{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"from IPython.display import Audio"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"import numpy\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# What does a sinusoid sound like?\n",
"\n",
"We all have advanced frequency detectors in our ears. This notebook will show how listening to signals gives you a whole different way to understand the frequency domain.\n",
"\n",
"We start by constructing a musically relevant note as a pure sine wave"
]
},
{
"cell_type": "code",
"execution_count": 48,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
" \n",
" "
],
"text/plain": [
""
]
},
"execution_count": 48,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"fs = 44100 # sampling frequency, Hz This is the rate at which CDs are sampled.\n",
"T = 0.5 # note length, seconds\n",
"A = 440 # Note frequency, Hz\n",
"twopi = 2*numpy.pi\n",
"\n",
"t = numpy.linspace(0, T, int(T*fs), endpoint=False) # time variable\n",
"dt = t[1] # Sampling time\n",
"def note(frequency):\n",
" return numpy.sin(twopi*frequency*t) # pure sine wave at 440 Hz\n",
"\n",
"# load a NumPy array\n",
"Audio(note(A), rate=fs)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we construct the Chromatic 12 note scale:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[Chromatic scale](https://en.wikipedia.org/wiki/Twelfth_root_of_two)"
]
},
{
"cell_type": "code",
"execution_count": 49,
"metadata": {},
"outputs": [],
"source": [
"scalet = numpy.linspace(0, T*13, int(T*fs*13), endpoint=False)\n",
"scale = numpy.concatenate([note(A*2**(i/12.)) for i in range(13)]) "
]
},
{
"cell_type": "code",
"execution_count": 50,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
" \n",
" "
],
"text/plain": [
""
]
},
"execution_count": 50,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Audio(scale, rate=fs)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Of course, this is quite a large number of points, you can't really see what's going on"
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[]"
]
},
"execution_count": 55,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(scalet, scale)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"You can see the sinusoids better if you zoom in"
]
},
{
"cell_type": "code",
"execution_count": 56,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[]"
]
},
"execution_count": 56,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"Nzoom = 1000\n",
"plt.plot(scalet[:Nzoom], scale[:Nzoom])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's listen to the effect of running this through a first order filter.\n",
"\n",
"$$G_f = \\frac{1}{\\tau s + 1}$$\n",
"\n",
"We'll use the convolution, so we first obtain the impulse response of the filter"
]
},
{
"cell_type": "code",
"execution_count": 57,
"metadata": {},
"outputs": [],
"source": [
"omega = 440*twopi # (440 cycles/second)*(2 pi radians / cycle)\n",
"tau = 1/omega\n",
"first_order_impulse = numpy.exp(-t/tau)"
]
},
{
"cell_type": "code",
"execution_count": 58,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[]"
]
},
"execution_count": 58,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(t[:Nzoom], first_order_impulse[:Nzoom])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Then we calculate the output signal via convolution. Recall that when we wrote $y(s) = G_f(s)u(s)$, this was equivalent to calculating $y(t) = g_f(t)*u(t)$ where the $*$ represents convolution. In this case the filtered signal is $y(t)$ and the original scale is $u(t)$."
]
},
{
"cell_type": "code",
"execution_count": 59,
"metadata": {},
"outputs": [],
"source": [
"def filtersignal(signal):\n",
" return numpy.convolve(signal, first_order_impulse, 'same')/len(signal)*len(first_order_impulse)"
]
},
{
"cell_type": "code",
"execution_count": 60,
"metadata": {},
"outputs": [],
"source": [
"filtered = filtersignal(scale)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As a side note: This is not how filtering is done in practice, you can see this process takes a while."
]
},
{
"cell_type": "code",
"execution_count": 61,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
" \n",
" "
],
"text/plain": [
""
]
},
"execution_count": 61,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Audio(filtered, rate=fs)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Can you hear how the sound gets softer as the frequency goes up? This is the effect of the filter. If we plot the whole waveform we can clearly see the amplitude going down in steps."
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[]"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(scalet, filtered)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"When we zoom in so that we can see the wave forms, we can see that the low frequencies are attenuated less than the high frequencies."
]
},
{
"cell_type": "code",
"execution_count": 62,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[,\n",
" ]"
]
},
"execution_count": 62,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(scalet[:Nzoom], scale[:Nzoom],\n",
" scalet[:Nzoom], filtered[:Nzoom])"
]
},
{
"cell_type": "code",
"execution_count": 63,
"metadata": {},
"outputs": [],
"source": [
"start = int(fs/T)*3"
]
},
{
"cell_type": "code",
"execution_count": 64,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[,\n",
" ]"
]
},
"execution_count": 64,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(scalet[start:start+Nzoom], scale[start:start+Nzoom],\n",
" scalet[start:start+Nzoom], filtered[start:start+Nzoom])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## But signals aren't pure sinusoids\n",
"\n",
"Why have I chosen pure sinusoids to play with here? Because they can be combined to form all the other signals via Fourier series. Just to show that everything still works even when we don't have pure sinusoids, let's form a chord, which will be three sinusoids playing together. I'll build a [major chord](https://en.wikipedia.org/wiki/Major_chord) in just intonation.\n",
"\n",
"I'll also use the highest note an octave higher so that we can hear the filtering effect more clearly. I'm using `tile` here to repeat the sample a couple of times to make the sound longer."
]
},
{
"cell_type": "code",
"execution_count": 65,
"metadata": {},
"outputs": [],
"source": [
"notes = [A, A*5/4, A*3/2*2]"
]
},
{
"cell_type": "code",
"execution_count": 66,
"metadata": {},
"outputs": [],
"source": [
"chord = numpy.tile(1/len(notes)*sum(note(n) for n in notes), 3)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can see that this is no longer a simple sinusoid"
]
},
{
"cell_type": "code",
"execution_count": 67,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[]"
]
},
"execution_count": 67,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(scalet[:Nzoom], chord[:Nzoom])"
]
},
{
"cell_type": "code",
"execution_count": 68,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
" \n",
" "
],
"text/plain": [
""
]
},
"execution_count": 68,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Audio(chord, rate=fs)"
]
},
{
"cell_type": "code",
"execution_count": 69,
"metadata": {},
"outputs": [],
"source": [
"filtered = filtersignal(chord)"
]
},
{
"cell_type": "code",
"execution_count": 70,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
" \n",
" "
],
"text/plain": [
""
]
},
"execution_count": 70,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Audio(filtered, rate=fs)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Numeric Fourier Transform\n",
"We can obtain an approximation of a Fourier transform of a signal by using the Fast Fourier Transform (fft). Functions relating to the fft are found in `numpy.fft`. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First we calculate the fft using `rfft`. The r stands for \"real\", because we have a signal containing only real values. If we use `numpy.fft.fft` it assumes that the signal could contain complex values and returns twice as many values. `numpy.fft.tfftfreq` is used to calculate the frequencies for which `rfft` has calculated the values."
]
},
{
"cell_type": "code",
"execution_count": 74,
"metadata": {},
"outputs": [],
"source": [
"fft = numpy.fft.rfft(chord)\n",
"fftfreq = numpy.fft.rfftfreq(len(chord), dt)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"When we plot the gain part of this signal, we can clearly see the peaks at the frequencies of the sinusoids from before."
]
},
{
"cell_type": "code",
"execution_count": 75,
"metadata": {},
"outputs": [],
"source": [
"def bodegain(fft):\n",
" plt.loglog(fftfreq, numpy.abs(fft))\n",
" \n",
"def shownotes():\n",
" for n in notes:\n",
" plt.axvline(n, color='grey', alpha=0.8)"
]
},
{
"cell_type": "code",
"execution_count": 76,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"bodegain(fft)\n",
"shownotes()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now, let's look at the filtered version"
]
},
{
"cell_type": "code",
"execution_count": 77,
"metadata": {},
"outputs": [],
"source": [
"filtered_fft = numpy.fft.rfft(filtered)"
]
},
{
"cell_type": "code",
"execution_count": 78,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"bodegain(filtered_fft)\n",
"shownotes()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It's clear how the lower frequencies are attenuated (made smaller) by the filter."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can also work backwards from the measured signals to obtain the frequency response of the system. Consider that \n",
"\n",
"$$G(s) = \\frac{y(s)}{u(s)} \\quad \\text{so} \\quad G(i\\omega) = \\frac{y(i\\omega)}{u(i\\omega)}$$"
]
},
{
"cell_type": "code",
"execution_count": 79,
"metadata": {},
"outputs": [],
"source": [
"Gfreq = filtered_fft/fft"
]
},
{
"cell_type": "code",
"execution_count": 80,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[]"
]
},
"execution_count": 80,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.loglog(fftfreq, numpy.abs(Gfreq))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The gain is a bit strange (very large) here because we used a pure sinusoidal signal to start with, with no low frequency content, but we can still see the characteristic shape of a first order transfer function."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## But that sounds terrible\n",
"\n",
"Pure sinusoids are not in fact all that musical, let's rather use a proper song."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"You can convert from MP3 to wav using one of [these techniques](http://www.wikihow.com/Convert-MP3-to-WAV)"
]
},
{
"cell_type": "code",
"execution_count": 81,
"metadata": {},
"outputs": [],
"source": [
"import scipy.io.wavfile"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"I've used \"Wedding Day\" by SAINt JHN here. I think 7 seconds falls within fair use. You might want to use your own favourite song to hear the differences clearly."
]
},
{
"cell_type": "code",
"execution_count": 88,
"metadata": {},
"outputs": [],
"source": [
"samplingrate, song = scipy.io.wavfile.read('../../assets/weddingday.wav')"
]
},
{
"cell_type": "code",
"execution_count": 89,
"metadata": {},
"outputs": [],
"source": [
"dt = 1/samplingrate"
]
},
{
"cell_type": "code",
"execution_count": 90,
"metadata": {},
"outputs": [],
"source": [
"samplelength = 7*samplingrate\n",
"songsample = song.sum(axis=1)[:samplelength]"
]
},
{
"cell_type": "code",
"execution_count": 91,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[]"
]
},
"execution_count": 91,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(songsample)"
]
},
{
"cell_type": "code",
"execution_count": 92,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[]"
]
},
"execution_count": 92,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(songsample[100000:105000])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's first hear what it sounds like unfiltered."
]
},
{
"cell_type": "code",
"execution_count": 99,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([-5346, -4772, -4268, ..., 35405, 34417, 33684])"
]
},
"execution_count": 99,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"songsample[100000:105000]"
]
},
{
"cell_type": "code",
"execution_count": 93,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
" \n",
" "
],
"text/plain": [
""
]
},
"execution_count": 93,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Audio(songsample, rate=samplingrate)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now with one pass through the filter"
]
},
{
"cell_type": "code",
"execution_count": 94,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
" \n",
" "
],
"text/plain": [
""
]
},
"execution_count": 94,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"filtered = filtersignal(songsample)\n",
"Audio(filtered, rate=samplingrate)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can filter the signal a second time to really hear the high notes fall away."
]
},
{
"cell_type": "code",
"execution_count": 96,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
" \n",
" "
],
"text/plain": [
""
]
},
"execution_count": 96,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"filtered = filtersignal(filtered)\n",
"Audio(filtered, rate=samplingrate)"
]
},
{
"cell_type": "code",
"execution_count": 97,
"metadata": {},
"outputs": [],
"source": [
"songfft = numpy.fft.rfft(songsample)\n",
"filteredfft = numpy.fft.rfft(filtered)\n",
"fftfreq = numpy.fft.rfftfreq(len(songsample), dt)"
]
},
{
"cell_type": "code",
"execution_count": 98,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"bodegain(songfft)\n",
"bodegain(filteredfft)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's see what the effect of the filter looks like as a function of frequency."
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {},
"outputs": [],
"source": [
"Gfft = filteredfft/songfft"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {},
"outputs": [],
"source": [
"omega = numpy.logspace(0, 5, 1000)"
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {},
"outputs": [],
"source": [
"s = 1j*omega"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {},
"outputs": [],
"source": [
"Gw = 1/(tau*s + 1)"
]
},
{
"cell_type": "code",
"execution_count": 45,
"metadata": {},
"outputs": [],
"source": [
"gain = numpy.abs(Gw)"
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 46,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.loglog(fftfreq, numpy.abs(Gfft))\n",
"plt.loglog(omega, gain)\n",
"plt.axvline(1/tau, color='red')"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}