Transfer function for a low pass filter

In summary, the conversation discusses finding an expression for V_out, the output signal of a first-order lowpass filter with a transfer function given by eqn 1 and a half-power frequency of 200 Hz. The solution involves multiplying each component of the input signal by the transfer function and keeping the DC component (3) unchanged.
  • #1
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Homework Statement



The input signal of a first-order lowpass filter with a transfer function given by eqn 1 below and a half power frequency of 200 Hz is eqn 2 below. Find an expression for V_out

Homework Equations



eqn1:
H(f) = 1/(1+j*(f/f_B) where f is the frequency and f_B is the half-power frequency
eqn2:
v_in (t) = 3 + 2sin(800*PI*t + 30) + 5cos(20000*PI*t)

v_out/v_in = H(f)

The Attempt at a Solution



I have already gotten that v_in = 3 + 2cos(800*PI*t - 60) + 5cos(20000*PI*t)
then I would multiply each component by H(f) which will give me:
H(400) = 1/sqrt(5) phase(-arctan(2))
H(1000) = 1/sqrt(26) phase(-arctan(5))

v_out = 3*H(?) + 2 phase(-60)*H(400) + 5 phase(0)*H(1000)

pretty much I just do not know what I do about the 3. Do I simply leave it alone?

Thanks!
 
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  • #2
cseanm said:
pretty much I just do not know what I do about the 3. Do I simply leave it alone?

It's a DC component, frequency is zero. What does your transfer function do to a signal with zero frequency?
 

1. What is a transfer function for a low pass filter?

A transfer function for a low pass filter is a mathematical representation of how the filter affects the input signal. It shows how the output signal is related to the input signal, taking into account the filter's frequency response.

2. How is a transfer function for a low pass filter calculated?

A transfer function for a low pass filter is typically calculated by taking the ratio of the output signal to the input signal in the frequency domain. This can be done by using Laplace transforms or Fourier transforms.

3. What is the purpose of a transfer function for a low pass filter?

The purpose of a transfer function for a low pass filter is to understand how the filter affects the input signal in terms of frequency. This can be used for designing and analyzing filters in signal processing applications.

4. How does a low pass filter affect the frequency components of a signal?

A low pass filter attenuates or reduces the amplitude of high frequency components in a signal while allowing low frequency components to pass through. This results in a smoother output signal with less high frequency noise.

5. Can a transfer function for a low pass filter be used to design a filter for a specific frequency response?

Yes, a transfer function for a low pass filter can be used to design a filter for a specific frequency response. By manipulating the transfer function, different types of filters can be designed to achieve specific frequency cutoffs and attenuation levels.

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