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""" Zoom FFT function"""

import numpy as np
from time import time
from scipy.fftpack import fft, ifft
from numpy import swapaxes

def chirpz(x, A=None, W=None, M=None):
    """chirpz(x, A, W, M) - Chirp z-transform of variable x

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Weber (1978). "Comparison of Public Choice Systems".

I can't find any online OCRed copy of this content, so I'm transcribing a bunch of stuff.

Citation:

• Weber, Robert J. (September 1978). "Comparison of Public Choice Systems". Cowles Foundation Discussion Papers. Cowles Foundation for Research in Economics. No. 498.

Actually this contains three previous unpublished papers, which is why it's sometimes listed as "1977". Example citations for the individual papers:

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"""
Created on Wed Nov 04 11:34:53 2015
"""
from numpy import logspace, log10, sqrt, pi
import matplotlib.pyplot as plt
from audio_electronics_shortcuts import dB

import pint
u = pint.UnitRegistry()

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Dependencies

sudo apt install poppler-utils imagemagick

To extract all the images:

for file in **.pdf
    pdfimages -all "$file" "$file"
end

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Version 4
SHEET 1 880 680
FLAG 64 144 0
FLAG 64 64 signal
IOPIN 64 64 Out
SYMBOL voltage 64 48 R0
WINDOW 123 0 0 Left 0
WINDOW 39 0 0 Left 0
SYMATTR InstName V1
SYMATTR Value SINE(0 1 2000)

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----------| hyphens
++++++++++| plus
−−−−−−−−−−| minus
| space
          | figure space
          | en space
          | em space

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How to handle asymmetry of WAV data?

WAV files can store PCM audio (WAVE_FORMAT_PCM). The WAV file format specification says:

The data format and maximum and minimums values for PCM waveform samples of various sizes are as follows:

Sample Size	Data Format	Maximum Value	Minimum Value
One to eight bits	Unsigned integer	255 (0xFF)	0
Nine or more bits	Signed integer i	Largest positive value of i	Most negative value of i

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import numpy as np
import pylab as pl
from numpy import fft


def fourierExtrapolation(x, n_predict):
    n = x.size
    n_harm = 10                     # number of harmonics in model
    t = np.arange(0, n)
    p = np.polyfit(t, x, 1)         # find linear trend in x

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