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A sinusoid has just been fed into a system.

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Jonathan George
Jonathan George 2022-3-26
编辑： Sam Chak 2022-3-26
The system in question has a frequency response given by H(w) = 1/(1+0004jw), where w represents frequency in rads/second.
The input sinusoid has an amplitude of 3, phase of 0 radians and a frequency of 33Hz.
How would I determine the amplitude and phase (between -pi and pi rads) of the sinusoidal output?
Many thanks.
(Keep in mind that an LTI system never changes the frequency of a sinusoid.)
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Star Strider
Star Strider 2022-3-26
No worries!
This might be solved easily using Phasor notation.
Sam Chak
Sam Chak 2022-3-26
No wonder, I almost use
s = tf('s');
sys = 1/(1 + 4*s);
bode(sys)
Hz is equivalent to rad/s.
The Bode plot can tell you whether a sinusoidal input signal in amplified or attenuated (in dB), or how much it is shifted in phase when passing through a linear dynamical system at a certain frequency. These info are generally useful when designing low-pass and high-pass filters.

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采纳的回答

Star Strider
Star Strider 2022-3-26
Ran in:
Using phasors —
syms omega
sympref('AbbreviateOutput',false); % Optional
omega = 2*pi*33; % Radian Frequency
H = 1/(1+0.004*j*omega) % System
H = 0.5925 - 0.4914i
phasorH = [abs(H), angle(H)] % Phasor = [Amplitude PhaseAngle]
phasorH = 1×2
0.7697 -0.6924
phasorInput = [3, 0]
phasorInput = 1×2
3 0
phasorOutput = [phasorH(1)*phasorInput(1), phasorH(2)+phasorInput(2)] % Multiply Amplitudes, Add Phases
phasorOutput = 1×2
2.3091 -0.6924
So, the output has an amplitude of 2.3091 and a phase angle of -0.6924 radians.
I haven’t routinely worked with phasors in a while (since grad school, back in the Precambrian) so check this. However, I believe the approach is correct.
.

更多回答（1 个）

Sam Chak
Sam Chak 2022-3-26
编辑：Sam Chak 2022-3-26
Hi @Jonathan George
This is sort of the "control theorist's way", if you are interested to learn.
s = tf('s');
sys = 1/(1 + 0.004*s)
omega = 33*2*pi;
[mag, phase, wout] = bode(sys, omega)
Input_Amplitude = 3
Output_Amplitude = Input_Amplitude*mag
Output_phase_in_radian = (pi/180)*phase % the unit degree is commonly used
sys =
1
-----------
0.004 s + 1
Continuous-time transfer function.
mag =
0.7697
phase =
-39.6716
wout =
207.3451
Input_Amplitude =
3
Output_Amplitude =
2.3091
Output_phase_in_radian =
-0.6924

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