frequency to time domain

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ridham
ridham on 30 Jan 2026 at 5:01
Commented: Star Strider on 31 Jan 2026 at 3:26
i need help regarding time domain conversion of my frequency data. is this code correct?
% === STEP 1: Load SFRA Data ===
data = readmatrix('frequency data.csv'); % FAR END SHORTED
freq = data(:,1); % Frequency in Hz
mag_dB = data(:,2); % Magnitude in dB
phase_deg = data(:,3); % Phase in degrees
% === STEP 2: Convert to Linear Magnitude and Radians ===
mag_linear = 10.^(mag_dB / 20); % Convert dB to linear scale
phase_rad = deg2rad(phase_deg); % Convert degrees to radians
% === STEP 3: Interpolate to Uniform Frequency Grid ===
N = 2048; % Power-of-2 for IFFT
f_uniform = linspace(min(freq), max(freq), N);
mag_uniform = interp1(freq, mag_linear, f_uniform, 'linear');
phase_uniform = interp1(freq, phase_rad, f_uniform, 'linear');
% === STEP 4: Construct Complex Frequency Response ===
H_f = mag_uniform .* exp(1j * phase_uniform);
% === STEP 5: Create Hermitian Symmetry for Real IFFT ===
H_full = [H_f, fliplr(conj(H_f(2:end-1)))];
% === STEP 6: Apply IFFT ===
h_t = ifft(H_full, 'symmetric'); % Time-domain impulse response
% === STEP 7: Time Vector ===
Fs = 2 * max(f_uniform); % Sampling frequency (Nyquist)
t = (0:length(H_full)-1) / Fs; % Time in seconds

Answers (1)

Star Strider
Star Strider on 30 Jan 2026 at 7:55
Your code 'works' in the sensee that it appears to be appropriate and it does not produce any errors.
However it does not give an appropriate result. The reason is that it makes too many assumptions about your original data in the interpolation steps, since your original data are not represented in constant frequency steps.
An approach that avoids calculating the inverse fast Fourier transform would have the disadvantage of being 'kludgy' (inelegant), with the advantage of being reasonalby accurate. I did that here, in calculating 'wf' ('waveform') then tsking the mean over its rows, and then plotting it. That approach takes your 't' vector, the linear magnitude (recovered from the decibel magnitude), and phase in radians and simply calculates the sin() of each and takes the mean of them. (It makes no assumptions.) That is probably as accurate a reconstruction as is possible with your data.
T1 = readtable('frequency data.csv', VariableNamingRule='preserve');
disp(T1)
Frequency (Magnitude (dB)) (Degree (º)) __________ ________________ ____________ 20 -0.91392 -0.009252 20.931 -0.91018 -0.004584 21.933 -0.90816 -0.009923 22.957 -0.90694 -0.008398 24.051 -0.90559 -0.012893 25.169 -0.90532 -0.010318 26.356 -0.9045 -0.012964 27.614 -0.90346 -0.012553 28.918 -0.90306 -0.011418 30.268 -0.90293 -0.011981 31.688 -0.90278 -0.012869 33.202 -0.90253 -0.01474 34.762 -0.90277 -0.012068 36.391 -0.90142 -0.012532 38.114 -0.90148 -0.015554 39.907 -0.90127 -0.016935 41.793 -0.90139 -0.018441 43.749 -0.9015 -0.018685 45.821 -0.90117 -0.016276 47.986 -0.9011 -0.016392 50.245 -0.90062 -0.02161 52.596 -0.90097 -0.021076 55.088 -0.90038 -0.021155 57.672 -0.9002 -0.023923 60.396 -0.90038 -0.026164 63.237 -0.90011 -0.024519 66.217 -0.89992 -0.027121 69.337 -0.89911 -0.026681 72.62 -0.8993 -0.031876 76.043 -0.8995 -0.030752 79.628 -0.89901 -0.029062 83.377 -0.89878 -0.029536 87.312 -0.89853 -0.032818 91.409 -0.89871 -0.036083 95.717 -0.89803 -0.034211 100.23 -0.89846 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df = diff(T1.(1));
[dlo,dhi] = bounds(df) % Minimum & Maximum Frequency-Spacing Differences
dlo = 0.9313
dhi = 11480
figure
plot(T1.(1), T1.(2))
grid
xlabel('Frequency (Hz)')
ylabel('Magnitude (dB)')
figure
plot(T1.(1), db2mag(T1.(2)))
grid
xlabel('Frequency (Hz)')
ylabel('Magnitude')
% === STEP 1: Load SFRA Data ===
data = readmatrix('frequency data.csv'); % FAR END SHORTED
freq = data(:,1); % Frequency in Hz
mag_dB = data(:,2); % Magnitude in dB
phase_deg = data(:,3); % Phase in degrees
% === STEP 2: Convert to Linear Magnitude and Radians ===
mag_linear = 10.^(mag_dB / 20); % Convert dB to linear scale
phase_rad = deg2rad(phase_deg); % Convert degrees to radians
% === STEP 3: Interpolate to Uniform Frequency Grid ===
N = 2048; % Power-of-2 for IFFT
f_uniform = linspace(min(freq), max(freq), N);
mag_uniform = interp1(freq, mag_linear, f_uniform, 'linear');
phase_uniform = interp1(freq, phase_rad, f_uniform, 'linear');
% === STEP 4: Construct Complex Frequency Response ===
H_f = mag_uniform .* exp(1j * phase_uniform);
% === STEP 5: Create Hermitian Symmetry for Real IFFT ===
H_full = [H_f, fliplr(conj(H_f(2:end-1)))];
% === STEP 6: Apply IFFT ===
h_t = ifft(H_full, 'symmetric'); % Time-domain impulse response
% === STEP 7: Time Vector ===
Fs = 2 * max(f_uniform); % Sampling frequency (Nyquist)
t = (0:length(H_full)-1) / Fs; % Time in seconds
figure
plot(t, h_t)
grid
axis('padded')
xlabel('Time (s)')
ylabel('Amplitude')
title('''Interpolated'' Inverse Fourier Transform')
wf = mag_linear .* sin(freq * t + phase_rad);
disp(wf)
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figure
plot(t, wf(1:300:end,:))
grid
xlabel('Time (s)')
ylabel('Amplitude')
title('Selected Components')
figure
plot(t, mean(wf))
grid
xlabel('Time (s)')
ylabel('Amplitude')
title('''Direct'' Inverse Transform')
.
  2 Comments
Paul
Paul on 31 Jan 2026 at 1:51
I;m not following this methodology. Can it be illustrated by starting from a known input and then showing the method reconstructs that input?
For example, this system has a transfer function that's similar to the OP's in the frequency domain.
w0 = 50;
H = tf([1,2*.1*w0,w0^2],[1,2*.9*w0,w0^2])*tf(1,[1/1000,1]);
figure;
bode(H)
Its impulse response is
[x,tx] = impulse(H);
Can the Fourier transform of x be generated via bode or fft and then processed as above to show mean(wf) recovers x?
I tried and was not successful, but perhaps I incorrectly implemented the method.
Also, should this line
wf = mag_linear .* sin(freq * t + phase_rad);
be
wf = mag_linear .* sin(2*pi*freq * t + phase_rad);
because freq is in Hz?
Star Strider
Star Strider on 31 Jan 2026 at 3:26
It should use . My computer crashed (unusual for Ubuntu) and while I included it in the beginning, forgot when I rebooted and picked up where I left off. Corrected version follows.
The time domain version is simply the summed series of the available frequency domain data. That is all that is available to work with.
Corrected version --
data = readmatrix('frequency data.csv'); % FAR END SHORTED
freq = data(:,1); % Frequency in Hz
mag_dB = data(:,2); % Magnitude in dB
phase_deg = data(:,3); % Phase in degrees
% === STEP 2: Convert to Linear Magnitude and Radians ===
mag_linear = 10.^(mag_dB / 20); % Convert dB to linear scale
phase_rad = deg2rad(phase_deg); % Convert degrees to radians
N = 2048; % Power-of-2 for IFFT
f_uniform = linspace(min(freq), max(freq), N);
mag_uniform = interp1(freq, mag_linear, f_uniform, 'linear');
phase_uniform = interp1(freq, phase_rad, f_uniform, 'linear');
% === STEP 4: Construct Complex Frequency Response ===
H_f = mag_uniform .* exp(1j * phase_uniform);
% === STEP 5: Create Hermitian Symmetry for Real IFFT ===
H_full = [H_f, fliplr(conj(H_f(2:end-1)))];
Fs = 2 * max(freq); % Sampling frequency (Nyquist)
L = 1;
t = (0:length(H_full)-1) / Fs; % Time in seconds
wf = mag_linear .* sin(2*pi * freq * t + phase_rad);
Size_wf = size(wf)
Size_wf = 1×2
1051 4094
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disp(wf)
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0.6881 0.8210 0.8617 0.8057 0.6592 0.4388 0.1691 -0.1196 -0.3948 -0.6258 -0.7865 -...
figure
plot(t, mean(wf))
grid
xlabel('Time (s)')
ylabel('Amplitude')
title('''Direct'' Inverse Transform')
axis('padded')
.

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