A:
\nI have a theta_a_lst with size 1×721, It also represents one cycle of 50Hz sin wave. I also have voltage waveform va_lst. Perform FFT on va_lst.<\/p>\n
Q:
\nGot it. Since you have one cycle of a 50 Hz sine (theta_a_lst size 1×721) and a corresponding voltage waveform va_lst, here are concise MATLAB and Python options to compute the FFT, report amplitudes\/phases, and plot up to Nyquist.<\/p>\n
Assumptions
\n– theta_a_lst spans exactly one electrical cycle (0 to 2\u03c0 or 0 to 360\u00b0) with 721 samples.
\n– va_lst is the same length as theta_a_lst.
\n– Effective sampling frequency Fs is derived from 50 Hz fundamental: Fs = 50 \u00d7 N (samples per cycle).
\n– Frequency resolution df = Fs\/N = 50 Hz (harmonic bins at 0, 50, 100, …).<\/p>\n
\u8fd9\u91cc\u7684\u6709\u6548\u91c7\u6837\u9891\u7387\uff08effective sampling frequency\uff09Fs\u5f88\u91cd\u8981\uff0ctheta_lst\u4e3a\u4e00\u4e2a50Hz\u57fa\u6ce2\u5468\u671f\uff0c\u5176\u4e2d\u70b9\u6570N\u8d8a\u5927\uff0cFs\u8d8a\u5927\uff0c\u4f46\u662f\u9891\u7387\u5206\u8fa8\u7387df\u5374\u662f\u4e0d\u53d8\u7684\uff0c\u56e0\u4e3aFs = 50xN, \u800cdf = Fs\/N, \u6240\u4ee5df = 50Hz\u3002<\/p>\n
\u5982\u679c\u53ea\u7ed9\u4e00\u4e2a50Hz\u7684\u57fa\u6ce2\u6240\u5bf9\u5e94\u7684\u5e8f\u5217\uff0c\u80fd\u5206\u6790\u51fa\u6765\u7684\u8c10\u6ce2\u80af\u5b9a\u90fd\u662f50Hz\u7684\u500d\u6570\u3002<\/p>\n
MATLAB version<\/p>\n
function out = fft_va_from_theta(theta_a_lst, va_lst, varargin)\n% fft_va_from_theta FFT of va given one-cycle theta vector (50 Hz fundamental)\n% Usage:\n% out = fft_va_from_theta(theta_a_lst, va_lst, 'FmaxPlot', 2500, 'DoPlot', true)\n%\n% Inputs:\n% theta_a_lst : 1xN or Nx1 angles covering one cycle (rad or deg)\n% va_lst : 1xN or Nx1 voltage samples corresponding to theta_a_lst\n%\n% Name-Value:\n% 'F0' : fundamental frequency (default 50 Hz)\n% 'Window' : window name or vector (default 'hann')\n% 'DoPlot' : true\/false (default true)\n% 'FmaxPlot' : max frequency for plots (default min(2500, Fs\/2))\n%\n% Output struct out:\n% .Fs, .df, .N, .f1 (kmaxx1), .X1 (kmaxx1 complex)\n% .A1 (single-sided amplitude), .Sxx1 (single-sided PSD, arbitrary units if no Ts)\n% .DC, .peak_amp, .peak_freq\n% .idx_harm (indices at integer harmonics), .A1_harm, .phase_harm\n\n p = inputParser;\n p.addParameter('F0', 50, @(x)isnumeric(x)&&isscalar(x)&&x>0);\n p.addParameter('Window','hann');\n p.addParameter('DoPlot', true, @(x)islogical(x)&&isscalar(x));\n p.addParameter('FmaxPlot', 2500, @(x)isnumeric(x)&&isscalar(x)&&x>0);\n p.parse(varargin{:});\n F0 = p.Results.F0;\n wopt = p.Results.Window;\n DoPlot = p.Results.DoPlot;\n\n % Ensure column vectors\n theta = theta_a_lst(:);\n v = va_lst(:);\n N = numel(v);\n assert(numel(theta)==N, 'theta_a_lst and va_lst must have same length');\n\n % Sampling frequency from one-cycle assumption\n Fs = F0 * N;\n df = Fs \/ N; % equals F0\n\n % Window\n if ischar(wopt) || (isstring(wopt) && isscalar(wopt))\n switch lower(string(wopt))\n case \"hann\"\n w = hann(N, 'periodic');\n case \"hamming\"\n w = hamming(N, 'periodic');\n case \"rect\"\n w = ones(N,1);\n otherwise\n error('Unsupported Window option.');\n end\n else\n w = wopt(:);\n assert(numel(w)==N, 'Custom window must match data length');\n end\n W0 = sum(w)\/N; % coherent gain\n Pw = mean(w.^2); % window power (for PSD if needed)\n vw = v .* w;\n\n % FFT\n X = fft(vw);\n Nfft = N;\n f = (0:Nfft-1).' * (Fs\/Nfft);\n\n % Single-sided\n if mod(Nfft,2)==0\n kmax = Nfft\/2 + 1;\n else\n kmax = (Nfft+1)\/2;\n end\n f1 = f(1:kmax);\n X1 = X(1:kmax);\n\n % Amplitude spectrum (single-sided), window-corrected\n A2 = abs(X1) \/ (N * W0);\n A1 = A2;\n if kmax > 2\n A1(2:end-1) = 2*A1(2:end-1);\n end\n\n % PSD (single-sided). Units V^2\/Hz if Ts known; here Ts=1\/Fs.\n Sxx2 = (abs(X1).^2) \/ (Fs * N * Pw);\n Sxx1 = Sxx2;\n if kmax > 2\n Sxx1(2:end-1) = 2*Sxx1(2:end-1);\n end\n\n % Stats\n DC = A1(1);\n [peak_amp, idxp] = max(A1(2:end)); idxp = idxp + 1;\n peak_freq = f1(idxp);\n\n % Harmonic bins (0, F0, 2F0, ...)\n harmonics = (0:floor(f1(end)\/F0)).' * F0;\n [~, idx_harm] = ismember(harmonics, f1); % exact because df=F0\n A1_harm = A1(idx_harm);\n phase_harm = angle(X1(idx_harm));\n\n % Pack outputs\n out = struct('Fs',Fs,'df',df,'N',N,'f1',f1,'X1',X1, ...\n 'A1',A1,'Sxx1',Sxx1,'DC',DC, ...\n 'peak_amp',peak_amp,'peak_freq',peak_freq, ...\n 'idx_harm',idx_harm,'A1_harm',A1_harm,'phase_harm',phase_harm, ...\n 'W0',W0,'Pw',Pw);\n\n % Plots\n if DoPlot\n fmax_plot = min(2500, Fs\/2);\n idx_plot = f1 <= fmax_plot;\n\n fig = figure('Name','va FFT (one-cycle, 50 Hz)','Color','w');\n % scale 50%\n pos = get(fig,'Position'); pos(3:4) = 0.5*pos(3:4); set(fig,'Position',pos);\n\n tiledlayout(3,1);\n nexttile;\n plot((0:N-1)\/Fs, v, 'k-'); grid on;\n xlabel('Time (s)'); ylabel('v_a');\n title('Time-domain (one cycle)');\n\n nexttile;\n stem(f1(idx_plot), A1(idx_plot), 'filled'); grid on;\n xlim([0, fmax_plot]); xlabel('Frequency (Hz)'); ylabel('Amplitude (V)');\n title(sprintf('Single-Sided Amplitude Spectrum (df = %.1f Hz)', df));\n\n nexttile;\n plot(f1(idx_plot), 10*log10(Sxx1(idx_plot)+eps), 'b-'); grid on;\n xlim([0, fmax_plot]); xlabel('Frequency (Hz)'); ylabel('PSD (dBV^2\/Hz)');\n title('Single-Sided PSD');\n end\nend\n<\/code><\/pre>\nPython version (NumPy)<\/p>\n
import numpy as np\n\ndef fft_va_from_theta(theta_a_lst, va_lst, f0=50.0, window='hann'):\n \"\"\"\n FFT of va given one-cycle theta vector (50 Hz fundamental).\n Returns dict with Fs, df, f1, X1, A1, phases, etc.\n \"\"\"\n theta = np.asarray(theta_a_lst).ravel()\n v = np.asarray(va_lst).ravel()\n assert theta.size == v.size\n N = v.size\n Fs = f0 * N\n df = Fs \/ N # equals f0\n\n if isinstance(window, str):\n if window.lower() == 'hann':\n w = np.hanning(N)\n elif window.lower() == 'hamming':\n w = np.hamming(N)\n elif window.lower() == 'rect':\n w = np.ones(N)\n else:\n raise ValueError('Unsupported window')\n else:\n w = np.asarray(window).ravel()\n assert w.size == N\n W0 = w.sum()\/N\n Pw = np.mean(w**2)\n\n vw = v * w\n X = np.fft.fft(vw)\n Nfft = N\n f = np.arange(Nfft) * (Fs\/Nfft)\n\n kmax = Nfft\/\/2 + 1 if Nfft % 2 == 0 else (Nfft+1)\/\/2\n f1 = f[:kmax]\n X1 = X[:kmax]\n\n A2 = np.abs(X1) \/ (N * W0)\n A1 = A2.copy()\n if kmax > 2:\n A1[1:-1] *= 2.0\n\n Sxx2 = (np.abs(X1)**2) \/ (Fs * N * Pw)\n Sxx1 = Sxx2.copy()\n if kmax > 2:\n Sxx1[1:-1] *= 2.0\n\n DC = A1[0]\n idxp = 1 + np.argmax(A1[1:])\n peak_amp = A1[idxp]\n peak_freq = f1[idxp]\n\n harmonics = np.arange(int(f1[-1]\/\/f0)+1) * f0\n idx_harm = (harmonics \/ df).astype(int)\n A1_harm = A1[idx_harm]\n phase_harm = np.angle(X1[idx_harm])\n\n return dict(Fs=Fs, df=df, N=N, f1=f1, X1=X1, A1=A1, Sxx1=Sxx1, DC=DC,\n peak_amp=peak_amp, peak_freq=peak_freq, idx_harm=idx_harm,\n A1_harm=A1_harm, phase_harm=phase_harm, W0=W0, Pw=Pw)\n<\/code><\/pre>\nIf you share the units\/format of theta_a_lst (deg vs rad) or want a specific window, I can tailor the code further.<\/p>\n","protected":false},"excerpt":{"rendered":"
A: I have a theta_a_lst with size 1×721, It also r […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[18],"tags":[],"class_list":["post-193","post","type-post","status-publish","format-standard","hentry","category-undergraduate_competition"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"http:\/\/bluespider.top\/index.php?rest_route=\/wp\/v2\/posts\/193","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/bluespider.top\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/bluespider.top\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/bluespider.top\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/bluespider.top\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=193"}],"version-history":[{"count":1,"href":"http:\/\/bluespider.top\/index.php?rest_route=\/wp\/v2\/posts\/193\/revisions"}],"predecessor-version":[{"id":194,"href":"http:\/\/bluespider.top\/index.php?rest_route=\/wp\/v2\/posts\/193\/revisions\/194"}],"wp:attachment":[{"href":"http:\/\/bluespider.top\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=193"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/bluespider.top\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=193"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/bluespider.top\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=193"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}