel of audio.

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mingus.extra.fft.find_melody(file=440_480_clean.wav, chunksize=512)

Cut the sample into chunks and analyze each chunk.

Return a list [(Note, chunks)] where chunks is the number of chunks where that note is the most dominant.

If two consequent chunks turn out to return the same Note they are grouped together.

This is an experimental function.

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mingus.extra.fft.find_notes(freqTable, maxNote=100)

Convert the (frequencies, amplitude) list to a (Note, amplitude) list.

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