diff --git a/applications/lofar2/model/lofar2_station_sdp_firmware_model.ipynb b/applications/lofar2/model/lofar2_station_sdp_firmware_model.ipynb
index 37b96a1a9e81ae0b65511595761181dd09d2d34d..a4d28d6f91fada57045df40e3e262c42f2d37a23 100644
--- a/applications/lofar2/model/lofar2_station_sdp_firmware_model.ipynb
+++ b/applications/lofar2/model/lofar2_station_sdp_firmware_model.ipynb
@@ -146,6 +146,14 @@
"print(\"Unit_beamlet_scale =\", Unit_beamlet_scale)"
]
},
+ {
+ "cell_type": "markdown",
+ "id": "8e1d2552",
+ "metadata": {},
+ "source": [
+ "## 1.1 Subband gain factor"
+ ]
+ },
{
"cell_type": "code",
"execution_count": 5,
@@ -232,6 +240,14 @@
"print()\n"
]
},
+ {
+ "cell_type": "markdown",
+ "id": "ec61a040",
+ "metadata": {},
+ "source": [
+ "## 1.2 Beamlet gain factor"
+ ]
+ },
{
"cell_type": "code",
"execution_count": 6,
@@ -339,6 +355,14 @@
"print()"
]
},
+ {
+ "cell_type": "markdown",
+ "id": "bda7e827",
+ "metadata": {},
+ "source": [
+ "## 1.3 Maximum input level for beamlet_sum and BST"
+ ]
+ },
{
"cell_type": "code",
"execution_count": 7,
@@ -401,7 +425,9 @@
"id": "d942fcc6",
"metadata": {},
"source": [
- "# 2 Quantization model"
+ "# 2 Quantization noise\n",
+ "\n",
+ "## 2.1 dB full scale (dBFS)"
]
},
{
@@ -429,100 +455,115 @@
{
"cell_type": "code",
"execution_count": 10,
- "id": "a9fca052",
+ "id": "be2d952f",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
- "\n",
- "P_quant = 0.083333\n",
- "P_quant_dB = -10.79 dB = -1.8 bit\n",
- "sigma_quant = 0.29 q\n"
+ "W_adc = 14 bits\n",
+ "FS = 8192\n",
+ "sigma_fs_sine = 5792.6 q\n",
+ "P_fs_sine_dB = 75.26 dB = 12.5 bit\n"
]
}
],
"source": [
- "# Quantization noise\n",
- "# . The quantization noise power is q**2 * 1 / 12, so the standard deviation\n",
- "# of the quantization noise is q * sqrt(1 / 12) < q = one LSbit\n",
- "# . The quantization noise power is at a level of -10.79 dB or -1.8 bit.\n",
- "# . The 0 dB power level or 0 bit level corresponds to the power of one LSbit, so q**2 \n",
- "P_quant = 1 / 12 # for W >> 1 [2]\n",
- "P_quant_dB = 10 * np.log10(P_quant)\n",
- "sigma_quant = np.sqrt(P_quant)\n",
- "print()\n",
- "print(f\"P_quant = {P_quant:.6f}\")\n",
- "print(f\"P_quant_dB = {P_quant_dB:.2f} dB = {P_quant_dB / P_bit_dB:.1f} bit\")\n",
- "print(f\"sigma_quant = {sigma_quant:.2f} q\")"
+ "# Full scale (FS) sine\n",
+ "P_fs_sine = FS**2 / 2\n",
+ "P_fs_sine_dB = 10 * np.log10(P_fs_sine)\n",
+ "print(f\"W_adc = {W_adc} bits\")\n",
+ "print(\"FS =\", FS)\n",
+ "print(f\"sigma_fs_sine = {sigma_fs_sine:.1f} q\")\n",
+ "print(f\"P_fs_sine_dB = {P_fs_sine_dB:.2f} dB = {P_fs_sine_dB / P_bit_dB:.1f} bit\")"
]
},
{
"cell_type": "code",
"execution_count": 11,
- "id": "d9972b6b",
+ "id": "c827851e",
"metadata": {},
"outputs": [
{
- "data": {
- "image/png": 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\n",
- "text/plain": [
- "<Figure size 864x576 with 1 Axes>"
- ]
- },
- "metadata": {
- "needs_background": "light"
- },
- "output_type": "display_data"
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Power at -50dBFS = 25.26 dB corresponds to:\n",
+ " . sigma = 18.3 q (= 4.2 bits)\n",
+ " . Noise range 3 sigma = +-55 q\n",
+ " . Sine with amplitude A = = sigma * sqrt(2) = 25.9 q\n",
+ "\n",
+ "sigma = 16 q (= 4.0 bits) corresponds to:\n",
+ " . Power = 24.08 dB, so at -51.2 dBFS\n",
+ " . Noise range 3 sigma = +-48 q\n",
+ " . Sine with amplitude A = sigma * sqrt(2) = 22.6 q\n"
+ ]
}
],
"source": [
- "# Impact of quantization on the system noise\n",
- "# The quantization noise has sigma_quant = 0.29 q, this increases the system noise.\n",
- "# The system noise has sigma_sys = n * q. For n = 2 the quantization increases the\n",
- "# total power by 2% (so sigma_sys increase by sqrt(2 %) is about 1 %).\n",
- "step = 0.1\n",
- "n = np.arange(1, 9, step)\n",
- "sigma_sys = n # = n * q, so sigma of n LSbits\n",
- "P_sys = sigma_sys**2\n",
- "P_tot = P_sys + P_quant\n",
- "sigma_tot = np.sqrt(P_tot)\n",
+ "# dBFS: Signal level relative to FS sine\n",
+ "power_50dBFS = P_fs_sine_dB - 50 \n",
+ "sigma_50dBFS = 10**(power_50dBFS / 20)\n",
+ "sigma_50dBFS_bits = np.log2(sigma_50dBFS)\n",
+ "ampl_50dBFS = sigma_50dBFS * np.sqrt(2)\n",
"\n",
- "plt.figure(figsize=(12, 8))\n",
- "plt.plot(n, (P_tot / P_sys - 1) * 100)\n",
- "plt.title(\"Increase in total noise power due to quantization\")\n",
- "plt.xlabel(\"sigma_sys [q]\")\n",
- "plt.ylabel(\"[%]\")\n",
- "plt.grid()\n",
- "plt.savefig('plots/lofar2_station_sdp_firmware_model_incr_sigma_sys.jpg', dpi=dpi)"
+ "print(f\"Power at -50dBFS = {power_50dBFS:.2f} dB corresponds to:\")\n",
+ "print(f\" . sigma = {sigma_50dBFS:.1f} q (= {sigma_50dBFS_bits:.1f} bits)\")\n",
+ "print(f\" . Noise range 3 sigma = +-{3 * sigma_50dBFS:.0f} q\")\n",
+ "print(f\" . Sine with amplitude A = = sigma * sqrt(2) = {ampl_50dBFS:.1f} q\")\n",
+ "print()\n",
+ "\n",
+ "# Assume signal with sigma = 16 q is 4 bits noise\n",
+ "sigma_16q = 16\n",
+ "sigma_16q_bits = np.log2(sigma_16q)\n",
+ "power_16q = sigma_16q**2\n",
+ "power_16q_dB = 10 * np.log10(power_16q)\n",
+ "dBFS_16q = power_16q_dB - P_fs_sine_dB\n",
+ "print(f\"sigma = {sigma_16q:.0f} q (= {sigma_16q_bits:.1f} bits) corresponds to:\")\n",
+ "print(f\" . Power = {power_16q_dB:.2f} dB, so at {dBFS_16q:.1f} dBFS\")\n",
+ "print(f\" . Noise range 3 sigma = +-{3 * sigma_16q:.0f} q\")\n",
+ "print(f\" . Sine with amplitude A = sigma * sqrt(2) = {np.sqrt(2) * sigma_16q:.1f} q\")\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "982937ab",
+ "metadata": {},
+ "source": [
+ "## 2.2 Signal to noise ratio (SNR)"
]
},
{
"cell_type": "code",
"execution_count": 12,
- "id": "be2d952f",
+ "id": "a9fca052",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
- "W_adc = 14 bits\n",
- "FS = 8192\n",
- "sigma_fs_sine = 5792.6 q\n",
- "P_fs_sine_dB = 75.26 dB = 12.5 bit\n"
+ "\n",
+ "P_quant = 0.083333\n",
+ "P_quant_dB = -10.79 dB = -1.8 bit\n",
+ "sigma_quant = 0.29 q\n"
]
}
],
"source": [
- "# Full scale (FS) sine\n",
- "P_fs_sine = FS**2 / 2\n",
- "P_fs_sine_dB = 10 * np.log10(P_fs_sine)\n",
- "print(f\"W_adc = {W_adc} bits\")\n",
- "print(\"FS =\", FS)\n",
- "print(f\"sigma_fs_sine = {sigma_fs_sine:.1f} q\")\n",
- "print(f\"P_fs_sine_dB = {P_fs_sine_dB:.2f} dB = {P_fs_sine_dB / P_bit_dB:.1f} bit\")"
+ "# Quantization noise\n",
+ "# . The quantization noise power is q**2 * 1 / 12, so the standard deviation\n",
+ "# of the quantization noise is q * sqrt(1 / 12) < q = one LSbit\n",
+ "# . The quantization noise power is at a level of -10.79 dB or -1.8 bit.\n",
+ "# . The 0 dB power level or 0 bit level corresponds to the power of one LSbit, so q**2 \n",
+ "P_quant = 1 / 12 # for W >> 1 [2]\n",
+ "P_quant_dB = 10 * np.log10(P_quant)\n",
+ "sigma_quant = np.sqrt(P_quant)\n",
+ "print()\n",
+ "print(f\"P_quant = {P_quant:.6f}\")\n",
+ "print(f\"P_quant_dB = {P_quant_dB:.2f} dB = {P_quant_dB / P_bit_dB:.1f} bit\")\n",
+ "print(f\"sigma_quant = {sigma_quant:.2f} q\")"
]
},
{
@@ -549,51 +590,52 @@
"print(f\"SNR_dB = P_fs_sine_dB - P_quant_dB = {P_fs_sine_dB:.2f} - {P_quant_dB:.2f} = {SNR_dB:.2f} dB\")"
]
},
+ {
+ "cell_type": "markdown",
+ "id": "c1c19077",
+ "metadata": {},
+ "source": [
+ "## 2.3 Impact of quantization on the system noise"
+ ]
+ },
{
"cell_type": "code",
"execution_count": 14,
- "id": "92852a53",
+ "id": "d9972b6b",
"metadata": {},
"outputs": [
{
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Power at -50dBFS = 25.26 dB corresponds to:\n",
- " . sigma = 18.3 q (= 4.2 bits)\n",
- " . Noise range 3 sigma = +-55 q\n",
- " . Sine with amplitude A = = sigma * sqrt(2) = 25.9 q\n",
- "\n",
- "sigma = 16 q (= 4.0 bits) corresponds to:\n",
- " . Power = 24.08 dB, so at -51.2 dBFS\n",
- " . Noise range 3 sigma = +-48 q\n",
- " . Sine with amplitude A = sigma * sqrt(2) = 22.6 q\n"
- ]
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 864x576 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
}
],
"source": [
- "# Signal level relative to FS sine\n",
- "power_50dBFS = P_fs_sine_dB - 50 \n",
- "sigma_50dBFS = 10**(power_50dBFS / 20)\n",
- "sigma_50dBFS_bits = np.log2(sigma_50dBFS)\n",
- "ampl_50dBFS = sigma_50dBFS * np.sqrt(2)\n",
- "\n",
- "print(f\"Power at -50dBFS = {power_50dBFS:.2f} dB corresponds to:\")\n",
- "print(f\" . sigma = {sigma_50dBFS:.1f} q (= {sigma_50dBFS_bits:.1f} bits)\")\n",
- "print(f\" . Noise range 3 sigma = +-{3 * sigma_50dBFS:.0f} q\")\n",
- "print(f\" . Sine with amplitude A = = sigma * sqrt(2) = {ampl_50dBFS:.1f} q\")\n",
+ "# Impact of quantization on the system noise\n",
+ "# The quantization noise has sigma_quant = 0.29 q, this increases the system noise.\n",
+ "# The system noise has sigma_sys = n * q. For n = 2 the quantization increases the\n",
+ "# total power by 2% (so sigma_sys increase by sqrt(2 %) is about 1 %).\n",
+ "step = 0.1\n",
+ "n = np.arange(1, 9, step)\n",
+ "sigma_sys = n # = n * q, so sigma of n LSbits\n",
+ "P_sys = sigma_sys**2\n",
+ "P_tot = P_sys + P_quant\n",
+ "sigma_tot = np.sqrt(P_tot)\n",
"\n",
- "# Assume signal with sigma = 16 q is 4 bits noise\n",
- "sigma_16q = 16\n",
- "sigma_16q_bits = np.log2(sigma_16q)\n",
- "power_16q = sigma_16q**2\n",
- "power_16q_dB = 10 * np.log10(power_16q)\n",
- "dBFS_16q = power_16q_dB - P_fs_sine_dB\n",
- "print()\n",
- "print(f\"sigma = {sigma_16q:.0f} q (= {sigma_16q_bits:.1f} bits) corresponds to:\")\n",
- "print(f\" . Power = {power_16q_dB:.2f} dB, so at {dBFS_16q:.1f} dBFS\")\n",
- "print(f\" . Noise range 3 sigma = +-{3 * sigma_16q:.0f} q\")\n",
- "print(f\" . Sine with amplitude A = sigma * sqrt(2) = {np.sqrt(2) * sigma_16q:.1f} q\")\n"
+ "plt.figure(figsize=(12, 8))\n",
+ "plt.plot(n, (P_tot / P_sys - 1) * 100)\n",
+ "plt.title(\"Increase in total noise power due to quantization\")\n",
+ "plt.xlabel(\"sigma_sys [q]\")\n",
+ "plt.ylabel(\"[%]\")\n",
+ "plt.grid()\n",
+ "plt.savefig('plots/lofar2_station_sdp_firmware_model_incr_sigma_sys.jpg', dpi=dpi)"
]
},
{
@@ -609,7 +651,7 @@
"id": "f7fff7a0",
"metadata": {},
"source": [
- "## 3.1 Signal input power and DC level"
+ "## 3.1 ADC Statistics (AST)"
]
},
{
@@ -629,7 +671,7 @@
}
],
"source": [
- "# Signal input power statistic for ADC / WG (AST)\n",
+ "# Signal input power and DC level statistic for ADC / WG\n",
"si_sigma = sigma_fs_sine\n",
"si_sigma_bits = np.log2(si_sigma)\n",
"P_ast = (si_sigma)**2 * N_int_adc\n",
@@ -689,6 +731,14 @@
"* ampl real = ampl imag = std complex = std real * sqrt(2) = std imag * sqrt(2)"
]
},
+ {
+ "cell_type": "markdown",
+ "id": "22c393ba",
+ "metadata": {},
+ "source": [
+ "### 3.2.1 Coherent, narrow band, sine input"
+ ]
+ },
{
"cell_type": "code",
"execution_count": 16,
@@ -781,6 +831,14 @@
" f\"at {dBFS_16q:.1f} dBFS (= FS / {10**(-dBFS_16q/20):.0f})\")"
]
},
+ {
+ "cell_type": "markdown",
+ "id": "b6378f26",
+ "metadata": {},
+ "source": [
+ "### 3.2.2 Incoherent, wide band, noise input"
+ ]
+ },
{
"cell_type": "code",
"execution_count": 17,
@@ -855,6 +913,14 @@
"* For sigma = FS / 4 white noise input the subband sigma uses 11 bits, so 10.5 bits for the subband real and imaginary parts. The 4 sigma just fits in FS and corresponds to 2 bits, so including the sign bit the 4 sigma range of the subband real and imag fits in 1 + 10.5 + 2 = 13.5 bits."
]
},
+ {
+ "cell_type": "markdown",
+ "id": "e9bcdc19",
+ "metadata": {},
+ "source": [
+ "### 3.2.3 From SST level to input level"
+ ]
+ },
{
"cell_type": "code",
"execution_count": 18,
@@ -974,7 +1040,7 @@
"source": [
"## 3.3 Crosslet statistics (XST)\n",
"\n",
- "The crosslet statistics have W_crosslet = 16b, but use the same LSbit level as the subbands. The subbands have W_subband = 18b and the maximum subband sine amplitude is 17b (for W_fft_proc = 5 bits). Therefore the maximum sine input for no XST overflow is A = 0.25. If subband_weight = 1.0 then the auto correlations of the XST are equal to the SST."
+ "The crosslet statistics have W_crosslet = 16b, but use the same LSbit level as the subbands. The subbands have W_subband = 18b and the maximum subband sine amplitude is 17b (for W_fft_proc = 5 bits). Therefore the maximum sine input for no XST overflow is A = 0.25. If subband_weight = 1.0 then the auto correlations of the XST are equal to the SST. Hence the crosslets have the same sensitivity as the subbands, but less dynamic range."
]
},
{
@@ -982,7 +1048,9 @@
"id": "ba543d00",
"metadata": {},
"source": [
- "## 3.4 Beamlet statistics (BST)"
+ "## 3.4 Beamlet statistics (BST)\n",
+ "\n",
+ "### 3.4.1 Coherent, narrow band, sine input"
]
},
{
@@ -1094,6 +1162,14 @@
" f\"at {dBFS_16q:.1f} dBFS (= FS / {10**(-dBFS_16q/20):.0f})\")"
]
},
+ {
+ "cell_type": "markdown",
+ "id": "29e97579",
+ "metadata": {},
+ "source": [
+ "### 3.4.2 Icoherent, wide band, noise input"
+ ]
+ },
{
"cell_type": "code",
"execution_count": 20,
@@ -1194,7 +1270,7 @@
},
{
"cell_type": "code",
- "execution_count": 21,
+ "execution_count": 42,
"id": "def6eba7",
"metadata": {},
"outputs": [
@@ -1206,8 +1282,8 @@
"sigma = 4\n",
"sigma_y = 4.000000\n",
"sigma_z = 4.000000\n",
- "mean_y = -0.031990\n",
- "mean_z = 0.041970+0.136082j\n",
+ "mean_y = -0.000000\n",
+ "mean_z = -0.000000-0.000000j\n",
"\n",
"The DFT of the sine plot shows:\n",
". G_fft_real_input_dc = 1\n",
@@ -1215,20 +1291,32 @@
"\n",
"The DFT of the block plot shows that the first harmonic has an amplitude of 4/pi * A/2 = 0.6364949321522198, which is larger than A / 2 = 0.5000000000000007 for sine input. Hence the bin samples need 1 bit more than for a full scale sine, because to also fit e.g. this harmonic of a block wave.\n",
"\n",
- "len(Y_fft) = 1024\n",
- "len(Y_rfft) = 513\n",
- "\n",
- ". mean(Y_fft) = 0.003193+0.000000j\n",
- ". mean(Y_rfft) = 0.003014+0.005344j\n",
+ "The rfft = fft without the negative frequencies.\n",
+ ". len(Y_fft) = 1024\n",
+ ". len(Y_rfft) = 513\n",
+ ". Y_fft[512-3:512] = \n",
+ "[ 0.05435461+0.03298198j -0.01792691-0.07715472j -0.07958293-0.07965155j]\n",
+ ". Y_fft[512:512+3] = \n",
+ "[-4.85722573e-17+0.j -7.95829258e-02+0.07965155j\n",
+ " -1.79269069e-02+0.07715472j]\n",
+ ". Y_rfft[0:3] = \n",
+ "[-4.85722573e-17+0.j -7.95829258e-02+0.07965155j\n",
+ " -1.79269069e-02+0.07715472j]\n",
"\n",
"For the DFT of the real input noise the expected std() = 0.125000:\n",
- ". std(Y_fft) = 0.12496321601460109\n",
- ". std(Y_rfft) = 0.12481753522674345\n",
- "The slight difference with fft() and rfft() std() results is due to that mean_Y_fft and mean_Y_rfft are not 0, so rms != std\n",
+ ". mean(Y_fft) = 0.001807+0.000000j\n",
+ ". mean(Y_rfft) = 0.001785+0.005602j\n",
+ ". std(Y_fft) = 0.12498694451650419\n",
+ ". std(Y_rfft) = 0.1247408771285474\n",
+ ". rms(Y_fft) = 0.12499999999999999\n",
+ ". rms(Y_rfft) = 0.12487937485529345\n",
+ ". rms_adjust(Y_rfft) = 0.12488532642537446\n",
+ "The slight difference with fft() and rfft() for std() and rms() results is due to that mean_Y_fft and mean_Y_rfft are not 0, so rms != std and due to that rfft has length N_fft//2 + 1.\n",
"\n",
"For the DFT of the complex input noise the expected std() = 0.125000:\n",
- ". std(Z_fft) = 0.12499195618198528\n",
- ". rms(Z_fft) = 0.1250791927160722\n"
+ ". mean(Z_fft) = (0.0028379522458180655+9.531007055261684e-05j)\n",
+ ". std(Z_fft) = 0.12496774361026493\n",
+ ". rms(Z_fft) = 0.125\n"
]
},
{
@@ -1257,7 +1345,7 @@
},
{
"data": {
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\n",
+ "image/png": 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\n",
"text/plain": [
"<Figure size 720x288 with 2 Axes>"
]
@@ -1309,7 +1397,7 @@
"dc = ampl * np.cos(2 * np.pi * dc_bin * t_axis) # equivalent to dc = ampl\n",
"noise = np.random.randn(N_fft)\n",
"noise *= sigma / np.std(noise) # apply requested sigma\n",
- "#noise -= np.mean(noise) # apply zero mean\n",
+ "noise -= np.mean(noise) # apply zero mean to have std = rms for input\n",
"b = ampl * np.sign(s) # block wave, sign: -1 if x < 0, 0 if x==0, 1 if x > 0\n",
"\n",
"x = s + dc\n",
@@ -1319,7 +1407,7 @@
"\n",
"noise_complex = np.random.randn(N_fft) + np.random.randn(N_fft) * 1j\n",
"noise_complex *= sigma / np.std(noise_complex) # apply requested sigma\n",
- "#noise_complex -= np.mean(noise_complex) # apply zero mean\n",
+ "noise_complex -= np.mean(noise_complex) # apply zero mean to have std = rms for input\n",
"z = noise_complex\n",
"mean_z = np.mean(z)\n",
"sigma_z = np.std(z)\n",
@@ -1394,31 +1482,42 @@
"scale sine, because to also fit e.g. this harmonic of a block wave.\")\n",
"print()\n",
"\n",
- "print(f\"len(Y_fft) = {len(Y_fft)}\")\n",
- "print(f\"len(Y_rfft) = {len(Y_rfft)}\")\n",
+ "print(\"The rfft = fft without the negative frequencies.\")\n",
+ "print(f\". len(Y_fft) = {len(Y_fft)}\")\n",
+ "print(f\". len(Y_rfft) = {len(Y_rfft)}\")\n",
+ "print(f\". Y_fft[512-3:512] = \\n{Y_fft[512-3:512]}\")\n",
+ "print(f\". Y_fft[512:512+3] = \\n{Y_fft[512:512+3]}\")\n",
+ "print(f\". Y_rfft[0:3] = \\n{Y_rfft[0:3]}\")\n",
"print()\n",
"\n",
"mean_Y_fft = np.mean(Y_fft)\n",
"mean_Y_rfft = np.mean(Y_rfft)\n",
- "print(f\". mean(Y_fft) = {mean_Y_fft:.6f}\")\n",
- "print(f\". mean(Y_rfft) = {mean_Y_rfft:.6f}\")\n",
- "print()\n",
- "\n",
"sigma_Y_fft = np.std(Y_fft)\n",
"sigma_Y_rfft = np.std(Y_rfft)\n",
+ "rms_Y_fft = np.sqrt(sigma_Y_fft**2 + np.abs(mean_Y_fft)**2)\n",
+ "rms_Y_rfft = np.sqrt(np.sum(np.abs(Y_rfft)**2) / (N_fft // 2 + 1)) # equivalent\n",
+ "rms_Y_rfft = np.sqrt(sigma_Y_rfft**2 + np.abs(mean_Y_rfft)**2) # equivalent\n",
+ "\n",
"print(f\"For the DFT of the real input noise the expected std() = {sigma_y / np.sqrt(N_fft):.6f}:\")\n",
+ "print(f\". mean(Y_fft) = {mean_Y_fft:.6f}\")\n",
+ "print(f\". mean(Y_rfft) = {mean_Y_rfft:.6f}\")\n",
"print(f\". std(Y_fft) = {sigma_Y_fft}\")\n",
"print(f\". std(Y_rfft) = {sigma_Y_rfft}\")\n",
- "print(\"The slight difference with fft() and rfft() std() results is due to that \\\n",
- "mean_Y_fft and mean_Y_rfft are not 0, so rms != std\")\n",
+ "print(f\". rms(Y_fft) = {rms_Y_fft}\")\n",
+ "print(f\". rms(Y_rfft) = {rms_Y_rfft}\")\n",
+ "print(f\". rms_adjust(Y_rfft) = {rms_Y_rfft_adj}\")\n",
+ "print(\"The slight difference with fft() and rfft() for std() and rms() results is due to that mean_Y_fft \\\n",
+ "and mean_Y_rfft are not 0, so rms != std and due to that rfft has length N_fft//2 + 1.\")\n",
"print()\n",
"\n",
+ "mean_Z_fft = np.mean(Z_fft)\n",
"sigma_Z_fft = np.std(Z_fft)\n",
- "rms_Z_fft = np.sqrt(np.sum(np.abs(Z_fft)**2) / N_fft)\n",
+ "rms_Z_fft = np.sqrt(np.sum(np.abs(Z_fft)**2) / N_fft) # equivalent\n",
+ "rms_Z_fft = np.sqrt(sigma_Z_fft**2 + np.abs(mean_Z_fft)**2) # equivalent\n",
"print(f\"For the DFT of the complex input noise the expected std() = {sigma_z / np.sqrt(N_fft):.6f}:\")\n",
+ "print(f\". mean(Z_fft) = {mean_Z_fft}\")\n",
"print(f\". std(Z_fft) = {sigma_Z_fft}\")\n",
- "print(f\". rms(Z_fft) = {rms_Z_fft}\")\n",
- "\n"
+ "print(f\". rms(Z_fft) = {rms_Z_fft}\")\n"
]
},
{
@@ -1466,7 +1565,7 @@
"# . The amplitude of the phasor is equal to the std() of a rotating phasor.\n",
"# . The amplitude of the bin phasor is A/2, so the bin phasor A/2 exp(jwt) has power\n",
"# (A/2)**2\n",
- "# . The total power in the N_sidebands = 2 bins is eual to the input power as expected\n",
+ "# . The total power in the N_sidebands = 2 bins is equal to the input power as expected\n",
"\n",
"# . input sine\n",
"sin_std = np.std(s)\n",
@@ -1503,7 +1602,7 @@
},
{
"cell_type": "code",
- "execution_count": 23,
+ "execution_count": 48,
"id": "97e9a32d",
"metadata": {},
"outputs": [
@@ -1511,32 +1610,25 @@
"name": "stdout",
"output_type": "stream",
"text": [
- "noise mean = -0.031990173370045484)\n",
- "noise sigma = 4.0 (= 4)\n",
- "noise var = 16.0)\n",
- "noise power = 16.001023371192247)\n",
+ "noise mean = -0.000000)\n",
+ "noise sigma = 4.000000\n",
+ "noise var = 16.000000)\n",
+ "noise power = 16.000000)\n",
"\n",
"N_fft = 1024\n",
"sqrt(N_fft) = 32.0\n",
- "sigma / std(Y_fft) = 32.009419\n",
- "sigma / std(Y_rfft) = 32.046779\n",
+ "sigma / std(Y_fft) = 32.003343\n",
"\n",
- "noise bin std (fft) = 0.124963\n",
- "noise bin std (rfft) = 0.124818\n",
- "noise bin.re std = 0.088304\n",
- "noise bin.im std = 0.088215\n",
- "noise bin power ~= 0.015617\n"
- ]
- },
- {
- "ename": "NameError",
- "evalue": "name 'bin_re_power' is not defined",
- "output_type": "error",
- "traceback": [
- "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
- "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)",
- "Input \u001b[0;32mIn [23]\u001b[0m, in \u001b[0;36m<cell line: 39>\u001b[0;34m()\u001b[0m\n\u001b[1;32m 37\u001b[0m \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mnoise bin.im std = \u001b[39m\u001b[38;5;132;01m{\u001b[39;00mbin_im_std\u001b[38;5;132;01m:\u001b[39;00m\u001b[38;5;124mf\u001b[39m\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m\"\u001b[39m)\n\u001b[1;32m 38\u001b[0m \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mnoise bin power ~= \u001b[39m\u001b[38;5;132;01m{\u001b[39;00mbin_power\u001b[38;5;132;01m:\u001b[39;00m\u001b[38;5;124mf\u001b[39m\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m\"\u001b[39m)\n\u001b[0;32m---> 39\u001b[0m \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mnoise bin.re power + bin.im power ~= \u001b[39m\u001b[38;5;132;01m{\u001b[39;00mbin_re_power \u001b[38;5;241m+\u001b[39m bin_im_power\u001b[38;5;132;01m:\u001b[39;00m\u001b[38;5;124mf\u001b[39m\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m\"\u001b[39m)\n\u001b[1;32m 40\u001b[0m \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mnoise bins power ~= \u001b[39m\u001b[38;5;132;01m{\u001b[39;00mbins_power\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m (= \u001b[39m\u001b[38;5;132;01m{\u001b[39;00mnoise_power\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m)\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[1;32m 42\u001b[0m \u001b[38;5;28mprint\u001b[39m()\n",
- "\u001b[0;31mNameError\u001b[0m: name 'bin_re_power' is not defined"
+ "noise bin std(fft) = 0.124987\n",
+ "noise bin power = 0.015625\n",
+ "noise bins power = 16.000000 (= noise power)\n",
+ "\n",
+ "noise bin.re std = 0.089990\n",
+ "noise bin.im std = 0.086738\n",
+ "noise bin.re power + bin.im power = 0.015625 (= bin power)\n",
+ "\n",
+ "The ratio of real input noise std and DFT bin noise std shows:\n",
+ ". G_fft_real_input_noise = 0.03125 = (1 / sqrt(1024))\n"
]
}
],
@@ -1548,10 +1640,10 @@
"noise_std = np.std(y)\n",
"noise_var = noise_std**2\n",
"noise_power = np.sum(y**2) / N_fft\n",
- "print(f\"noise mean = {noise_mean})\")\n",
- "print(f\"noise sigma = {noise_std} (= {sigma})\")\n",
- "print(f\"noise var = {noise_var})\")\n",
- "print(f\"noise power = {noise_power})\")\n",
+ "print(f\"noise mean = {noise_mean:f})\")\n",
+ "print(f\"noise sigma = {noise_std:f}\")\n",
+ "print(f\"noise var = {noise_var:f})\")\n",
+ "print(f\"noise power = {noise_power:f})\")\n",
"print()\n",
"\n",
"# . fft bin\n",
@@ -1559,28 +1651,33 @@
"# be modelled by averaging over all bins. This however does cause small \n",
"# differences in fft input and output std, due to that fft output mean != 0,\n",
"# so rms != std.\n",
- "bin_std = np.std(Y_rfft)\n",
+ "bin_std = np.std(Y_fft)\n",
"bin_var = bin_std**2\n",
- "bin_mean = np.mean(Y_rfft)\n",
+ "bin_mean = np.mean(Y_fft)\n",
"bin_power = bin_var + np.abs(bin_mean)**2\n",
- "bin_re_std = np.std(Y_rfft.real)\n",
+ "bins_power = bin_power * N_fft\n",
+ "\n",
+ "bin_re_mean = np.mean(Y_fft.real)\n",
+ "bin_re_std = np.std(Y_fft.real)\n",
"bin_re_var = bin_re_std**2\n",
- "bin_im_std = np.std(Y_rfft.imag)\n",
+ "bin_re_power = bin_re_var + np.abs(bin_re_mean)**2\n",
+ "bin_im_mean = np.mean(Y_fft.imag)\n",
+ "bin_im_std = np.std(Y_fft.imag)\n",
"bin_im_var = bin_im_std**2\n",
- "bins_var = bin_var * N_fft\n",
+ "bin_im_power = bin_im_var + np.abs(bin_im_mean)**2\n",
+ "\n",
"\n",
"print(f\"N_fft = {N_fft}\")\n",
"print(f\"sqrt(N_fft) = {np.sqrt(N_fft)}\")\n",
- "print(f\"sigma / std(Y_fft) = {sigma / np.std(Y_fft):f}\")\n",
- "print(f\"sigma / std(Y_rfft) = {sigma / bin_std:f}\")\n",
+ "print(f\"sigma / std(Y_fft) = {sigma / bin_std:f}\")\n",
+ "print()\n",
+ "print(f\"noise bin std(fft) = {bin_std:f}\")\n",
+ "print(f\"noise bin power = {bin_power:f}\")\n",
+ "print(f\"noise bins power = {bins_power:f} (= noise power)\")\n",
"print()\n",
- "print(f\"noise bin std (fft) = {np.std(Y_fft):f}\")\n",
- "print(f\"noise bin std (rfft) = {bin_std:f}\")\n",
"print(f\"noise bin.re std = {bin_re_std:f}\")\n",
"print(f\"noise bin.im std = {bin_im_std:f}\")\n",
- "print(f\"noise bin power ~= {bin_power:f}\")\n",
- "print(f\"noise bin.re power + bin.im power ~= {bin_re_power + bin_im_power:f}\")\n",
- "print(f\"noise bins power ~= {bins_power} (= {noise_power})\")\n",
+ "print(f\"noise bin.re power + bin.im power = {bin_re_power + bin_im_power:f} (= bin power)\")\n",
"\n",
"print()\n",
"print(\"The ratio of real input noise std and DFT bin noise std shows:\")\n",