From 78e937579c00fa96bb91dbc490074d7e89bcc4f3 Mon Sep 17 00:00:00 2001
From: Eric Kooistra <kooistra@astron.nl>
Date: Thu, 28 Nov 2024 14:09:43 +0100
Subject: [PATCH] Try Ncoefs < Ndelays.
---
.../lofar2/model/pfb_os/multirate_mixer.ipynb | 257 ++++++++++++------
1 file changed, 173 insertions(+), 84 deletions(-)
diff --git a/applications/lofar2/model/pfb_os/multirate_mixer.ipynb b/applications/lofar2/model/pfb_os/multirate_mixer.ipynb
index 493dc8bdac..a38afe203e 100644
--- a/applications/lofar2/model/pfb_os/multirate_mixer.ipynb
+++ b/applications/lofar2/model/pfb_os/multirate_mixer.ipynb
@@ -100,6 +100,7 @@
"text": [
"Ntaps = 8\n",
"Ndft = 16\n",
+ "Ndelays = 128\n",
"Ncoefs = 128\n",
"\n",
"wgSub = 1.5\n",
@@ -123,12 +124,17 @@
"else:\n",
" Ntaps = 8 # number of taps per polyphase FIR filter\n",
" Ndft = 16 # DFT size\n",
+ " #Ntaps = 4\n",
+ " #Ndft = 8\n",
" #Ntaps = 12\n",
" #Ndft = 192\n",
- "Ncoefs = Ndft * Ntaps\n",
- "#Ncoefs = Ncoefs - 1 # try odd length\n",
+ "Ndelays = Ndft * Ntaps\n",
+ "Ncoefs = Ndelays\n",
+ "#Ncoefs = Ndelays - 2 # try shorter length to verify impact of hPairGroupDelay\n",
+ "#Ncoefs = Ndelays - 1 # try odd length\n",
"print('Ntaps =', Ntaps)\n",
"print('Ndft =', Ndft)\n",
+ "print('Ndelays =', Ndelays)\n",
"print('Ncoefs =', Ncoefs)\n",
"\n",
"# Waveform generator\n",
@@ -282,6 +288,11 @@
" # are not symmetrical (so not exactly linear phase), which makes it possible to verify\n",
" # whether the coefficients are applied in the correct order.\n",
" hPrototype = read_coefficients_file('../pfb_bunton_annotated/cl.txt')\n",
+ " if Ncoefs < Ndelays:\n",
+ " dDiv = (Ndelays - Ncoefs) // 2\n",
+ " dRem = (Ndelays - Ncoefs) % 2\n",
+ " hPrototype = hPrototype[dDiv : -dDiv - dRem]\n",
+ " print(len(hPrototype))\n",
" #hPrototype /= np.sum(hPrototype)\n",
" print(is_symmetrical(hPrototype))\n",
"else:\n",
@@ -305,11 +316,7 @@
" fcutoff = fpass\n",
" hPrototype = signal.firwin(Ncoefs, fcutoff, window='hann', fs=fs)\n",
" verify_result(is_symmetrical(hPrototype))\n",
- "print('DC gain = %.10f' % np.sum(hPrototype))\n",
- "\n",
- "# Impulse response for upconverter or synthesis\n",
- "fPrototype = np.flip(hPrototype)\n",
- "fPrototype = hPrototype"
+ "print('DC gain = %.10f' % np.sum(hPrototype))"
]
},
{
@@ -504,6 +511,8 @@
"source": [
"# FIR filter group delay\n",
"w, gd = signal.group_delay((hPrototype, [1.0]), w=1024, fs=1)\n",
+ "#w, gd = signal.group_delay((np.convolve(hPrototype, hPrototype), [1.0]), w=1024, fs=1)\n",
+ "#w, gd = signal.group_delay((np.convolve(hPrototype, np.flip(hPrototype)), [1.0]), w=1024, fs=1)\n",
"#plt.title('FIR filter group delay')\n",
"plt.plot(w, gd)\n",
"plt.ylabel('Group delay [samples]')\n",
@@ -513,6 +522,20 @@
"print('FIR filter group delay = %f' % hGroupDelay)"
]
},
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "id": "ea14000d",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Select impulse response for downconverter / analysys and for upconverter / synthesis\n",
+ "aPrototype = hPrototype\n",
+ "sPrototype = hPrototype\n",
+ "sPrototype = np.flip(hPrototype)\n",
+ "#hPrototype"
+ ]
+ },
{
"cell_type": "markdown",
"id": "ce7e672e",
@@ -523,7 +546,7 @@
},
{
"cell_type": "code",
- "execution_count": 15,
+ "execution_count": 16,
"id": "e74340e4",
"metadata": {},
"outputs": [],
@@ -543,7 +566,7 @@
},
{
"cell_type": "code",
- "execution_count": 16,
+ "execution_count": 17,
"id": "bd2add56",
"metadata": {},
"outputs": [],
@@ -568,7 +591,7 @@
},
{
"cell_type": "code",
- "execution_count": 17,
+ "execution_count": 18,
"id": "7106ad3f",
"metadata": {},
"outputs": [
@@ -578,7 +601,7 @@
"(0.0, 10.0)"
]
},
- "execution_count": 17,
+ "execution_count": 18,
"metadata": {},
"output_type": "execute_result"
},
@@ -618,7 +641,7 @@
},
{
"cell_type": "code",
- "execution_count": 18,
+ "execution_count": 19,
"id": "da53b25e",
"metadata": {},
"outputs": [],
@@ -630,17 +653,17 @@
},
{
"cell_type": "code",
- "execution_count": 19,
+ "execution_count": 20,
"id": "9acf0ec2",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
- "<matplotlib.legend.Legend at 0x7fcff66a6ca0>"
+ "<matplotlib.legend.Legend at 0x7f06500e35b0>"
]
},
- "execution_count": 19,
+ "execution_count": 20,
"metadata": {},
"output_type": "execute_result"
},
@@ -658,7 +681,7 @@
"source": [
"# x[n] --> LO --> LPF --> D --> y[mD, k] [HARRIS Fig 6.2] \n",
"xLoData = xData * LO\n",
- "yData = signal.lfilter(hPrototype, [1.0], xLoData) # = y[n, k], Eq. 6.1\n",
+ "yData = signal.lfilter(aPrototype, [1.0], xLoData) # = y[n, k], Eq. 6.1\n",
"yDown = down(yData, Ndown) # = y[mD, k]\n",
"\n",
"plt.plot(n_sub, yData.real, 'g-')\n",
@@ -686,7 +709,7 @@
},
{
"cell_type": "code",
- "execution_count": 20,
+ "execution_count": 21,
"id": "b8036250",
"metadata": {},
"outputs": [
@@ -731,7 +754,7 @@
},
{
"cell_type": "code",
- "execution_count": 21,
+ "execution_count": 22,
"id": "0663df66",
"metadata": {},
"outputs": [],
@@ -747,7 +770,7 @@
},
{
"cell_type": "code",
- "execution_count": 22,
+ "execution_count": 23,
"id": "3a039428",
"metadata": {},
"outputs": [
@@ -761,8 +784,8 @@
],
"source": [
"# x[n] --> BPF --> D --> LOdown --> y[m D, k] [HARRIS Fig 6.7]\n",
- "hBpf = hPrototype * np.exp(1j * w_k * np.arange(Ncoefs))\n",
- "yBpfData = signal.lfilter(hBpf, [1.0], xData)\n",
+ "aBpf = aPrototype * np.exp(1j * w_k * np.arange(Ncoefs))\n",
+ "yBpfData = signal.lfilter(aBpf, [1.0], xData)\n",
"yBpfDown = down(yBpfData, Ndown)\n",
"yBpfDownLo = yBpfDown * LOdown # = y[m D, k]\n",
"\n",
@@ -791,7 +814,7 @@
},
{
"cell_type": "code",
- "execution_count": 23,
+ "execution_count": 24,
"id": "327236c2",
"metadata": {},
"outputs": [
@@ -806,7 +829,7 @@
"source": [
"print('Ros =', Ros)\n",
"if Ndown == Ndft:\n",
- " yMaxDownBpf = maximal_downsample_bpf(xData, Ndown, kLo, hPrototype)\n",
+ " yMaxDownBpf = maximal_downsample_bpf(xData, Ndown, kLo, aPrototype)\n",
" yMaxDownBpfLo = yMaxDownBpf # = yMaxDownBpf * LOdown, because LOdown = 1 when Ndown == Ndft\n",
"\n",
" result = np.all(np.isclose(yDown, yMaxDownBpfLo))\n",
@@ -828,7 +851,7 @@
},
{
"cell_type": "code",
- "execution_count": 24,
+ "execution_count": 25,
"id": "aefa8615",
"metadata": {},
"outputs": [
@@ -851,7 +874,7 @@
}
],
"source": [
- "yDownBpf = non_maximal_downsample_bpf(xData, Ndown, kLo, Ndft, hPrototype)\n",
+ "yDownBpf = non_maximal_downsample_bpf(xData, Ndown, kLo, Ndft, aPrototype)\n",
"yDownBpfLo = yDownBpf # = yDownBpf * LOdown * LOshift, because LOdown = 1 when Ndown == Ndft\n",
" # and LOshift phase shifts compensate for time shift due to Ndown < Ndft\n",
"\n",
@@ -872,7 +895,7 @@
},
{
"cell_type": "code",
- "execution_count": 25,
+ "execution_count": 26,
"id": "f814c9b9",
"metadata": {},
"outputs": [
@@ -891,7 +914,7 @@
"print('wgSub = %.1f, SNR_WG_dB = %.1f dB, Nsim = %d [Tsub]' % (wgSub, SNR_WG_dB, Nsim))\n",
"if verifyPhase: \n",
" # The phaseMargin >> c_atol, because it depends on the stop band attenuation of the\n",
- " # hPrototype LPF. This is because the LO downconverts the positive frequency band\n",
+ " # aPrototype LPF. This is because the LO downconverts the positive frequency band\n",
" # of the WG cos() wave, so the negative frequency band will appear in the stop band.\n",
" if SNR_WG_dB < 100: \n",
" # Determine some appropriate phase margin dependent on SNR.\n",
@@ -914,7 +937,7 @@
},
{
"cell_type": "code",
- "execution_count": 26,
+ "execution_count": 27,
"id": "dd7a9503",
"metadata": {},
"outputs": [],
@@ -951,7 +974,7 @@
},
{
"cell_type": "code",
- "execution_count": 27,
+ "execution_count": 28,
"id": "3cf6aa74",
"metadata": {},
"outputs": [],
@@ -965,7 +988,7 @@
},
{
"cell_type": "code",
- "execution_count": 28,
+ "execution_count": 29,
"id": "373ab5bb",
"metadata": {},
"outputs": [],
@@ -976,14 +999,14 @@
"# yDown ycUp ycUpLpf\n",
"# y[mD, k] --> U ------> LPF --------> LOp --> ycUpLpfLo\n",
"ycUp = up(yDown, Nup) # insert Nup - 1 zeros\n",
- "ycUpLpf = Nup * signal.lfilter(fPrototype, [1.0], ycUp) # interpolate by Nup\n",
+ "ycUpLpf = Nup * signal.lfilter(sPrototype, [1.0], ycUp) # interpolate by Nup\n",
"ycUpLpfLo = ycUpLpf * LOp * LOadjust # upconvert to positive bin kLo\n",
"yrUpLpfLo = ycUpLpfLo.real * nofSsb # = ycUpLpfLo + np.conj(ycUpLpfLo), add negative bin -kLo"
]
},
{
"cell_type": "code",
- "execution_count": 29,
+ "execution_count": 30,
"id": "a5c60be5",
"metadata": {},
"outputs": [
@@ -991,7 +1014,11 @@
"name": "stdout",
"output_type": "stream",
"text": [
- "0.507261028720982\n"
+ "wgSub = 1.500000\n",
+ "kLo = 2\n",
+ "xLen = 129 input samples\n",
+ "yrSNR = 5.98613 [dB], single bin\n",
+ "yrAmpl = 0.507261\n"
]
},
{
@@ -1012,11 +1039,21 @@
"plt.plot(xDelayed, 'r.-')\n",
"plt.plot(yrUpLpfLo[hPairGroupDelay:], 'b.-')\n",
"plt.plot(xyDiff, 'g')\n",
- "#plt.xlim([100, 250])\n",
+ "#plt.xlim([0, 250])\n",
"\n",
"if not wgModulation:\n",
+ " offset = Ncoefs\n",
+ " xLen = len(xDelayed[offset:])\n",
+ " if xLen < Ncoefs:\n",
+ " print('Too low Nsim for proper yrSNR calculation %d < %d' % (xLen, Ncoefs))\n",
+ " verify_result(False)\n",
+ " yrSNR = snr_db(xDelayed[offset:], xyDiff[offset:])\n",
" yrAmpl = np.sqrt(np.mean(np.abs(yrUpLpfLo[Ncoefs:]**2)) * nofSsb)\n",
- " print(yrAmpl)"
+ " print('wgSub = %f' % wgSub)\n",
+ " print('kLo = %d' % kLo)\n",
+ " print('xLen = %d input samples' % xLen)\n",
+ " print('yrSNR = %.5f [dB], single bin' % yrSNR)\n",
+ " print('yrAmpl = %f' % yrAmpl)"
]
},
{
@@ -1033,7 +1070,7 @@
},
{
"cell_type": "code",
- "execution_count": 30,
+ "execution_count": 31,
"id": "7049249e",
"metadata": {},
"outputs": [
@@ -1067,7 +1104,7 @@
},
{
"cell_type": "code",
- "execution_count": 31,
+ "execution_count": 32,
"id": "64cc34f3",
"metadata": {},
"outputs": [],
@@ -1083,7 +1120,7 @@
},
{
"cell_type": "code",
- "execution_count": 32,
+ "execution_count": 33,
"id": "71a91beb",
"metadata": {},
"outputs": [
@@ -1098,10 +1135,10 @@
"source": [
"# ycDownLo ycLoUp \n",
"# y[mD, k] --> LOpDown ---------> U -------> BPF --> ycLoUpBpf\n",
- "fBpf = fPrototype * np.exp(1j * w_k * np.arange(Ncoefs))\n",
+ "sBpf = sPrototype * np.exp(1j * w_k * np.arange(Ncoefs))\n",
"ycDownLo = yDown * LOpDown * LOadjust # upconvert to positive bin kLo\n",
"ycLoUp = Nup * up(ycDownLo, Nup) # insert Nup - 1 zeros\n",
- "ycLoUpBpf = signal.lfilter(fBpf, [1.0], ycLoUp) # interpolate by Nup with BPF at kLo\n",
+ "ycLoUpBpf = signal.lfilter(sBpf, [1.0], ycLoUp) # interpolate by Nup with BPF at kLo\n",
"yrLoUpBpf = ycLoUpBpf.real * nofSsb # = ycLoUpBpf + np.conj(ycLoUpBpf), add negative bin -kLo\n",
"\n",
"# result is True for any Ndft, Ndown, because LOdown is in equation of yBpfDownLo\n",
@@ -1133,7 +1170,7 @@
},
{
"cell_type": "code",
- "execution_count": 33,
+ "execution_count": 34,
"id": "a3aae48a",
"metadata": {},
"outputs": [
@@ -1149,7 +1186,7 @@
"print('Ndft =', Ndft)\n",
"if Nup == Ndft:\n",
" # ycDownLo = yDown * LOdown = yDown, because LOdown = 1 when Ndown == Ndft\n",
- " ycLoBpfMaxUp = maximal_upsample_bpf(yDown, Nup, kLo, hPrototype)\n",
+ " ycLoBpfMaxUp = maximal_upsample_bpf(yDown, Nup, kLo, sPrototype)\n",
" yrLoBpfMaxUp = ycLoBpfMaxUp.real * nofSsb # add negative bin -kLo to make real\n",
"\n",
" result = np.all(np.isclose(yrUpLpfLo, yrLoBpfMaxUp))\n",
@@ -1170,12 +1207,12 @@
},
{
"cell_type": "code",
- "execution_count": 34,
+ "execution_count": 35,
"id": "3c2c8ec5",
"metadata": {},
"outputs": [],
"source": [
- "ycLoBpfUp = None #non_maximal_upsample_bpf(yDown, Nup, kLo, Ndft, hPrototype)\n",
+ "ycLoBpfUp = None #non_maximal_upsample_bpf(yDown, Nup, kLo, Ndft, sPrototype)\n",
"if ycLoBpfUp is not None:\n",
" yrLoBpfUp = ycLoBpfUp.real * nofSsb # add negative bin -kLo to make real\n",
"\n",
@@ -1197,6 +1234,30 @@
"Can use 'cw' or 'ccw' independently for analysis and synthesis PFB, because with fold() the IDFT can be expressed as a DFT and vice versa. However to have back to back DFT - IDFT in pipeline, use analysis 'cw' and synthesis 'ccw' [CROCHIERE 7.2.3]."
]
},
+ {
+ "cell_type": "code",
+ "execution_count": 36,
+ "id": "abb548f6",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "wgSub = 1.500000\n",
+ "kLo = 2\n",
+ "Ndft = 16\n",
+ "Ndown = 12\n"
+ ]
+ }
+ ],
+ "source": [
+ "print('wgSub = %f' % wgSub)\n",
+ "print('kLo = %d' % kLo)\n",
+ "print('Ndft = %d' % Ndft)\n",
+ "print('Ndown = %d' % Ndown)"
+ ]
+ },
{
"cell_type": "markdown",
"id": "d8bb436d",
@@ -1207,33 +1268,51 @@
},
{
"cell_type": "code",
- "execution_count": 35,
+ "execution_count": 37,
+ "id": "a6de2be1",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "PASSED\n",
+ "PASSED\n",
+ "PASSED\n"
+ ]
+ }
+ ],
+ "source": [
+ "vb = 0\n",
+ "Ac0 = analysis_dft_filterbank(xData, Ndown, Ndft, aPrototype, 'wola', coefsOrder='bwin', verbosity=vb)\n",
+ "Ac1 = analysis_dft_filterbank(xData, Ndown, Ndft, aPrototype, 'wola', coefsOrder='bfir', verbosity=vb)\n",
+ "Ac2 = analysis_dft_filterbank(xData, Ndown, Ndft, aPrototype, 'pfs', commutator='cw', verbosity=vb)\n",
+ "Ac3 = analysis_dft_filterbank(xData, Ndown, Ndft, aPrototype, 'pfs', commutator='ccw', verbosity=vb)\n",
+ "verify_result(np.all(np.isclose(Ac0, Ac1)))\n",
+ "verify_result(np.all(np.isclose(Ac0, Ac2)))\n",
+ "verify_result(np.all(np.isclose(Ac2, Ac3)))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 38,
"id": "b0f997d3",
"metadata": {
- "scrolled": true
+ "scrolled": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
- "128\n",
- "> analysis_dft_filterbank():\n",
- " . len(x) = 384\n",
- " . Nx = 373\n",
- " . Nblocks = 32\n",
- " . Ros = 1.3333333333333333\n",
- " . Ndown = 12\n",
- " . Ndft = 16\n",
- " . commutator = ccw\n",
- "\n",
"PASSED\n"
]
}
],
"source": [
- "Ac = analysis_dft_filterbank(xData, Ndown, Ndft, hPrototype, commutator='ccw')\n",
+ "Ac = Ac0\n",
"yDownBin = Ac[kLo]\n",
+ "#yDownBin = yDownBin[:len(yDown)]\n",
"\n",
"result = np.all(np.isclose(yDown, yDownBin))\n",
"if not result:\n",
@@ -1241,6 +1320,8 @@
" plt.plot(m_sub, yDown.imag, 'g.--')\n",
" plt.plot(m_sub, yDownBin.real, 'r.-')\n",
" plt.plot(m_sub, yDownBin.imag, 'r.--')\n",
+ " #plt.plot(m_sub, yDown.real - yDownBin.real, 'b.-')\n",
+ " #plt.plot(m_sub, yDown.imag - yDownBin.imag, 'b.--')\n",
" plt.xlim([0, 20])\n",
"verify_result(result)"
]
@@ -1255,7 +1336,7 @@
},
{
"cell_type": "code",
- "execution_count": 36,
+ "execution_count": 39,
"id": "47d5bf5b",
"metadata": {},
"outputs": [
@@ -1268,8 +1349,10 @@
" . Ros = 1.3333333333333333\n",
" . Nup = 12\n",
" . Ndft = 16\n",
- " . commutator = cw\n",
- "\n"
+ " . structure = wola\n",
+ " . commutator = ccw\n",
+ "\n",
+ "PASSED\n"
]
}
],
@@ -1285,20 +1368,20 @@
" Yc[Ndft - kLo] = np.conjugate(yDownBin)\n",
"\n",
"# Single bin synthesis from PFB\n",
- "yr = synthesis_dft_filterbank(Yc, Nup, Ndft, fPrototype, commutator='cw')\n",
+ "yr = synthesis_dft_filterbank(Yc, Nup, Ndft, sPrototype, structure='wola', commutator='ccw')\n",
"yr = yr[0 : len(yrUpLpfLo)]\n",
"\n",
"result = np.all(np.isclose(yrUpLpfLo, yr))\n",
"if not result:\n",
" plt.plot(n_sub, yrUpLpfLo, 'g.-')\n",
- " plt.plot(n_sub, yr, 'r-')\n",
- " plt.xlim((20, 21))\n",
- "#verify_result(result)"
+ " plt.plot(n_sub, yr, 'r.-')\n",
+ " #plt.xlim((20, 21))\n",
+ "verify_result(result)"
]
},
{
"cell_type": "code",
- "execution_count": 37,
+ "execution_count": 40,
"id": "4818ad5a",
"metadata": {
"scrolled": true
@@ -1313,10 +1396,13 @@
" . Ros = 1.3333333333333333\n",
" . Nup = 12\n",
" . Ndft = 16\n",
+ " . structure = wola\n",
" . commutator = ccw\n",
"\n",
"wgSub = 1.500000\n",
"kLo = 2\n",
+ "xLen = 129 input samples\n",
+ "yrSNR = 5.98613 [dB], single bin\n",
"SNR_yr = 5.98613 [dB], single bin\n",
"SNR_sr = 44.05325 [dB], all bins\n"
]
@@ -1336,7 +1422,7 @@
"# . Use yr for comparison between single channel pipeline and using PFB for single bin\n",
"# . Use sr to see impact of aliasing in the other bins, due to limited stopband attenuation\n",
"# of both LPF.\n",
- "sr = synthesis_dft_filterbank(Ac, Nup, Ndft, fPrototype, commutator='ccw')\n",
+ "sr = synthesis_dft_filterbank(Ac, Nup, Ndft, sPrototype, structure='wola', commutator='ccw')\n",
"sr = sr[0 : len(yrUpLpfLo)]\n",
"\n",
"# Output time aligned with input\n",
@@ -1351,32 +1437,37 @@
"# . The SNR for CW input calculated for refBunton and with construct.m are about equal within \n",
"# +-0.0005 dB. The difference is probably due to that the selected ranges for calculating the\n",
"# SNR are not exactly the same. Varying the offset shows a similar spread in SNR.\n",
- "offset = Ncoefs # + Ncoefs // 7\n",
- "if len(xDelayed[offset:]) < Ncoefs:\n",
- " print('Too low Nsim for proper SNR calculation')\n",
+ "offset = Ncoefs\n",
+ "#offset = 10000\n",
+ "endset = 70000\n",
+ "xLen = len(xDelayed[offset:endset])\n",
+ "if xLen < Ncoefs:\n",
+ " print('Too low Nsim for proper SNR_yr calculation %d < %d' % (xLen, Ncoefs))\n",
" verify_result(False)\n",
- "SNR_yr = snr_db(xDelayed[offset:], xDelayed[offset:] - x_yr[offset:])\n",
- "SNR_sr = snr_db(xDelayed[offset:], xDelayed[offset:] - x_sr[offset:])\n",
+ "SNR_yr = snr_db(xDelayed[offset:endset], xDelayed[offset:endset] - x_yr[offset:endset])\n",
+ "SNR_sr = snr_db(xDelayed[offset:endset], xDelayed[offset:endset] - x_sr[offset:endset])\n",
"\n",
"print('wgSub = %f' % wgSub)\n",
"print('kLo = %d' % kLo)\n",
+ "print('xLen = %d input samples' % xLen)\n",
+ "print('yrSNR = %.5f [dB], single bin' % yrSNR)\n",
"print('SNR_yr = %.5f [dB], single bin' % SNR_yr)\n",
"print('SNR_sr = %.5f [dB], all bins' % SNR_sr)"
]
},
{
"cell_type": "code",
- "execution_count": 38,
+ "execution_count": 41,
"id": "2c1ec80d",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
- "[<matplotlib.lines.Line2D at 0x7fcffa407f40>]"
+ "[<matplotlib.lines.Line2D at 0x7f06515e56a0>]"
]
},
- "execution_count": 38,
+ "execution_count": 41,
"metadata": {},
"output_type": "execute_result"
},
@@ -1392,31 +1483,29 @@
}
],
"source": [
- "# Plot original real xData recovered yr and sr\n",
+ "# Plot original real xData recovered with sr for all bins\n",
"plt.plot(xDelayed[offset:], 'r.-')\n",
- "#lt.plot(x_yr[offset:], 'b.-')\n",
- "#plt.plot(x_yr[offset:] - xDelayed[offset:], 'm.-')\n",
"plt.plot(x_sr[offset:], 'g.-')\n",
"plt.plot(x_sr[offset:] - xDelayed[offset:], 'y.-')\n",
- "#plt.xlim([0, 1250])\n",
+ "#plt.xlim([0, 2500])\n",
"#plt.ylim([-0.01, 0.01])"
]
},
{
"cell_type": "code",
"execution_count": null,
- "id": "a16ef270",
+ "id": "758be965",
"metadata": {},
"outputs": [],
"source": []
},
{
- "cell_type": "markdown",
- "id": "77c01d0d",
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "5eb4fafb",
"metadata": {},
- "source": [
- "# "
- ]
+ "outputs": [],
+ "source": []
}
],
"metadata": {
--
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