Add python fft algorithm

algorithms/python/fft.py

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+import matplotlib.pylab as plt
+import numpy as np
+from random import uniform
+
+# sampling rate (must be of base 2)
+sr = 1024
+# sampling interval
+ts = 1/sr
+t = np.arange(-0.5, 0.5, ts)
+
+old_freqs = []
+def randomSine():
+    # frequency of the signal
+    freq = uniform(1, 500)
+    randPhase = uniform(0,1)
+
+    # prevent from picking the same frequencies
+    while freq in old_freqs:
+        freq = uniform(1, 100)
+    old_freqs.append(freq)
+
+    t = np.arange(randPhase, randPhase+1, ts)
+    return np.sin(2*np.pi*freq*t)
+
+def sum_curves(curves: list[list]):
+    summed = []
+    for i in range(sr):
+        sm = 0
+        for curve in curves:
+            sm += curve[i]
+        summed.append(sm)
+    return summed
+
+complexJ = 0 + 1j
+def ditff2(x: list) -> list:
+    n = len(x)
+    if n == 1:
+        return x
+    wn = np.e ** ((2*np.pi*complexJ)/n)
+    w = 1
+    half = int(n/2)
+    halfLeft = [even for (index, even) in enumerate(x[:-1]) if index % 2 == 0]
+    halfRight = [odd for (index, odd) in enumerate(x) if not index % 2 == 0]
+
+    yk_0 = ditff2(halfLeft)
+    yk_1 = ditff2(halfRight)
+    y = [None] * n
+    for i in range(half):
+        y[i] = yk_0[i] + w * yk_1[i]
+        y[i+half] = yk_0[i] - w * yk_1[i]
+        w = w*wn
+    return y
+
+# number of peaks you want to see in fft
+# number of different frequencies on the curve
+N = 20
+# Generate a radom curve with different frequencies
+input = sum_curves([randomSine() for _ in range(N)])
+
+fft = ditff2(input)
+
+## plot stuff
+fig, ax = plt.subplots()
+bx = ax.twinx()
+
+plt_1 = ax.plot(t, input, 'r')
+plt_2 = bx.plot(t, fft)
+
+# plot input
+_, bx = plt.subplots()
+bx.plot(t, input)
+
+#Plot FFT
+_, bx = plt.subplots()
+half = len(fft)//2
+bx.plot(t, fft[half:] + fft[:half])
+plt.plot()
+
+# numpy fft
+sp = np.fft.fft(input)
+freq = np.fft.fftfreq(t.shape[-1])
+plt.plot(freq, sp.real)
+
+plt.legend()
+plt.show()

algorithms/python/requirements.txt

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+anyio==3.6.2
+appnope==0.1.3
+argon2-cffi==21.3.0
+argon2-cffi-bindings==21.2.0
+asttokens==2.1.0
+attrs==22.1.0
+autopep8==2.0.0
+backcall==0.2.0
+beautifulsoup4==4.11.1
+bleach==5.0.1
+cffi==1.15.1
+contourpy==1.0.6
+cycler==0.11.0
+debugpy==1.6.3
+decorator==5.1.1
+defusedxml==0.7.1
+entrypoints==0.4
+executing==1.2.0
+fastjsonschema==2.16.2
+fonttools==4.38.0
+idna==3.4
+importlib-metadata==5.1.0
+ipykernel==6.17.1
+ipython==8.6.0
+ipython-genutils==0.2.0
+ipywidgets==8.0.2
+jedi==0.18.2
+Jinja2==3.1.2
+jsonschema==4.17.1
+jupyter==1.0.0
+jupyter-console==6.4.4
+jupyter-server==1.23.3
+jupyter_client==7.4.7
+jupyter_core==5.0.0
+jupyterlab-pygments==0.2.2
+jupyterlab-widgets==3.0.3
+kiwisolver==1.4.4
+MarkupSafe==2.1.1
+matplotlib==3.6.2
+matplotlib-inline==0.1.6
+mistune==2.0.4
+nbclassic==0.4.8
+nbclient==0.7.0
+nbconvert==7.2.5
+nbformat==5.7.0
+nest-asyncio==1.5.6
+notebook==6.5.2
+notebook_shim==0.2.2
+numpy==1.23.5
+packaging==21.3
+pandocfilters==1.5.0
+parso==0.8.3
+pexpect==4.8.0
+pickleshare==0.7.5
+Pillow==9.3.0
+platformdirs==2.5.4
+prometheus-client==0.15.0
+prompt-toolkit==3.0.33
+psutil==5.9.4
+ptyprocess==0.7.0
+pure-eval==0.2.2
+pycodestyle==2.10.0
+pycparser==2.21
+Pygments==2.13.0
+pyparsing==3.0.9
+pyrsistent==0.19.2
+python-dateutil==2.8.2
+pyzmq==24.0.1
+qtconsole==5.4.0
+QtPy==2.3.0
+Send2Trash==1.8.0
+six==1.16.0
+sniffio==1.3.0
+soupsieve==2.3.2.post1
+stack-data==0.6.1
+terminado==0.17.0
+tinycss2==1.2.1
+tomli==2.0.1
+tornado==6.2
+traitlets==5.5.0
+wcwidth==0.2.5
+webencodings==0.5.1
+websocket-client==1.4.2
+widgetsnbextension==4.0.3
+zipp==3.11.0